|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(2.0)/(c(1.0) - c(2.0)*c(x)));
> end;
exact_soln_y := proc(x) return c(2.0)/(c(1.0) - c(2.0)*c(x)) end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> ;
> if (true) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp1[1] := (array_y[1] * (array_y[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_y,array_y,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_y,array_y,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_y,array_y,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_y,array_y,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult FULL FULL $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_y,array_y,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_y[1]*array_y[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_y, array_y, 1);
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_y, array_y, 1);
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_y, array_y, 1);
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_y, array_y, 1);
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := ats(kkk, array_y, array_y, 1);
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 20;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=20;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(20),[]);
> array_norms:= Array(0..(20),[]);
> array_fact_1:= Array(0..(20),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(20),[]);
> array_x:= Array(0..(20),[]);
> array_tmp0:= Array(0..(20),[]);
> array_tmp1:= Array(0..(20),[]);
> array_tmp2:= Array(0..(20),[]);
> array_m1:= Array(0..(20),[]);
> array_y_higher := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..20+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(20) ,(0..20+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 20) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=20) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 20;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/nonlinear2postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=20;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_start := 0.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(2.0)/(c(1.0) - c(2.0)*c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(0.5);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(0.0);
> array_given_ord_poles[1,2] := c(0.0);
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=10000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> found_h := true;
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1
> #left paren 0001C
> if (true) then # if number 10
> omniout_str(INFO," ");
> fi;# end if 10;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> atomall();
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10
> display_alot(current_iter);
> fi;# end if 10;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (true) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = y * y ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T16:21:47-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"nonlinear2")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"nonlinear2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"nonlinear2 maple results")
> ;
> logitem_str(html_log_file,"OK - a little surprising")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init,
array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error,
array_est_rel_error, array_max_est_error, array_type_pole,
array_type_real_pole, array_type_complex_pole, array_est_digits, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 20;
Digits := 32;
max_terms := 20;
glob_html_log := true;
array_y_init := Array(0 .. 20, []);
array_norms := Array(0 .. 20, []);
array_fact_1 := Array(0 .. 20, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 20, []);
array_x := Array(0 .. 20, []);
array_tmp0 := Array(0 .. 20, []);
array_tmp1 := Array(0 .. 20, []);
array_tmp2 := Array(0 .. 20, []);
array_m1 := Array(0 .. 20, []);
array_y_higher := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []);
array_y_set_initial := Array(0 .. 2, 0 .. 21, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 20, 0 .. 21, []);
term := 1;
while term <= 20 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 20 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 20 do
term := 1;
while term <= 20 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 20;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/nonlinear2postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=20;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_start := 0.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(2.0)/(c(1.0) - c(2.0)*c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 0.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(0.5);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(0.);
array_given_ord_poles[1, 2] := c(0.);
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 10000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
found_h := true;
glob_h := next_delta();
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius
;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new :=
glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] :=
array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
atomall();
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = y * y ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T16:21:47-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"nonlinear2");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = y * y ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file, "nonlinear2 diffeq.mxt");
logitem_str(html_log_file, "nonlinear2 maple results");
logitem_str(html_log_file, "OK - a little surprising");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/nonlinear2postcpx.cpx#################
diff ( y , x , 1 ) = y * y ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(0.5);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(0.0);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(2.0)/(c(1.0) - c(2.0)*c(x)));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 2.35294117647 0.588235294118
y[1] (closed_form) = 2.35294117647 0.588235294118
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4123
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4123
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4123
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 2.33934877655 0.614232611996
y[1] (closed_form) = 2.33934877655 0.614232611996
absolute error = 1e-32
relative error = 4.135e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 0.4135
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4135
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4135
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 2.33114042095 0.629722775044
y[1] (closed_form) = 2.33114042095 0.629722775044
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4141
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4141
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4141
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 2.33322201579 0.637716147745
y[1] (closed_form) = 2.33322201579 0.637716147745
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4134
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4134
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4134
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 2.32919200107 0.655780553343
y[1] (closed_form) = 2.32919200107 0.655780553343
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4133
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4133
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4133
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1023 0.116
h = 0.003 0.006
y[1] (numeric) = 2.31731156432 0.675906817855
y[1] (closed_form) = 2.31731156432 0.675906817855
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4143
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4143
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4143
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = 2.31262182352 0.714821034886
y[1] (closed_form) = 2.31262182352 0.714821034886
absolute error = 1e-31
relative error = 4.131e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4131
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4131
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4131
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = 2.29634674859 0.739067503982
y[1] (closed_form) = 2.29634674859 0.739067503982
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4145
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4145
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4145
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1055 0.13
h = 0.001 0.001
y[1] (numeric) = 2.28655554606 0.753491054467
y[1] (closed_form) = 2.28655554606 0.753491054467
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4154
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4154
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4154
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1065 0.131
h = 0.001 0.003
y[1] (numeric) = 2.28774746989 0.761613516024
y[1] (closed_form) = 2.28774746989 0.761613516024
absolute error = 1e-31
relative error = 4.147e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4147
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4147
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4147
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=30.3MB, alloc=40.3MB, time=0.38
x[1] = 0.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = 2.28181423125 0.77901428532
y[1] (closed_form) = 2.28181423125 0.77901428532
absolute error = 1e-31
relative error = 4.147e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4147
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4147
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4147
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1076 0.138
h = 0.003 0.006
y[1] (numeric) = 2.26792283237 0.797587540434
y[1] (closed_form) = 2.26792283237 0.797587540434
absolute error = 1e-31
relative error = 4.160e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.416
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.416
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.416
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = 2.25911530399 0.835420143233
y[1] (closed_form) = 2.25911530399 0.835420143233
absolute error = 1.005e-31
relative error = 4.172e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4152
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4152
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4152
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = 2.24050474607 0.857526861453
y[1] (closed_form) = 2.24050474607 0.857526861453
absolute error = 1e-32
relative error = 4.168e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 0.4168
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4168
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4168
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1108 0.152
h = 0.001 0.001
y[1] (numeric) = 2.22934226842 0.870657823227
y[1] (closed_form) = 2.22934226842 0.870657823227
absolute error = 1.005e-31
relative error = 4.199e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4178
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4178
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4178
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1118 0.153
h = 0.001 0.003
y[1] (numeric) = 2.22964748825 0.878763693206
y[1] (closed_form) = 2.22964748825 0.878763693206
absolute error = 1e-32
relative error = 4.173e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 0.4173
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4173
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4173
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = 2.22196921563 0.895214869932
y[1] (closed_form) = 2.22196921563 0.895214869932
absolute error = 2e-32
relative error = 8.349e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 0.4174
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4174
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4174
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1129 0.16
h = 0.003 0.006
y[1] (numeric) = 2.20637173482 0.911959384065
y[1] (closed_form) = 2.20637173482 0.911959384065
absolute error = 1.020e-31
relative error = 4.272e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4189
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4189
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4189
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = 2.19374384919 0.948090286295
y[1] (closed_form) = 2.19374384919 0.948090286295
absolute error = 2e-32
relative error = 8.369e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 0.4184
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4184
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4184
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.116 0.171
h = 0.0001 0.003
y[1] (numeric) = 2.1732117693 0.967758366016
y[1] (closed_form) = 2.1732117693 0.967758366016
absolute error = 2e-32
relative error = 8.407e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 0.4204
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4204
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4204
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1161 0.174
h = 0.001 0.001
y[1] (numeric) = 2.16092733785 0.979425258623
y[1] (closed_form) = 2.16092733785 0.979425258623
absolute error = 2e-32
relative error = 8.430e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 0.4215
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4215
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4215
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1171 0.175
h = 0.001 0.003
y[1] (numeric) = 2.16037912086 0.987376197835
y[1] (closed_form) = 2.16037912086 0.987376197835
absolute error = 2e-32
relative error = 8.420e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 0.421
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.421
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.421
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = 2.1511662064 1.00263834705
y[1] (closed_form) = 2.1511662064 1.00263834705
absolute error = 1e-31
relative error = 4.213e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4213
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4213
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4213
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1182 0.182
h = 0.003 0.006
y[1] (numeric) = 2.1342099432 1.01735518508
y[1] (closed_form) = 2.1342099432 1.01735518508
absolute error = 1e-31
relative error = 4.230e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.423
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.423
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.423
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = 2.11817208236 1.05125752767
y[1] (closed_form) = 2.11817208236 1.05125752767
absolute error = 1e-31
relative error = 4.229e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4229
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4229
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4229
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = 2.09617160023 1.06828919685
y[1] (closed_form) = 2.09617160023 1.06828919685
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.425
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.425
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.425
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1214 0.196
h = 0.001 0.001
y[1] (numeric) = 2.08303576989 1.0783809057
y[1] (closed_form) = 2.08303576989 1.0783809057
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4263
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4263
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4263
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = 2.08169368715 1.08605311538
y[1] (closed_form) = 2.08169368715 1.08605311538
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4259
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4259
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4259
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1225 0.201
h = 0.003 0.006
y[1] (numeric) = 2.06388757143 1.09891762082
y[1] (closed_form) = 2.06388757143 1.09891762082
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4277
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4277
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4277
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = 2.04533879849 1.13053439596
y[1] (closed_form) = 2.04533879849 1.13053439596
absolute error = 1e-31
relative error = 4.279e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4279
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4279
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4279
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = 2.02247890226 1.14520707072
y[1] (closed_form) = 2.02247890226 1.14520707072
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4303
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4303
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4303
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=75.5MB, alloc=52.3MB, time=0.93
x[1] = 0.1257 0.215
h = 0.001 0.001
y[1] (numeric) = 2.00885021153 1.15389472476
y[1] (closed_form) = 2.00885021153 1.15389472476
absolute error = 1e-31
relative error = 4.317e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4317
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4317
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4317
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1267 0.216
h = 0.001 0.003
y[1] (numeric) = 2.00689332644 1.16123482055
y[1] (closed_form) = 2.00689332644 1.16123482055
absolute error = 1e-31
relative error = 4.313e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4313
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4313
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4313
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = 1.99551595826 1.17383291662
y[1] (closed_form) = 1.99551595826 1.17383291662
absolute error = 1e-31
relative error = 4.319e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4319
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4319
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4319
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1278 0.223
h = 0.003 0.006
y[1] (numeric) = 1.97703368882 1.184520453
y[1] (closed_form) = 1.97703368882 1.184520453
absolute error = 1e-31
relative error = 4.339e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4339
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4339
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4339
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = 1.95603022077 1.21324734712
y[1] (closed_form) = 1.95603022077 1.21324734712
absolute error = 1e-31
relative error = 4.345e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4345
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4345
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4345
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = 1.93255371816 1.22518984029
y[1] (closed_form) = 1.93255371816 1.22518984029
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.437
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.437
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.437
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.131 0.237
h = 0.001 0.001
y[1] (numeric) = 1.91857744502 1.23225705818
y[1] (closed_form) = 1.91857744502 1.23225705818
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4386
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4386
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4386
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.132 0.238
h = 0.001 0.003
y[1] (numeric) = 1.91598808755 1.23914446967
y[1] (closed_form) = 1.91598808755 1.23914446967
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4383
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4383
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4383
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.133 0.241
h = 0.0001 0.004
y[1] (numeric) = 1.90382320901 1.25019453234
y[1] (closed_form) = 1.90382320901 1.25019453234
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4391
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4391
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4391
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1331 0.245
h = 0.003 0.006
y[1] (numeric) = 1.88501258807 1.25873012831
y[1] (closed_form) = 1.88501258807 1.25873012831
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4412
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4412
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4412
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = 1.86210296053 1.2843853891
y[1] (closed_form) = 1.86210296053 1.2843853891
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4421
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4421
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4421
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = 1.83842814091 1.29367125913
y[1] (closed_form) = 1.83842814091 1.29367125913
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4448
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4448
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4448
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1363 0.259
h = 0.001 0.001
y[1] (numeric) = 1.82434986907 1.29916584022
y[1] (closed_form) = 1.82434986907 1.29916584022
absolute error = 1e-31
relative error = 4.465e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4465
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4465
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4465
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1373 0.26
h = 0.001 0.003
y[1] (numeric) = 1.82122847409 1.3055401248
y[1] (closed_form) = 1.82122847409 1.3055401248
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4463
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4463
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4463
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = 1.80853716544 1.31502702381
y[1] (closed_form) = 1.80853716544 1.31502702381
absolute error = 1.414e-31
relative error = 6.324e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4472
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4472
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4472
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1384 0.267
h = 0.003 0.006
y[1] (numeric) = 1.7897130698 1.32149720585
y[1] (closed_form) = 1.7897130698 1.32149720585
absolute error = 1e-31
relative error = 4.495e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4495
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4495
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4495
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = 1.765433115 1.34401349803
y[1] (closed_form) = 1.765433115 1.34401349803
absolute error = 1e-31
relative error = 4.507e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4507
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4507
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4507
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = 1.74192960612 1.35078502232
y[1] (closed_form) = 1.74192960612 1.35078502232
absolute error = 1e-31
relative error = 4.537e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4537
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4537
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4537
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1416 0.281
h = 0.001 0.001
y[1] (numeric) = 1.72796540366 1.35479430365
y[1] (closed_form) = 1.72796540366 1.35479430365
absolute error = 1e-31
relative error = 4.554e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4554
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4554
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4554
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1426 0.282
h = 0.001 0.003
y[1] (numeric) = 1.72441444695 1.36061800235
y[1] (closed_form) = 1.72441444695 1.36061800235
absolute error = 1e-31
relative error = 4.553e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4553
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4553
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4553
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = 1.71143776331 1.36857396897
y[1] (closed_form) = 1.71143776331 1.36857396897
absolute error = 1e-31
relative error = 4.563e-30 %
Correct digits = 31
memory used=120.9MB, alloc=52.3MB, time=1.46
Radius of convergence (given) for eq 1 = 0.4563
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4563
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4563
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1437 0.289
h = 0.003 0.006
y[1] (numeric) = 1.69287229495 1.3731128073
y[1] (closed_form) = 1.69287229495 1.3731128073
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4588
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4588
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4588
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = 1.66772175755 1.39252170528
y[1] (closed_form) = 1.66772175755 1.39252170528
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4603
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4603
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4603
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = 1.64470130511 1.39697166345
y[1] (closed_form) = 1.64470130511 1.39697166345
absolute error = 1e-31
relative error = 4.634e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4634
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4634
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4634
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1469 0.303
h = 0.001 0.001
y[1] (numeric) = 1.63103269036 1.39961173939
y[1] (closed_form) = 1.63103269036 1.39961173939
absolute error = 1.414e-31
relative error = 6.580e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4653
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4653
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4653
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = 1.62715159142 1.40486817322
y[1] (closed_form) = 1.62715159142 1.40486817322
absolute error = 1e-31
relative error = 4.652e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4652
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4652
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4652
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.148 0.308
h = 0.003 0.006
y[1] (numeric) = 1.60901045857 1.40788415125
y[1] (closed_form) = 1.60901045857 1.40788415125
absolute error = 1.414e-31
relative error = 6.615e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4677
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4677
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4677
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151 0.314
h = 0.0001 0.005
y[1] (numeric) = 1.58350612758 1.42470178814
y[1] (closed_form) = 1.58350612758 1.42470178814
absolute error = 1.414e-31
relative error = 6.639e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4695
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4695
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4695
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = 1.56112823798 1.42734281432
y[1] (closed_form) = 1.56112823798 1.42734281432
absolute error = 1e-31
relative error = 4.727e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4727
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4727
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4727
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1512 0.322
h = 0.001 0.001
y[1] (numeric) = 1.54784583172 1.42891731024
y[1] (closed_form) = 1.54784583172 1.42891731024
absolute error = 1e-31
relative error = 4.747e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4747
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4747
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4747
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1522 0.323
h = 0.001 0.003
y[1] (numeric) = 1.54376169362 1.43368322898
y[1] (closed_form) = 1.54376169362 1.43368322898
absolute error = 1e-31
relative error = 4.747e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4747
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4747
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4747
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = 1.53081331211 1.43899982626
y[1] (closed_form) = 1.53081331211 1.43899982626
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.476
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.476
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.476
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1533 0.33
h = 0.003 0.006
y[1] (numeric) = 1.51330708493 1.44041343532
y[1] (closed_form) = 1.51330708493 1.44041343532
absolute error = 1e-31
relative error = 4.786e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4786
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4786
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4786
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = 1.48771333612 1.45438370945
y[1] (closed_form) = 1.48771333612 1.45438370945
absolute error = 1e-31
relative error = 4.807e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4807
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4807
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = 1.46623336256 1.45513846517
y[1] (closed_form) = 1.46623336256 1.45513846517
absolute error = 1.414e-31
relative error = 6.846e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4841
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4841
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4841
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1565 0.344
h = 0.001 0.001
y[1] (numeric) = 1.45348683452 1.45560253588
y[1] (closed_form) = 1.45348683452 1.45560253588
absolute error = 1.414e-31
relative error = 6.875e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4861
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4861
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4861
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1575 0.345
h = 0.001 0.003
y[1] (numeric) = 1.44923703488 1.4598154074
y[1] (closed_form) = 1.44923703488 1.4598154074
absolute error = 1e-31
relative error = 4.861e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4861
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4861
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4861
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = 1.43652625657 1.46386863041
y[1] (closed_form) = 1.43652625657 1.46386863041
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4876
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4876
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4876
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1586 0.352
h = 0.003 0.006
y[1] (numeric) = 1.41979080252 1.46387335233
y[1] (closed_form) = 1.41979080252 1.46387335233
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4904
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4904
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4904
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = 1.39443715176 1.47520242414
y[1] (closed_form) = 1.39443715176 1.47520242414
absolute error = 1.414e-31
relative error = 6.967e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4926
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4926
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4926
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = 1.37399742965 1.47431589407
y[1] (closed_form) = 1.37399742965 1.47431589407
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4962
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4962
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4962
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=166.1MB, alloc=52.3MB, time=1.98
x[1] = 0.1618 0.366
h = 0.001 0.001
y[1] (numeric) = 1.3618687384 1.47381418763
y[1] (closed_form) = 1.3618687384 1.47381418763
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.4983
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4983
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4983
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1628 0.367
h = 0.001 0.003
y[1] (numeric) = 1.35752705271 1.4774983047
y[1] (closed_form) = 1.35752705271 1.4774983047
absolute error = 1e-31
relative error = 4.984e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4984
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4984
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4984
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = 1.34517428129 1.48041190981
y[1] (closed_form) = 1.34517428129 1.48041190981
absolute error = 1e-31
relative error = 4.999e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.4999
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.4999
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.4999
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1639 0.374
h = 0.003 0.006
y[1] (numeric) = 1.32930331494 1.47920095147
y[1] (closed_form) = 1.32930331494 1.47920095147
absolute error = 1e-31
relative error = 5.028e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5028
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5028
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5028
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = 1.30445538283 1.488120821
y[1] (closed_form) = 1.30445538283 1.488120821
absolute error = 2e-31
relative error = 1.011e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5053
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5053
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5053
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.167 0.385
h = 0.0001 0.003
y[1] (numeric) = 1.28514862184 1.48583249072
y[1] (closed_form) = 1.28514862184 1.48583249072
absolute error = 2e-31
relative error = 1.018e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.509
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.509
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.509
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1671 0.388
h = 0.001 0.001
y[1] (numeric) = 1.2736908312 1.48450598529
y[1] (closed_form) = 1.2736908312 1.48450598529
absolute error = 2e-31
relative error = 1.022e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5112
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5112
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5112
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1681 0.389
h = 0.001 0.003
y[1] (numeric) = 1.26931988815 1.48769339106
y[1] (closed_form) = 1.26931988815 1.48769339106
absolute error = 2e-31
relative error = 1.023e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5113
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5113
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5113
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = 1.25741562671 1.48959481919
y[1] (closed_form) = 1.25741562671 1.48959481919
absolute error = 2e-31
relative error = 1.026e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.513
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.513
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.513
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1692 0.396
h = 0.003 0.006
y[1] (numeric) = 1.24246632721 1.48735388626
y[1] (closed_form) = 1.24246632721 1.48735388626
absolute error = 3e-31
relative error = 1.548e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.516
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.516
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.516
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = 1.21832992612 1.49410808512
y[1] (closed_form) = 1.21832992612 1.49410808512
absolute error = 3e-31
relative error = 1.556e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5187
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5187
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5187
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = 1.2002067564 1.49064433889
y[1] (closed_form) = 1.2002067564 1.49064433889
absolute error = 3.162e-31
relative error = 1.652e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5225
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5225
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5225
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1724 0.41
h = 0.001 0.001
y[1] (numeric) = 1.18944850254 1.48862602577
y[1] (closed_form) = 1.18944850254 1.48862602577
absolute error = 3.162e-31
relative error = 1.660e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5248
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5248
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5248
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = 1.18509999109 1.49135363239
y[1] (closed_form) = 1.18509999109 1.49135363239
absolute error = 3.162e-31
relative error = 1.660e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.525
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.525
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.525
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1735 0.415
h = 0.003 0.006
y[1] (numeric) = 1.17097593582 1.48837676375
y[1] (closed_form) = 1.17097593582 1.48837676375
absolute error = 3e-31
relative error = 1.584e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.528
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.528
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.528
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = 1.14759753914 1.49347314985
y[1] (closed_form) = 1.14759753914 1.49347314985
absolute error = 3e-31
relative error = 1.593e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5309
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5309
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5309
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = 1.13051798698 1.48917953758
y[1] (closed_form) = 1.13051798698 1.48917953758
absolute error = 3e-31
relative error = 1.605e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5348
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5348
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5348
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1767 0.429
h = 0.001 0.001
y[1] (numeric) = 1.12037580308 1.48667250085
y[1] (closed_form) = 1.12037580308 1.48667250085
absolute error = 3e-31
relative error = 1.612e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5372
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5372
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5372
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1777 0.43
h = 0.001 0.003
y[1] (numeric) = 1.11608499408 1.48903675909
y[1] (closed_form) = 1.11608499408 1.48903675909
absolute error = 3e-31
relative error = 1.612e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5374
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5374
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5374
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = 1.10517689555 1.48939183247
y[1] (closed_form) = 1.10517689555 1.48939183247
absolute error = 3.162e-31
relative error = 1.705e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5392
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5392
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5392
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1788 0.437
h = 0.003 0.006
y[1] (numeric) = 1.09200279977 1.48569496731
y[1] (closed_form) = 1.09200279977 1.48569496731
absolute error = 3.162e-31
relative error = 1.715e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5423
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5423
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5423
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=211.3MB, alloc=52.3MB, time=2.51
x[1] = 0.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = 1.06957896908 1.48907442898
y[1] (closed_form) = 1.06957896908 1.48907442898
absolute error = 3.162e-31
relative error = 1.725e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5454
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5454
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5454
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = 1.05368943509 1.48397631852
y[1] (closed_form) = 1.05368943509 1.48397631852
absolute error = 3.162e-31
relative error = 1.738e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5494
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5494
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5494
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.182 0.451
h = 0.001 0.001
y[1] (numeric) = 1.04424924062 1.4809949922
y[1] (closed_form) = 1.04424924062 1.4809949922
absolute error = 2.236e-31
relative error = 1.234e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5518
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5518
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5518
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.183 0.452
h = 0.001 0.003
y[1] (numeric) = 1.04005013238 1.48297369034
y[1] (closed_form) = 1.04005013238 1.48297369034
absolute error = 2.236e-31
relative error = 1.234e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5521
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5521
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5521
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.184 0.455
h = 0.0001 0.004
y[1] (numeric) = 1.02971510129 1.48265940218
y[1] (closed_form) = 1.02971510129 1.48265940218
absolute error = 2.236e-31
relative error = 1.239e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.554
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.554
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.554
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1841 0.459
h = 0.003 0.006
y[1] (numeric) = 1.01747712633 1.47838556817
y[1] (closed_form) = 1.01747712633 1.47838556817
absolute error = 1.414e-31
relative error = 7.880e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5572
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5572
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5572
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.996079952654 1.48027222111
y[1] (closed_form) = 0.996079952654 1.48027222111
absolute error = 1.640e-31
relative error = 9.192e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5605
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5605
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5605
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.981352298448 1.4745383001
y[1] (closed_form) = 0.981352298448 1.4745383001
absolute error = 1.640e-31
relative error = 9.260e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5646
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5646
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5646
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1873 0.473
h = 0.001 0.001
y[1] (numeric) = 0.972597175661 1.4711815289
y[1] (closed_form) = 0.972597175661 1.4711815289
absolute error = 1.3e-31
relative error = 7.371e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.567
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.567
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.567
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1883 0.474
h = 0.001 0.003
y[1] (numeric) = 0.968515057613 1.47281404334
y[1] (closed_form) = 0.968515057613 1.47281404334
absolute error = 1.720e-31
relative error = 9.760e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5673
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5673
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5673
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.958762741215 1.4719337868
y[1] (closed_form) = 0.958762741215 1.4719337868
absolute error = 1.720e-31
relative error = 9.794e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5693
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5693
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5693
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1894 0.481
h = 0.003 0.006
y[1] (numeric) = 0.94743256147 1.46720882829
y[1] (closed_form) = 0.94743256147 1.46720882829
absolute error = 1.720e-31
relative error = 9.851e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5726
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5726
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5726
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.927101491331 1.46781022847
y[1] (closed_form) = 0.927101491331 1.46781022847
absolute error = 1.720e-31
relative error = 9.910e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.576
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.576
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.576
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.91349228099 1.46158764958
y[1] (closed_form) = 0.91349228099 1.46158764958
absolute error = 1.720e-31
relative error = 9.982e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5802
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5802
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5802
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1926 0.495
h = 0.001 0.001
y[1] (numeric) = 0.905396492976 1.45794165264
y[1] (closed_form) = 0.905396492976 1.45794165264
absolute error = 1.720e-31
relative error = 1.002e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5827
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5827
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5827
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1936 0.496
h = 0.001 0.003
y[1] (numeric) = 0.901449662863 1.45926577278
y[1] (closed_form) = 0.901449662863 1.45926577278
absolute error = 1.720e-31
relative error = 1.003e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.583
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.583
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.583
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.892277609009 1.45791266174
y[1] (closed_form) = 0.892277609009 1.45791266174
absolute error = 1.4e-31
relative error = 8.191e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.585
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.585
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.585
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1947 0.503
h = 0.003 0.006
y[1] (numeric) = 0.881816665954 1.45284566975
y[1] (closed_form) = 0.881816665954 1.45284566975
absolute error = 1.720e-31
relative error = 1.012e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5884
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5884
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5884
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.862565127162 1.45235080955
y[1] (closed_form) = 0.862565127162 1.45235080955
absolute error = 1.720e-31
relative error = 1.019e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.592
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.592
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.592
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.850020493876 1.44576616099
y[1] (closed_form) = 0.850020493876 1.44576616099
absolute error = 1.5e-31
relative error = 8.944e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5963
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5963
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5963
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1979 0.517
h = 0.001 0.001
y[1] (numeric) = 0.842552299252 1.44190512649
y[1] (closed_form) = 0.842552299252 1.44190512649
absolute error = 1.5e-31
relative error = 8.982e-30 %
Correct digits = 31
memory used=256.6MB, alloc=52.3MB, time=3.04
Radius of convergence (given) for eq 1 = 0.5988
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5988
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5988
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.838753217716 1.44295638252
y[1] (closed_form) = 0.838753217716 1.44295638252
absolute error = 1.5e-31
relative error = 8.987e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.5992
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.5992
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.5992
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.199 0.522
h = 0.003 0.006
y[1] (numeric) = 0.829006981836 1.43767988212
y[1] (closed_form) = 0.829006981836 1.43767988212
absolute error = 1.4e-31
relative error = 8.436e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6026
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6026
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6026
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.202 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.810690229278 1.43639074181
y[1] (closed_form) = 0.810690229278 1.43639074181
absolute error = 1.4e-31
relative error = 8.488e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6063
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6063
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6063
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.799016375705 1.42959291121
y[1] (closed_form) = 0.799016375705 1.42959291121
absolute error = 1.4e-31
relative error = 8.548e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6106
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6106
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6106
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2022 0.536
h = 0.001 0.001
y[1] (numeric) = 0.792061638035 1.42560456006
y[1] (closed_form) = 0.792061638035 1.42560456006
absolute error = 1.4e-31
relative error = 8.584e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6132
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6132
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6132
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2032 0.537
h = 0.001 0.003
y[1] (numeric) = 0.788398765295 1.42644924853
y[1] (closed_form) = 0.788398765295 1.42644924853
absolute error = 1.4e-31
relative error = 8.590e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6136
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6136
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6136
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.780273915712 1.42443514025
y[1] (closed_form) = 0.780273915712 1.42443514025
absolute error = 1.4e-31
relative error = 8.620e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6157
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6157
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6157
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2043 0.544
h = 0.003 0.006
y[1] (numeric) = 0.771308492644 1.41897808589
y[1] (closed_form) = 0.771308492644 1.41897808589
absolute error = 1.4e-31
relative error = 8.668e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6192
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6192
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6192
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.75404466907 1.41689295521
y[1] (closed_form) = 0.75404466907 1.41689295521
absolute error = 1.4e-31
relative error = 8.722e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.623
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.623
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.623
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.743319221615 1.40991855091
y[1] (closed_form) = 0.743319221615 1.40991855091
absolute error = 1.720e-31
relative error = 1.079e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6274
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6274
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6274
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2075 0.558
h = 0.001 0.001
y[1] (numeric) = 0.736923853091 1.4058239659
y[1] (closed_form) = 0.736923853091 1.4058239659
absolute error = 1.5e-31
relative error = 9.450e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.63
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.63
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.63
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2085 0.559
h = 0.001 0.003
y[1] (numeric) = 0.733419590858 1.4064547214
y[1] (closed_form) = 0.733419590858 1.4064547214
absolute error = 1.5e-31
relative error = 9.457e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6304
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6304
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6304
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.72582493877 1.40417767845
y[1] (closed_form) = 0.72582493877 1.40417767845
absolute error = 1.720e-31
relative error = 1.088e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6326
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6326
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6326
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2096 0.566
h = 0.003 0.006
y[1] (numeric) = 0.717589563283 1.39860775764
y[1] (closed_form) = 0.717589563283 1.39860775764
absolute error = 1.803e-31
relative error = 1.147e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6362
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6362
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6362
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.701347221147 1.39586155357
y[1] (closed_form) = 0.701347221147 1.39586155357
absolute error = 1.4e-31
relative error = 8.962e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6401
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6401
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6401
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.691505522573 1.38878763148
y[1] (closed_form) = 0.691505522573 1.38878763148
absolute error = 1.4e-31
relative error = 9.024e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6446
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6446
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6446
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2128 0.58
h = 0.001 0.001
y[1] (numeric) = 0.685631606127 1.38463207366
y[1] (closed_form) = 0.685631606127 1.38463207366
absolute error = 1.720e-31
relative error = 1.114e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6472
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6472
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6472
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2138 0.581
h = 0.001 0.003
y[1] (numeric) = 0.682287213642 1.38507641903
y[1] (closed_form) = 0.682287213642 1.38507641903
absolute error = 1.720e-31
relative error = 1.114e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6477
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6477
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6477
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.675197322393 1.38259199256
y[1] (closed_form) = 0.675197322393 1.38259199256
absolute error = 1.720e-31
relative error = 1.118e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6499
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6499
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6499
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2149 0.588
h = 0.003 0.006
y[1] (numeric) = 0.66764083059 1.37696530476
y[1] (closed_form) = 0.66764083059 1.37696530476
absolute error = 1.640e-31
relative error = 1.072e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6535
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6535
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6535
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=301.9MB, alloc=52.3MB, time=3.58
x[1] = 0.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.652380421918 1.37367589727
y[1] (closed_form) = 0.652380421918 1.37367589727
absolute error = 1.640e-31
relative error = 1.079e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6576
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6576
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6576
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.218 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.64335823875 1.36656590429
y[1] (closed_form) = 0.64335823875 1.36656590429
absolute error = 1.640e-31
relative error = 1.086e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6621
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6621
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6621
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2181 0.602
h = 0.001 0.001
y[1] (numeric) = 0.637968119291 1.36238668965
y[1] (closed_form) = 0.637968119291 1.36238668965
absolute error = 1.640e-31
relative error = 1.090e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6647
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6647
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6647
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2191 0.603
h = 0.001 0.003
y[1] (numeric) = 0.634782448936 1.36266933681
y[1] (closed_form) = 0.634782448936 1.36266933681
absolute error = 1.3e-31
relative error = 8.648e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6652
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6652
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6652
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.628170011487 1.36002510526
y[1] (closed_form) = 0.628170011487 1.36002510526
absolute error = 1.3e-31
relative error = 8.678e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6675
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6675
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6675
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2202 0.61
h = 0.003 0.006
y[1] (numeric) = 0.621242073835 1.35438765203
y[1] (closed_form) = 0.621242073835 1.35438765203
absolute error = 1.562e-31
relative error = 1.048e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6711
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6711
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6711
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.606918733231 1.3506572965
y[1] (closed_form) = 0.606918733231 1.3506572965
absolute error = 1.2e-31
relative error = 8.104e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6753
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6753
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6753
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.598653550925 1.34356290251
y[1] (closed_form) = 0.598653550925 1.34356290251
absolute error = 1.487e-31
relative error = 1.011e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6799
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6799
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6799
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2234 0.624
h = 0.001 0.001
y[1] (numeric) = 0.593710582962 1.33939046915
y[1] (closed_form) = 0.593710582962 1.33939046915
absolute error = 1.1e-31
relative error = 7.508e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6826
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6826
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6826
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.590680670742 1.33953345143
y[1] (closed_form) = 0.590680670742 1.33953345143
absolute error = 1.1e-31
relative error = 7.514e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6831
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6831
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6831
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2245 0.629
h = 0.003 0.006
y[1] (numeric) = 0.584254293765 1.33392359629
y[1] (closed_form) = 0.584254293765 1.33392359629
absolute error = 1.1e-31
relative error = 7.554e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6867
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6867
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6867
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.570703038077 1.32989515295
y[1] (closed_form) = 0.570703038077 1.32989515295
absolute error = 1.414e-31
relative error = 9.772e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.691
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.691
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.691
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.563040531312 1.32285587386
y[1] (closed_form) = 0.563040531312 1.32285587386
absolute error = 1.414e-31
relative error = 9.837e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6956
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6956
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6956
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2277 0.643
h = 0.001 0.001
y[1] (numeric) = 0.558453797915 1.31871388931
y[1] (closed_form) = 0.558453797915 1.31871388931
absolute error = 2.236e-31
relative error = 1.561e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6983
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6983
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6983
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2287 0.644
h = 0.001 0.003
y[1] (numeric) = 0.555555908224 1.31875416475
y[1] (closed_form) = 0.555555908224 1.31875416475
absolute error = 1.345e-31
relative error = 9.402e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.6988
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.6988
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.6988
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.549757765908 1.31592036457
y[1] (closed_form) = 0.549757765908 1.31592036457
absolute error = 1.345e-31
relative error = 9.434e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7012
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7012
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7012
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2298 0.651
h = 0.003 0.006
y[1] (numeric) = 0.543870940835 1.31036262947
y[1] (closed_form) = 0.543870940835 1.31036262947
absolute error = 1.414e-31
relative error = 9.968e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7048
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7048
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7048
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.531165372852 1.30604659418
y[1] (closed_form) = 0.531165372852 1.30604659418
absolute error = 2.236e-31
relative error = 1.586e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7093
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7093
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7093
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.524150555742 1.29909272894
y[1] (closed_form) = 0.524150555742 1.29909272894
absolute error = 1.414e-31
relative error = 1.010e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7139
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7139
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7139
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.233 0.665
h = 0.001 0.001
y[1] (numeric) = 0.51994687584 1.29499877316
y[1] (closed_form) = 0.51994687584 1.29499877316
absolute error = 1.414e-31
relative error = 1.013e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7166
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7166
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7166
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.234 0.666
h = 0.001 0.003
y[1] (numeric) = 0.517195787771 1.29493381449
y[1] (closed_form) = 0.517195787771 1.29493381449
absolute error = 1.414e-31
relative error = 1.014e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7172
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7172
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7172
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=347.1MB, alloc=52.3MB, time=4.11
x[1] = 0.235 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.511794447899 1.29203956847
y[1] (closed_form) = 0.511794447899 1.29203956847
absolute error = 1.487e-31
relative error = 1.070e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7196
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7196
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7196
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2351 0.673
h = 0.003 0.006
y[1] (numeric) = 0.506403151468 1.28655840294
y[1] (closed_form) = 0.506403151468 1.28655840294
absolute error = 1.414e-31
relative error = 1.023e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7233
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7233
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7233
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.494493720845 1.28202075775
y[1] (closed_form) = 0.494493720845 1.28202075775
absolute error = 1.0e-31
relative error = 7.278e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7278
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7278
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7278
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.488072936665 1.27517910114
y[1] (closed_form) = 0.488072936665 1.27517910114
absolute error = 1.414e-31
relative error = 1.036e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7324
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7324
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7324
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2383 0.687
h = 0.001 0.001
y[1] (numeric) = 0.484220830677 1.27114906639
y[1] (closed_form) = 0.484220830677 1.27114906639
absolute error = 1.345e-31
relative error = 9.891e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7352
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7352
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7352
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2393 0.688
h = 0.001 0.003
y[1] (numeric) = 0.481610772445 1.27099429015
y[1] (closed_form) = 0.481610772445 1.27099429015
absolute error = 1.345e-31
relative error = 9.898e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7357
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7357
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7357
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.47657926707 1.2680642031
y[1] (closed_form) = 0.47657926707 1.2680642031
absolute error = 2.236e-31
relative error = 1.651e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7382
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7382
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7382
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2404 0.695
h = 0.003 0.006
y[1] (numeric) = 0.4716422722 1.26267865631
y[1] (closed_form) = 0.4716422722 1.26267865631
absolute error = 2.236e-31
relative error = 1.659e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7419
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7419
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7419
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.460480044884 1.25797549284
y[1] (closed_form) = 0.460480044884 1.25797549284
absolute error = 2.193e-31
relative error = 1.637e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7465
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7465
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7465
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.454603256749 1.2512666638
y[1] (closed_form) = 0.454603256749 1.2512666638
absolute error = 2.193e-31
relative error = 1.647e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7512
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7512
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7512
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2436 0.709
h = 0.001 0.001
y[1] (numeric) = 0.451073354027 1.24731282373
y[1] (closed_form) = 0.451073354027 1.24731282373
absolute error = 2.193e-31
relative error = 1.654e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7539
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7539
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7539
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2446 0.71
h = 0.001 0.003
y[1] (numeric) = 0.448598136094 1.2470817409
y[1] (closed_form) = 0.448598136094 1.2470817409
absolute error = 3.132e-31
relative error = 2.363e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7545
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7545
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7545
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.443910603942 1.24413624454
y[1] (closed_form) = 0.443910603942 1.24413624454
absolute error = 2.154e-31
relative error = 1.631e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.757
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.757
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.757
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2457 0.717
h = 0.003 0.006
y[1] (numeric) = 0.439389561939 1.2388608569
y[1] (closed_form) = 0.439389561939 1.2388608569
absolute error = 3.105e-31
relative error = 2.362e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7608
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7608
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7608
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.428926920257 1.23403964722
y[1] (closed_form) = 0.428926920257 1.23403964722
absolute error = 3.081e-31
relative error = 2.358e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7654
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7654
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7654
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.423547743812 1.22747913016
y[1] (closed_form) = 0.423547743812 1.22747913016
absolute error = 2.119e-31
relative error = 1.632e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7701
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7701
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7701
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2489 0.731
h = 0.001 0.001
y[1] (numeric) = 0.42031280211 1.22361074609
y[1] (closed_form) = 0.42031280211 1.22361074609
absolute error = 2.119e-31
relative error = 1.638e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7729
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7729
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7729
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.417966014266 1.22331516371
y[1] (closed_form) = 0.417966014266 1.22331516371
absolute error = 2.119e-31
relative error = 1.639e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7735
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7735
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7735
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.25 0.736
h = 0.003 0.006
y[1] (numeric) = 0.413773014055 1.21814775338
y[1] (closed_form) = 0.413773014055 1.21814775338
absolute error = 2.088e-31
relative error = 1.623e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7773
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7773
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7773
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.253 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.403876560934 1.21326481058
y[1] (closed_form) = 0.403876560934 1.21326481058
absolute error = 2.119e-31
relative error = 1.657e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.782
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.782
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.782
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.398889371789 1.20684633749
y[1] (closed_form) = 0.398889371789 1.20684633749
absolute error = 2.088e-31
relative error = 1.643e-29 %
Correct digits = 31
memory used=392.3MB, alloc=52.3MB, time=4.64
Radius of convergence (given) for eq 1 = 0.7867
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7867
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7867
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2532 0.75
h = 0.001 0.001
y[1] (numeric) = 0.395886984468 1.20306012298
y[1] (closed_form) = 0.395886984468 1.20306012298
absolute error = 1.166e-31
relative error = 9.208e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7896
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7896
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7896
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2542 0.751
h = 0.001 0.003
y[1] (numeric) = 0.393646160211 1.20271874011
y[1] (closed_form) = 0.393646160211 1.20271874011
absolute error = 2.088e-31
relative error = 1.650e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7902
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7902
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7902
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.389534109567 1.19979051721
y[1] (closed_form) = 0.389534109567 1.19979051721
absolute error = 2.088e-31
relative error = 1.655e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7927
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7927
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7927
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.385693200147 1.1947504933
y[1] (closed_form) = 0.385693200147 1.1947504933
absolute error = 2.062e-31
relative error = 1.642e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.7965
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.7965
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.7965
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2554 0.762
h = 0.003 0.006
y[1] (numeric) = 0.381905152747 1.18974540635
y[1] (closed_form) = 0.381905152747 1.18974540635
absolute error = 2.062e-31
relative error = 1.650e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8003
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8003
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8003
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.372727595863 1.1848294438
y[1] (closed_form) = 0.372727595863 1.1848294438
absolute error = 1.118e-31
relative error = 9.001e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8051
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8051
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8051
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.368223739758 1.17862091442
y[1] (closed_form) = 0.368223739758 1.17862091442
absolute error = 1.118e-31
relative error = 9.054e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8098
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8098
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8098
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2586 0.776
h = 0.001 0.001
y[1] (numeric) = 0.365508387645 1.17495654024
y[1] (closed_form) = 0.365508387645 1.17495654024
absolute error = 1.118e-31
relative error = 9.086e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8127
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8127
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8127
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2596 0.777
h = 0.001 0.003
y[1] (numeric) = 0.363404853142 1.17456560271
y[1] (closed_form) = 0.363404853142 1.17456560271
absolute error = 1.118e-31
relative error = 9.093e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8133
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8133
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8133
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.359614774165 1.17167720906
y[1] (closed_form) = 0.359614774165 1.17167720906
absolute error = 1.118e-31
relative error = 9.122e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8159
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8159
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8159
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2607 0.784
h = 0.003 0.006
y[1] (numeric) = 0.356143328804 1.1668047212
y[1] (closed_form) = 0.356143328804 1.1668047212
absolute error = 1.077e-31
relative error = 8.829e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8197
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8197
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8197
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.347531845161 1.16187117087
y[1] (closed_form) = 0.347531845161 1.16187117087
absolute error = 1.077e-31
relative error = 8.881e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8246
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8246
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8246
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.343406074164 1.15583331482
y[1] (closed_form) = 0.343406074164 1.15583331482
absolute error = 1.118e-31
relative error = 9.272e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8293
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8293
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8293
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2639 0.798
h = 0.001 0.001
y[1] (numeric) = 0.340915386837 1.1522680165
y[1] (closed_form) = 0.340915386837 1.1522680165
absolute error = 4e-32
relative error = 3.329e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8322
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8322
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8322
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2649 0.799
h = 0.001 0.003
y[1] (numeric) = 0.338920495119 1.15183953892
y[1] (closed_form) = 0.338920495119 1.15183953892
absolute error = 1.077e-31
relative error = 8.970e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8329
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8329
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8329
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.335383547332 1.14898592465
y[1] (closed_form) = 0.335383547332 1.14898592465
absolute error = 1.077e-31
relative error = 8.998e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8355
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8355
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8355
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.266 0.806
h = 0.003 0.006
y[1] (numeric) = 0.332201387864 1.14424922486
y[1] (closed_form) = 0.332201387864 1.14424922486
absolute error = 1.077e-31
relative error = 9.039e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8393
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8393
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8393
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.269 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.324117271522 1.13932131808
y[1] (closed_form) = 0.324117271522 1.13932131808
absolute error = 1.077e-31
relative error = 9.093e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8442
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8442
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8442
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.320336819529 1.13345682787
y[1] (closed_form) = 0.320336819529 1.13345682787
absolute error = 1.077e-31
relative error = 9.144e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.849
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.849
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.849
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2692 0.82
h = 0.001 0.001
y[1] (numeric) = 0.318051500751 1.12999233369
y[1] (closed_form) = 0.318051500751 1.12999233369
absolute error = 1.077e-31
relative error = 9.175e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8519
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8519
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8519
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=437.3MB, alloc=52.3MB, time=5.16
x[1] = 0.2702 0.821
h = 0.001 0.003
y[1] (numeric) = 0.316159184856 1.12953303206
y[1] (closed_form) = 0.316159184856 1.12953303206
absolute error = 1.118e-31
relative error = 9.532e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8526
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8526
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8526
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.312856612782 1.12672136771
y[1] (closed_form) = 0.312856612782 1.12672136771
absolute error = 1.077e-31
relative error = 9.211e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8552
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8552
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8552
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2713 0.828
h = 0.003 0.006
y[1] (numeric) = 0.309938765885 1.1221219858
y[1] (closed_form) = 0.309938765885 1.1221219858
absolute error = 2.062e-31
relative error = 1.771e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.859
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.859
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.859
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.302345694887 1.11721891686
y[1] (closed_form) = 0.302345694887 1.11721891686
absolute error = 2.062e-31
relative error = 1.781e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.864
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.864
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.864
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.298880644293 1.11152863724
y[1] (closed_form) = 0.298880644293 1.11152863724
absolute error = 2.040e-31
relative error = 1.772e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8688
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8688
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8688
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2745 0.842
h = 0.001 0.001
y[1] (numeric) = 0.296783062439 1.10816558126
y[1] (closed_form) = 0.296783062439 1.10816558126
absolute error = 2.062e-31
relative error = 1.797e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8717
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8717
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8717
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2755 0.843
h = 0.001 0.003
y[1] (numeric) = 0.294987479457 1.1076812703
y[1] (closed_form) = 0.294987479457 1.1076812703
absolute error = 2.062e-31
relative error = 1.798e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8724
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8724
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8724
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.291901877869 1.10491717529
y[1] (closed_form) = 0.291901877869 1.10491717529
absolute error = 2.062e-31
relative error = 1.804e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.875
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.875
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.875
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2766 0.85
h = 0.003 0.006
y[1] (numeric) = 0.289225548233 1.10045530885
y[1] (closed_form) = 0.289225548233 1.10045530885
absolute error = 2.062e-31
relative error = 1.812e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8789
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8789
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8789
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.282089555601 1.09559282938
y[1] (closed_form) = 0.282089555601 1.09559282938
absolute error = 2.062e-31
relative error = 1.822e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8839
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8839
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8839
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.278912626651 1.09007613049
y[1] (closed_form) = 0.278912626651 1.09007613049
absolute error = 2.062e-31
relative error = 1.832e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8887
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8887
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8887
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2798 0.864
h = 0.001 0.001
y[1] (numeric) = 0.276986692714 1.08681427114
y[1] (closed_form) = 0.276986692714 1.08681427114
absolute error = 1.118e-31
relative error = 9.969e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8916
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8916
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8916
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.275282250961 1.08630997756
y[1] (closed_form) = 0.275282250961 1.08630997756
absolute error = 2.062e-31
relative error = 1.840e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8923
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8923
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8923
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2809 0.869
h = 0.003 0.006
y[1] (numeric) = 0.27279547669 1.08196836715
y[1] (closed_form) = 0.27279547669 1.08196836715
absolute error = 1.118e-31
relative error = 1.002e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.8962
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.8962
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.8962
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.266026787506 1.07715612711
y[1] (closed_form) = 0.266026787506 1.07715612711
absolute error = 2.040e-31
relative error = 1.838e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9013
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9013
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9013
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.284 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.263075843791 1.07179047471
y[1] (closed_form) = 0.263075843791 1.07179047471
absolute error = 1.077e-31
relative error = 9.759e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9061
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9061
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9061
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2841 0.883
h = 0.001 0.001
y[1] (numeric) = 0.261284675148 1.0686168048
y[1] (closed_form) = 0.261284675148 1.0686168048
absolute error = 1.077e-31
relative error = 9.790e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.909
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.909
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.909
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2851 0.884
h = 0.001 0.003
y[1] (numeric) = 0.259654580147 1.06809980851
y[1] (closed_form) = 0.259654580147 1.06809980851
absolute error = 2.040e-31
relative error = 1.856e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9097
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9097
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9097
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.256930082382 1.06543704101
y[1] (closed_form) = 0.256930082382 1.06543704101
absolute error = 1.077e-31
relative error = 9.827e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9124
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9124
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9124
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2862 0.891
h = 0.003 0.006
y[1] (numeric) = 0.254647665298 1.06123044799
y[1] (closed_form) = 0.254647665298 1.06123044799
absolute error = 2.040e-31
relative error = 1.869e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9163
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9163
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9163
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.248278761552 1.05648030888
y[1] (closed_form) = 0.248278761552 1.05648030888
absolute error = 1.077e-31
relative error = 9.924e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9214
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9214
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9214
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=482.4MB, alloc=52.3MB, time=5.68
x[1] = 0.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.245571527754 1.05128390144
y[1] (closed_form) = 0.245571527754 1.05128390144
absolute error = 1.077e-31
relative error = 9.976e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9263
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9263
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9263
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2894 0.905
h = 0.001 0.001
y[1] (numeric) = 0.243925784665 1.04820909365
y[1] (closed_form) = 0.243925784665 1.04820909365
absolute error = 1.077e-31
relative error = 1.001e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9292
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9292
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9292
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2904 0.906
h = 0.001 0.003
y[1] (numeric) = 0.242377101396 1.0476796463
y[1] (closed_form) = 0.242377101396 1.0476796463
absolute error = 1.077e-31
relative error = 1.002e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9299
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9299
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9299
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.239826636843 1.0450738873
y[1] (closed_form) = 0.239826636843 1.0450738873
absolute error = 1.077e-31
relative error = 1.004e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9326
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9326
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9326
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2915 0.913
h = 0.003 0.006
y[1] (numeric) = 0.237731121541 1.04100006699
y[1] (closed_form) = 0.237731121541 1.04100006699
absolute error = 1.077e-31
relative error = 1.009e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9365
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9365
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9365
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.231734356874 1.03632055458
y[1] (closed_form) = 0.231734356874 1.03632055458
absolute error = 1.077e-31
relative error = 1.014e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9417
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9417
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9417
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.229249985569 1.03129010061
y[1] (closed_form) = 0.229249985569 1.03129010061
absolute error = 1.044e-31
relative error = 9.882e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9466
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9466
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9466
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2947 0.927
h = 0.001 0.001
y[1] (numeric) = 0.227737346048 1.02831232239
y[1] (closed_form) = 0.227737346048 1.02831232239
absolute error = 1.044e-31
relative error = 9.913e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9495
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9495
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9495
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2957 0.928
h = 0.001 0.003
y[1] (numeric) = 0.226265268905 1.02777371289
y[1] (closed_form) = 0.226265268905 1.02777371289
absolute error = 4e-32
relative error = 3.801e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9502
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9502
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9502
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.223876022062 1.02522664309
y[1] (closed_form) = 0.223876022062 1.02522664309
absolute error = 1.077e-31
relative error = 1.026e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9529
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9529
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9529
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2968 0.935
h = 0.003 0.006
y[1] (numeric) = 0.221951520982 1.02128283523
y[1] (closed_form) = 0.221951520982 1.02128283523
absolute error = 1.044e-31
relative error = 9.990e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9568
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9568
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9568
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.2163012393 1.01668065026
y[1] (closed_form) = 0.2163012393 1.01668065026
absolute error = 1.077e-31
relative error = 1.036e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9621
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9621
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9621
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.214020764464 1.01181230976
y[1] (closed_form) = 0.214020764464 1.01181230976
absolute error = 1.044e-31
relative error = 1.010e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9669
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9669
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9669
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3 0.949
h = 0.001 0.001
y[1] (numeric) = 0.212630009962 1.00892939727
y[1] (closed_form) = 0.212630009962 1.00892939727
absolute error = 2.022e-31
relative error = 1.961e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9698
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9698
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9698
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.301 0.95
h = 0.001 0.003
y[1] (numeric) = 0.211230006125 1.00838445135
y[1] (closed_form) = 0.211230006125 1.00838445135
absolute error = 2.022e-31
relative error = 1.963e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9706
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9706
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9706
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.302 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.208990165852 1.0058971114
y[1] (closed_form) = 0.208990165852 1.0058971114
absolute error = 1.077e-31
relative error = 1.048e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9734
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9734
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9734
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3021 0.957
h = 0.003 0.006
y[1] (numeric) = 0.207222221099 1.00208016974
y[1] (closed_form) = 0.207222221099 1.00208016974
absolute error = 1.077e-31
relative error = 1.053e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9772
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9772
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9772
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.201894637704 0.997560472598
y[1] (closed_form) = 0.201894637704 0.997560472598
absolute error = 1.360e-31
relative error = 1.336e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9825
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9825
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9825
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.199800806391 0.992850003011
y[1] (closed_form) = 0.199800806391 0.992850003011
absolute error = 1.360e-31
relative error = 1.343e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9874
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9874
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9874
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3053 0.971
h = 0.001 0.001
y[1] (numeric) = 0.198521723839 0.990059547239
y[1] (closed_form) = 0.198521723839 0.990059547239
absolute error = 1.265e-31
relative error = 1.253e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9903
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9903
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9903
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=527.6MB, alloc=52.3MB, time=6.21
x[1] = 0.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.197189526999 0.989510687881
y[1] (closed_form) = 0.197189526999 0.989510687881
absolute error = 1.393e-31
relative error = 1.380e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.9911
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.9911
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.9911
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3064 0.976
h = 0.003 0.006
y[1] (numeric) = 0.195544304845 0.9858018674
y[1] (closed_form) = 0.195544304845 0.9858018674
absolute error = 1.393e-31
relative error = 1.386e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 0.995
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 0.995
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 0.995
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.190475741245 0.981359800121
y[1] (closed_form) = 0.190475741245 0.981359800121
absolute error = 1.300e-31
relative error = 1.300e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.188528137082 0.976783576379
y[1] (closed_form) = 0.188528137082 0.976783576379
absolute error = 1.432e-31
relative error = 1.439e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.005
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.005
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.005
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3096 0.99
h = 0.001 0.001
y[1] (numeric) = 0.187336641268 0.97407182172
y[1] (closed_form) = 0.187336641268 0.97407182172
absolute error = 1.393e-31
relative error = 1.404e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.008
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.008
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3106 0.991
h = 0.001 0.003
y[1] (numeric) = 0.186059604931 0.973522008906
y[1] (closed_form) = 0.186059604931 0.973522008906
absolute error = 1.432e-31
relative error = 1.445e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.009
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.009
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.009
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.184068759022 0.971148335815
y[1] (closed_form) = 0.184068759022 0.971148335815
absolute error = 1.342e-31
relative error = 1.357e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.012
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.012
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.012
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3117 0.998
h = 0.003 0.006
y[1] (numeric) = 0.182556606679 0.967559710383
y[1] (closed_form) = 0.182556606679 0.967559710383
absolute error = 1.342e-31
relative error = 1.363e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.016
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.016
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.016
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.177771025527 0.963206204153
y[1] (closed_form) = 0.177771025527 0.963206204153
absolute error = 1.253e-31
relative error = 1.279e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.021
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.021
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.021
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.175982053023 0.958779111774
y[1] (closed_form) = 0.175982053023 0.958779111774
absolute error = 1.300e-31
relative error = 1.334e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.026
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.026
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.026
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3149 1.012
h = 0.001 0.001
y[1] (numeric) = 0.174885628248 0.956154812462
y[1] (closed_form) = 0.174885628248 0.956154812462
absolute error = 1.300e-31
relative error = 1.337e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.029
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.029
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.029
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3159 1.013
h = 0.001 0.003
y[1] (numeric) = 0.173669118407 0.955604654789
y[1] (closed_form) = 0.173669118407 0.955604654789
absolute error = 1.342e-31
relative error = 1.381e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.03
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.03
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.03
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.171798798442 0.953290984257
y[1] (closed_form) = 0.171798798442 0.953290984257
absolute error = 1.300e-31
relative error = 1.342e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.032
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.032
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.032
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.317 1.02
h = 0.003 0.006
y[1] (numeric) = 0.170408673522 0.949818836025
y[1] (closed_form) = 0.170408673522 0.949818836025
absolute error = 1.300e-31
relative error = 1.347e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.036
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.036
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.036
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.165886997777 0.94555588733
y[1] (closed_form) = 0.165886997777 0.94555588733
absolute error = 1.300e-31
relative error = 1.354e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.042
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.042
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.042
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.164243487876 0.941273129516
y[1] (closed_form) = 0.164243487876 0.941273129516
absolute error = 1.300e-31
relative error = 1.361e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.047
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.047
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.047
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3202 1.034
h = 0.001 0.001
y[1] (numeric) = 0.163234321579 0.938733528994
y[1] (closed_form) = 0.163234321579 0.938733528994
absolute error = 1.300e-31
relative error = 1.364e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.05
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.05
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.05
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3212 1.035
h = 0.001 0.003
y[1] (numeric) = 0.162074783481 0.938184568805
y[1] (closed_form) = 0.162074783481 0.938184568805
absolute error = 1.300e-31
relative error = 1.365e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.05
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.05
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.05
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = 0.160316400014 0.935930389285
y[1] (closed_form) = 0.160316400014 0.935930389285
absolute error = 1.265e-31
relative error = 1.332e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.053
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.053
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.053
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3223 1.042
h = 0.003 0.006
y[1] (numeric) = 0.159038246944 0.932570924681
y[1] (closed_form) = 0.159038246944 0.932570924681
absolute error = 1.208e-31
relative error = 1.277e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.057
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.057
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.057
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = 0.154762820485 0.928399747387
y[1] (closed_form) = 0.154762820485 0.928399747387
absolute error = 1.170e-31
relative error = 1.244e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.062
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.062
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.062
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=572.7MB, alloc=52.3MB, time=6.74
x[1] = 0.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = 0.153252782407 0.924256471217
y[1] (closed_form) = 0.153252782407 0.924256471217
absolute error = 1.170e-31
relative error = 1.249e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.067
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.067
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.067
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3255 1.056
h = 0.001 0.001
y[1] (numeric) = 0.152323755632 0.921798773335
y[1] (closed_form) = 0.152323755632 0.921798773335
absolute error = 1.170e-31
relative error = 1.253e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.07
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.07
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.07
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3265 1.057
h = 0.001 0.003
y[1] (numeric) = 0.151217859396 0.9212523192
y[1] (closed_form) = 0.151217859396 0.9212523192
absolute error = 1.170e-31
relative error = 1.254e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.071
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.071
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.071
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = 0.14956350217 0.919056882902
y[1] (closed_form) = 0.14956350217 0.919056882902
absolute error = 1.170e-31
relative error = 1.257e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.074
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.074
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.074
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3276 1.064
h = 0.003 0.006
y[1] (numeric) = 0.148388160291 0.915806279291
y[1] (closed_form) = 0.148388160291 0.915806279291
absolute error = 1.170e-31
relative error = 1.262e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.078
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.078
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.078
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = 0.144342642644 0.911727435828
y[1] (closed_form) = 0.144342642644 0.911727435828
absolute error = 1.044e-31
relative error = 1.131e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.083
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.083
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.083
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = 0.142955153567 0.907718783722
y[1] (closed_form) = 0.142955153567 0.907718783722
absolute error = 1.044e-31
relative error = 1.136e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.088
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.088
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.088
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3308 1.078
h = 0.001 0.001
y[1] (numeric) = 0.142099776483 0.905340183506
y[1] (closed_form) = 0.142099776483 0.905340183506
absolute error = 1.044e-31
relative error = 1.139e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.091
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.091
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.091
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = 0.141044404804 0.90479734116
y[1] (closed_form) = 0.141044404804 0.90479734116
absolute error = 1.044e-31
relative error = 1.140e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.092
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.092
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3319 1.083
h = 0.003 0.006
y[1] (numeric) = 0.139949610314 0.901638476922
y[1] (closed_form) = 0.139949610314 0.901638476922
absolute error = 1.020e-31
relative error = 1.118e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.096
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.096
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = 0.136088737638 0.897641643174
y[1] (closed_form) = 0.136088737638 0.897641643174
absolute error = 9.220e-32
relative error = 1.015e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.101
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.101
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.335 1.094
h = 0.0001 0.003
y[1] (numeric) = 0.134797203734 0.893746308395
y[1] (closed_form) = 0.134797203734 0.893746308395
absolute error = 9.487e-32
relative error = 1.050e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.106
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.106
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.106
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3351 1.097
h = 0.001 0.001
y[1] (numeric) = 0.133999564977 0.891434340689
y[1] (closed_form) = 0.133999564977 0.891434340689
absolute error = 9.487e-32
relative error = 1.052e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.109
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.109
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.109
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3361 1.098
h = 0.001 0.003
y[1] (numeric) = 0.132985282424 0.89089591276
y[1] (closed_form) = 0.132985282424 0.89089591276
absolute error = 9.487e-32
relative error = 1.053e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.11
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.11
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.11
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = 0.131504868332 0.888808226111
y[1] (closed_form) = 0.131504868332 0.888808226111
absolute error = 9.487e-32
relative error = 1.056e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.113
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.113
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.113
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3372 1.105
h = 0.003 0.006
y[1] (numeric) = 0.130497985121 0.885751066084
y[1] (closed_form) = 0.130497985121 0.885751066084
absolute error = 9.487e-32
relative error = 1.060e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.117
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.117
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.117
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = 0.126839788108 0.881846086283
y[1] (closed_form) = 0.126839788108 0.881846086283
absolute error = 8.544e-32
relative error = 9.590e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.122
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.122
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.122
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = 0.125653040765 0.8780763525
y[1] (closed_form) = 0.125653040765 0.8780763525
absolute error = 8.246e-32
relative error = 9.297e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.127
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.127
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.127
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3404 1.119
h = 0.001 0.001
y[1] (numeric) = 0.124918485992 0.875838257047
y[1] (closed_form) = 0.124918485992 0.875838257047
absolute error = 8.246e-32
relative error = 9.321e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.13
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.13
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.13
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3414 1.12
h = 0.001 0.003
y[1] (numeric) = 0.123949442507 0.875305016445
y[1] (closed_form) = 0.123949442507 0.875305016445
absolute error = 8.246e-32
relative error = 9.328e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.131
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.131
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.131
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = 0.122553712042 0.873272960803
y[1] (closed_form) = 0.122553712042 0.873272960803
absolute error = 7.280e-32
relative error = 8.256e-30 %
Correct digits = 31
memory used=618.1MB, alloc=52.3MB, time=7.26
Radius of convergence (given) for eq 1 = 1.134
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.134
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.134
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3425 1.127
h = 0.003 0.006
y[1] (numeric) = 0.121627703007 0.87031378596
y[1] (closed_form) = 0.121627703007 0.87031378596
absolute error = 7.280e-32
relative error = 8.284e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.138
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.138
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.138
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = 0.11815908151 0.866499931074
y[1] (closed_form) = 0.11815908151 0.866499931074
absolute error = 7.616e-32
relative error = 8.709e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.143
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.143
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.143
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = 0.11706873002 0.862851131885
y[1] (closed_form) = 0.11706873002 0.862851131885
absolute error = 7.616e-32
relative error = 8.746e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.148
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.148
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.148
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3457 1.141
h = 0.001 0.001
y[1] (numeric) = 0.116392263169 0.860684201396
y[1] (closed_form) = 0.116392263169 0.860684201396
absolute error = 7.616e-32
relative error = 8.769e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.151
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.151
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.151
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3467 1.142
h = 0.001 0.003
y[1] (numeric) = 0.115465883865 0.860156812613
y[1] (closed_form) = 0.115465883865 0.860156812613
absolute error = 8.544e-32
relative error = 9.845e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.152
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.152
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.152
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = 0.114149066044 0.858179124228
y[1] (closed_form) = 0.114149066044 0.858179124228
absolute error = 8.246e-32
relative error = 9.525e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.155
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.155
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.155
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3478 1.149
h = 0.003 0.006
y[1] (numeric) = 0.113297506508 0.855314290261
y[1] (closed_form) = 0.113297506508 0.855314290261
absolute error = 8.544e-32
relative error = 9.903e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.159
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.159
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.159
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = 0.110006325806 0.85159052484
y[1] (closed_form) = 0.110006325806 0.85159052484
absolute error = 8.544e-32
relative error = 9.950e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.165
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.165
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.165
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = 0.109004709435 0.848058101572
y[1] (closed_form) = 0.109004709435 0.848058101572
absolute error = 8.544e-32
relative error = 9.993e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.17
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.17
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.17
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.351 1.163
h = 0.001 0.001
y[1] (numeric) = 0.108381765677 0.845959687802
y[1] (closed_form) = 0.108381765677 0.845959687802
absolute error = 8.944e-32
relative error = 1.049e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.173
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.173
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.173
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.352 1.164
h = 0.001 0.003
y[1] (numeric) = 0.107495642069 0.845438698431
y[1] (closed_form) = 0.107495642069 0.845438698431
absolute error = 8.944e-32
relative error = 1.049e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.173
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.173
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.173
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.353 1.167
h = 0.0001 0.004
y[1] (numeric) = 0.106252412363 0.843514049171
y[1] (closed_form) = 0.106252412363 0.843514049171
absolute error = 9.849e-32
relative error = 1.158e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.176
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.176
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.176
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3531 1.171
h = 0.003 0.006
y[1] (numeric) = 0.105469432995 0.84074000025
y[1] (closed_form) = 0.105469432995 0.84074000025
absolute error = 8.944e-32
relative error = 1.056e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.18
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.18
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.18
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = 0.102344448156 0.837105041555
y[1] (closed_form) = 0.102344448156 0.837105041555
absolute error = 8.944e-32
relative error = 1.061e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.186
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.186
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.186
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = 0.10142456801 0.833684557631
y[1] (closed_form) = 0.10142456801 0.833684557631
absolute error = 8.944e-32
relative error = 1.065e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.191
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.191
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.191
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3563 1.185
h = 0.001 0.001
y[1] (numeric) = 0.100850973779 0.831652080226
y[1] (closed_form) = 0.100850973779 0.831652080226
absolute error = 8.944e-32
relative error = 1.068e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.194
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.194
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.194
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = 0.10000285292 0.831137936668
y[1] (closed_form) = 0.10000285292 0.831137936668
absolute error = 8.944e-32
relative error = 1.068e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.195
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.195
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.195
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3574 1.19
h = 0.003 0.006
y[1] (numeric) = 0.0992735653376 0.828439991246
y[1] (closed_form) = 0.0992735653376 0.828439991246
absolute error = 8.989e-32
relative error = 1.077e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.199
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.199
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.199
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = 0.0962822259921 0.82488210807
y[1] (closed_form) = 0.0962822259921 0.82488210807
absolute error = 8.062e-32
relative error = 9.708e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.204
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.204
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.204
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = 0.095426293022 0.821555397272
y[1] (closed_form) = 0.095426293022 0.821555397272
absolute error = 8.944e-32
relative error = 1.081e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.209
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.209
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.209
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=663.3MB, alloc=52.3MB, time=7.79
x[1] = 0.3606 1.204
h = 0.001 0.001
y[1] (numeric) = 0.0948913621877 0.819578192783
y[1] (closed_form) = 0.0948913621877 0.819578192783
absolute error = 8.062e-32
relative error = 9.772e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.212
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.212
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.212
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3616 1.205
h = 0.001 0.003
y[1] (numeric) = 0.0940741726999 0.819070651036
y[1] (closed_form) = 0.0940741726999 0.819070651036
absolute error = 8.062e-32
relative error = 9.779e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.213
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.213
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.213
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = 0.0929544856682 0.817241766282
y[1] (closed_form) = 0.0929544856682 0.817241766282
absolute error = 8.062e-32
relative error = 9.802e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.216
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.216
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.216
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3627 1.212
h = 0.003 0.006
y[1] (numeric) = 0.0922842012761 0.814628200631
y[1] (closed_form) = 0.0922842012761 0.814628200631
absolute error = 8.013e-32
relative error = 9.774e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.22
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.22
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.22
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = 0.0894402862185 0.811156132644
y[1] (closed_form) = 0.0894402862185 0.811156132644
absolute error = 8.013e-32
relative error = 9.819e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.225
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.225
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.225
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = 0.0886546702673 0.807933395953
y[1] (closed_form) = 0.0886546702673 0.807933395953
absolute error = 7.965e-32
relative error = 9.800e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.23
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.23
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.23
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3659 1.226
h = 0.001 0.001
y[1] (numeric) = 0.0881622716481 0.806017487253
y[1] (closed_form) = 0.0881622716481 0.806017487253
absolute error = 7.965e-32
relative error = 9.823e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.233
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.233
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.233
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3669 1.227
h = 0.001 0.003
y[1] (numeric) = 0.0873792686521 0.805517375177
y[1] (closed_form) = 0.0873792686521 0.805517375177
absolute error = 7.965e-32
relative error = 9.830e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.234
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.234
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.234
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = 0.0863200997215 0.803737491729
y[1] (closed_form) = 0.0863200997215 0.803737491729
absolute error = 8.857e-32
relative error = 1.096e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.237
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.237
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.237
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.368 1.234
h = 0.003 0.006
y[1] (numeric) = 0.0857042683323 0.801205053955
y[1] (closed_form) = 0.0857042683323 0.801205053955
absolute error = 8.814e-32
relative error = 1.094e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.241
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.241
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.371 1.24
h = 0.0001 0.005
y[1] (numeric) = 0.0829987112681 0.797817069554
y[1] (closed_form) = 0.0829987112681 0.797817069554
absolute error = 8.773e-32
relative error = 1.094e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.247
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.247
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.247
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = 0.0822779851923 0.794694271252
y[1] (closed_form) = 0.0822779851923 0.794694271252
absolute error = 8.732e-32
relative error = 1.093e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.252
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.252
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3712 1.248
h = 0.001 0.001
y[1] (numeric) = 0.0818248756567 0.7928373045
y[1] (closed_form) = 0.0818248756567 0.7928373045
absolute error = 8.732e-32
relative error = 1.096e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.255
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.255
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.255
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3722 1.249
h = 0.001 0.003
y[1] (numeric) = 0.0810741968212 0.792344849997
y[1] (closed_form) = 0.0810741968212 0.792344849997
absolute error = 9.657e-32
relative error = 1.212e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.256
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.256
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.256
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.08007162293 0.790612554483
y[1] (closed_form) = 0.08007162293 0.790612554483
absolute error = 9.657e-32
relative error = 1.215e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.258
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.258
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.258
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3733 1.256
h = 0.003 0.006
y[1] (numeric) = 0.0795060763758 0.788158105194
y[1] (closed_form) = 0.0795060763758 0.788158105194
absolute error = 8.693e-32
relative error = 1.097e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.262
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.262
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.262
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.0769304590132 0.784852378938
y[1] (closed_form) = 0.0769304590132 0.784852378938
absolute error = 9.621e-32
relative error = 1.220e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.268
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.268
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.268
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.0762696508817 0.781825628375
y[1] (closed_form) = 0.0762696508817 0.781825628375
absolute error = 8.693e-32
relative error = 1.107e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.273
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.273
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.273
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3765 1.27
h = 0.001 0.001
y[1] (numeric) = 0.0758528571268 0.780025332398
y[1] (closed_form) = 0.0758528571268 0.780025332398
absolute error = 8.654e-32
relative error = 1.104e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.276
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.276
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.276
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3775 1.271
h = 0.001 0.003
y[1] (numeric) = 0.0751327588182 0.779540705779
y[1] (closed_form) = 0.0751327588182 0.779540705779
absolute error = 8.616e-32
relative error = 1.100e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.277
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.277
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.0741831496486 0.777854589731
y[1] (closed_form) = 0.0741831496486 0.777854589731
absolute error = 8.616e-32
relative error = 1.103e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.28
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.28
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.28
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=708.5MB, alloc=52.3MB, time=8.32
x[1] = 0.3786 1.278
h = 0.003 0.006
y[1] (numeric) = 0.0736640669521 0.775475103499
y[1] (closed_form) = 0.0736640669521 0.775475103499
absolute error = 8.580e-32
relative error = 1.101e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.284
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.284
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.284
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.0712105681102 0.772249742006
y[1] (closed_form) = 0.0712105681102 0.772249742006
absolute error = 8.580e-32
relative error = 1.106e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.289
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.289
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.289
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.0706051197163 0.769315294288
y[1] (closed_form) = 0.0706051197163 0.769315294288
absolute error = 8.544e-32
relative error = 1.106e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.294
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.294
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.294
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3818 1.292
h = 0.001 0.001
y[1] (numeric) = 0.0702219138425 0.767569481257
y[1] (closed_form) = 0.0702219138425 0.767569481257
absolute error = 8.544e-32
relative error = 1.108e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.297
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.297
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.297
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.0695307629843 0.767092803231
y[1] (closed_form) = 0.0695307629843 0.767092803231
absolute error = 8.544e-32
relative error = 1.109e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.298
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.298
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.298
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3829 1.297
h = 0.003 0.006
y[1] (numeric) = 0.0690480108981 0.764776004567
y[1] (closed_form) = 0.0690480108981 0.764776004567
absolute error = 9.487e-32
relative error = 1.235e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.302
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.302
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.302
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.0666928602242 0.761619604488
y[1] (closed_form) = 0.0666928602242 0.761619604488
absolute error = 9.456e-32
relative error = 1.237e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.308
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.308
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.308
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.386 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.0661306602624 0.758762312485
y[1] (closed_form) = 0.0661306602624 0.758762312485
absolute error = 9.456e-32
relative error = 1.241e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.313
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.313
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.313
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3861 1.311
h = 0.001 0.001
y[1] (numeric) = 0.0657737372697 0.757062068135
y[1] (closed_form) = 0.0657737372697 0.757062068135
absolute error = 8.509e-32
relative error = 1.120e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.316
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.316
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.316
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3871 1.312
h = 0.001 0.003
y[1] (numeric) = 0.0651061786334 0.756592616183
y[1] (closed_form) = 0.0651061786334 0.756592616183
absolute error = 8.509e-32
relative error = 1.121e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.317
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.317
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.317
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.0642458549123 0.754989269076
y[1] (closed_form) = 0.0642458549123 0.754989269076
absolute error = 8.509e-32
relative error = 1.123e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.32
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.32
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.32
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3882 1.319
h = 0.003 0.006
y[1] (numeric) = 0.0638033081205 0.752742069865
y[1] (closed_form) = 0.0638033081205 0.752742069865
absolute error = 9.456e-32
relative error = 1.252e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.324
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.324
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.324
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.0615571779845 0.7496623238
y[1] (closed_form) = 0.0615571779845 0.7496623238
absolute error = 8.476e-32
relative error = 1.127e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.329
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.329
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.329
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.0610428720376 0.746890706624
y[1] (closed_form) = 0.0610428720376 0.746890706624
absolute error = 8.443e-32
relative error = 1.127e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.334
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.334
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.334
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3914 1.333
h = 0.001 0.001
y[1] (numeric) = 0.0607150637808 0.745241068322
y[1] (closed_form) = 0.0607150637808 0.745241068322
absolute error = 8.443e-32
relative error = 1.129e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.337
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.337
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.337
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3924 1.334
h = 0.001 0.003
y[1] (numeric) = 0.0600736820459 0.744779664027
y[1] (closed_form) = 0.0600736820459 0.744779664027
absolute error = 8.443e-32
relative error = 1.130e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.338
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.338
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.0592573631554 0.743218522878
y[1] (closed_form) = 0.0592573631554 0.743218522878
absolute error = 8.412e-32
relative error = 1.128e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.341
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.341
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.341
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3935 1.341
h = 0.003 0.006
y[1] (numeric) = 0.0588520290066 0.741038224393
y[1] (closed_form) = 0.0588520290066 0.741038224393
absolute error = 8.412e-32
relative error = 1.132e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.345
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.345
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.345
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.0567085611435 0.738033158071
y[1] (closed_form) = 0.0567085611435 0.738033158071
absolute error = 8.412e-32
relative error = 1.136e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.351
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.351
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.351
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.0562385781025 0.735343883894
y[1] (closed_form) = 0.0562385781025 0.735343883894
absolute error = 8.412e-32
relative error = 1.141e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.356
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.356
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.356
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3967 1.355
h = 0.001 0.001
y[1] (numeric) = 0.0559377429491 0.73374290122
y[1] (closed_form) = 0.0559377429491 0.73374290122
absolute error = 8.382e-32
relative error = 1.139e-29 %
Correct digits = 31
memory used=753.8MB, alloc=52.3MB, time=8.85
Radius of convergence (given) for eq 1 = 1.359
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.359
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.359
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3977 1.356
h = 0.001 0.003
y[1] (numeric) = 0.055321181395 0.73328955984
y[1] (closed_form) = 0.055321181395 0.73328955984
absolute error = 8.412e-32
relative error = 1.144e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.36
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.36
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.36
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.0545461587553 0.731769296628
y[1] (closed_form) = 0.0545461587553 0.731769296628
absolute error = 8.382e-32
relative error = 1.142e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.363
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.363
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.363
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3988 1.363
h = 0.003 0.006
y[1] (numeric) = 0.0541752860867 0.729653309646
y[1] (closed_form) = 0.0541752860867 0.729653309646
absolute error = 8.382e-32
relative error = 1.146e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.367
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.367
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.0521285587509 0.726720946334
y[1] (closed_form) = 0.0521285587509 0.726720946334
absolute error = 8.352e-32
relative error = 1.146e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.373
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.373
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.373
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.0516996153691 0.724110820766
y[1] (closed_form) = 0.0516996153691 0.724110820766
absolute error = 8.352e-32
relative error = 1.151e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.377
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.377
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.377
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.402 1.377
h = 0.001 0.001
y[1] (numeric) = 0.0514237828699 0.72255662257
y[1] (closed_form) = 0.0514237828699 0.72255662257
absolute error = 8.352e-32
relative error = 1.153e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.38
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.38
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.38
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.403 1.378
h = 0.001 0.003
y[1] (numeric) = 0.0508307686503 0.72211133196
y[1] (closed_form) = 0.0508307686503 0.72211133196
absolute error = 8.382e-32
relative error = 1.158e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.381
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.381
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.381
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.404 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.0500945273294 0.720630648354
y[1] (closed_form) = 0.0500945273294 0.720630648354
absolute error = 8.382e-32
relative error = 1.160e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.384
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.384
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4041 1.385
h = 0.003 0.006
y[1] (numeric) = 0.0497555851565 0.71857649053
y[1] (closed_form) = 0.0497555851565 0.71857649053
absolute error = 8.352e-32
relative error = 1.160e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.388
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.388
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.388
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.0478000795478 0.715714861689
y[1] (closed_form) = 0.0478000795478 0.715714861689
absolute error = 7.400e-32
relative error = 1.032e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.394
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.394
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.394
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.0474091550675 0.713180824076
y[1] (closed_form) = 0.0474091550675 0.713180824076
absolute error = 7.400e-32
relative error = 1.035e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.399
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.399
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.399
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4073 1.399
h = 0.001 0.001
y[1] (numeric) = 0.0471565109694 0.711671616464
y[1] (closed_form) = 0.0471565109694 0.711671616464
absolute error = 8.324e-32
relative error = 1.167e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.402
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.402
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.402
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4083 1.4
h = 0.003 0.006
y[1] (numeric) = 0.0465858493456 0.711234341154
y[1] (closed_form) = 0.0465858493456 0.711234341154
absolute error = 7.368e-32
relative error = 1.034e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.403
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.403
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.403
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = 0.0446918098893 0.708418091368
y[1] (closed_form) = 0.0446918098893 0.708418091368
absolute error = 7.368e-32
relative error = 1.038e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.409
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.409
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.409
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = 0.0443272399755 0.705933810445
y[1] (closed_form) = 0.0443272399755 0.705933810445
absolute error = 7.368e-32
relative error = 1.042e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.414
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.414
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.414
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4115 1.414
h = 0.001 0.001
y[1] (numeric) = 0.0440906508764 0.704454015133
y[1] (closed_form) = 0.0440906508764 0.704454015133
absolute error = 7.338e-32
relative error = 1.040e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.417
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.417
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.417
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4125 1.415
h = 0.001 0.003
y[1] (numeric) = 0.0435349103336 0.704021692824
y[1] (closed_form) = 0.0435349103336 0.704021692824
absolute error = 7.368e-32
relative error = 1.045e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.418
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.418
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.418
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = 0.0428598415053 0.702604106989
y[1] (closed_form) = 0.0428598415053 0.702604106989
absolute error = 7.338e-32
relative error = 1.042e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.421
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.421
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.421
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4136 1.422
h = 0.003 0.006
y[1] (numeric) = 0.0425710350934 0.700648285913
y[1] (closed_form) = 0.0425710350934 0.700648285913
absolute error = 8.297e-32
relative error = 1.182e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.425
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.425
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.425
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = 0.0407596830785 0.697899609546
y[1] (closed_form) = 0.0407596830785 0.697899609546
absolute error = 8.271e-32
relative error = 1.183e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.43
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.43
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=798.8MB, alloc=52.3MB, time=9.38
x[1] = 0.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = 0.0404284956558 0.69548660594
y[1] (closed_form) = 0.0404284956558 0.69548660594
absolute error = 7.308e-32
relative error = 1.049e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.435
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.435
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.435
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4168 1.436
h = 0.001 0.001
y[1] (numeric) = 0.0402123086165 0.694048980448
y[1] (closed_form) = 0.0402123086165 0.694048980448
absolute error = 8.271e-32
relative error = 1.190e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.438
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.438
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.438
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4178 1.437
h = 0.001 0.003
y[1] (numeric) = 0.0396770646062 0.693624596583
y[1] (closed_form) = 0.0396770646062 0.693624596583
absolute error = 8.271e-32
relative error = 1.190e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.439
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.439
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.439
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = 0.0390348312992 0.69224331368
y[1] (closed_form) = 0.0390348312992 0.69224331368
absolute error = 8.271e-32
relative error = 1.193e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.442
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.442
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.442
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4189 1.444
h = 0.003 0.006
y[1] (numeric) = 0.038772045619 0.690343204363
y[1] (closed_form) = 0.038772045619 0.690343204363
absolute error = 7.308e-32
relative error = 1.057e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.446
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.446
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.446
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = 0.0370388003629 0.687660185994
y[1] (closed_form) = 0.0370388003629 0.687660185994
absolute error = 7.280e-32
relative error = 1.057e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.452
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.452
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.452
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.422 1.455
h = 0.0001 0.003
y[1] (numeric) = 0.0367385753628 0.68531573273
y[1] (closed_form) = 0.0367385753628 0.68531573273
absolute error = 7.280e-32
relative error = 1.061e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.457
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.457
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.457
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4221 1.458
h = 0.001 0.001
y[1] (numeric) = 0.036541333941 0.683918676328
y[1] (closed_form) = 0.036541333941 0.683918676328
absolute error = 7.280e-32
relative error = 1.063e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.46
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.46
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.46
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4231 1.459
h = 0.001 0.003
y[1] (numeric) = 0.0360255758352 0.683502147511
y[1] (closed_form) = 0.0360255758352 0.683502147511
absolute error = 7.280e-32
relative error = 1.064e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.461
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.461
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.461
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = 0.0354142542261 0.682155990495
y[1] (closed_form) = 0.0354142542261 0.682155990495
absolute error = 7.253e-32
relative error = 1.062e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.464
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.464
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.464
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4242 1.466
h = 0.003 0.006
y[1] (numeric) = 0.0351756194311 0.680309473429
y[1] (closed_form) = 0.0351756194311 0.680309473429
absolute error = 7.253e-32
relative error = 1.065e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.468
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.468
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.468
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = 0.0335162016582 0.677690231331
y[1] (closed_form) = 0.0335162016582 0.677690231331
absolute error = 7.253e-32
relative error = 1.069e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.474
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.474
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.474
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = 0.0332447068471 0.675411719575
y[1] (closed_form) = 0.0332447068471 0.675411719575
absolute error = 7.228e-32
relative error = 1.069e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.479
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.479
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.479
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4274 1.48
h = 0.001 0.001
y[1] (numeric) = 0.0330650666405 0.674053700109
y[1] (closed_form) = 0.0330650666405 0.674053700109
absolute error = 7.228e-32
relative error = 1.071e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.482
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.482
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.482
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = 0.03256784405 0.6736449307
y[1] (closed_form) = 0.03256784405 0.6736449307
absolute error = 6.264e-32
relative error = 9.288e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.483
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.483
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.483
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4285 1.485
h = 0.003 0.006
y[1] (numeric) = 0.0323480048124 0.671843176873
y[1] (closed_form) = 0.0323480048124 0.671843176873
absolute error = 7.228e-32
relative error = 1.075e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.487
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.487
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.487
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = 0.030748192169 0.669278168234
y[1] (closed_form) = 0.030748192169 0.669278168234
absolute error = 7.228e-32
relative error = 1.079e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.493
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.493
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.493
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = 0.0304990261358 0.667054723671
y[1] (closed_form) = 0.0304990261358 0.667054723671
absolute error = 7.228e-32
relative error = 1.082e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.498
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.498
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.498
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4317 1.499
h = 0.001 0.001
y[1] (numeric) = 0.0303330970653 0.665729319193
y[1] (closed_form) = 0.0303330970653 0.665729319193
absolute error = 7.228e-32
relative error = 1.085e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.501
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.501
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.501
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4327 1.5
h = 0.001 0.003
y[1] (numeric) = 0.0298510204762 0.665327350881
y[1] (closed_form) = 0.0298510204762 0.665327350881
absolute error = 7.228e-32
relative error = 1.085e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.502
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.502
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.502
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = 0.029292154555 0.664043865704
y[1] (closed_form) = 0.029292154555 0.664043865704
absolute error = 8.179e-32
relative error = 1.230e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.504
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.504
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.504
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=843.9MB, alloc=52.3MB, time=9.91
x[1] = 0.4338 1.507
h = 0.003 0.006
y[1] (numeric) = 0.0290933837145 0.662291982746
y[1] (closed_form) = 0.0290933837145 0.662291982746
absolute error = 8.200e-32
relative error = 1.237e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.508
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.508
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.508
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = 0.0275601836352 0.659787307597
y[1] (closed_form) = 0.0275601836352 0.659787307597
absolute error = 7.203e-32
relative error = 1.091e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.514
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.514
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.514
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = 0.0273360683813 0.65762522667
y[1] (closed_form) = 0.0273360683813 0.65762522667
absolute error = 7.203e-32
relative error = 1.094e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.519
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.519
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.519
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.437 1.521
h = 0.001 0.001
y[1] (numeric) = 0.0271855217678 0.656336168395
y[1] (closed_form) = 0.0271855217678 0.656336168395
absolute error = 7.203e-32
relative error = 1.097e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.522
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.522
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.522
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.438 1.522
h = 0.001 0.003
y[1] (numeric) = 0.0267203602249 0.655941746167
y[1] (closed_form) = 0.0267203602249 0.655941746167
absolute error = 6.236e-32
relative error = 9.499e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.523
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.523
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.523
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.439 1.525
h = 0.0001 0.004
y[1] (numeric) = 0.0261876080239 0.654690200597
y[1] (closed_form) = 0.0261876080239 0.654690200597
absolute error = 7.203e-32
relative error = 1.099e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.526
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.526
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.526
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4391 1.529
h = 0.003 0.006
y[1] (numeric) = 0.0260084153409 0.652986322764
y[1] (closed_form) = 0.0260084153409 0.652986322764
absolute error = 7.181e-32
relative error = 1.099e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.53
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.53
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.53
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = 0.024538292219 0.65054021686
y[1] (closed_form) = 0.024538292219 0.65054021686
absolute error = 7.181e-32
relative error = 1.103e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.536
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.536
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.536
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = 0.0243374483383 0.648437204861
y[1] (closed_form) = 0.0243374483383 0.648437204861
absolute error = 7.159e-32
relative error = 1.103e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.541
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.541
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4423 1.543
h = 0.001 0.001
y[1] (numeric) = 0.0242012102207 0.647183143338
y[1] (closed_form) = 0.0242012102207 0.647183143338
absolute error = 7.159e-32
relative error = 1.105e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.544
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.544
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4433 1.544
h = 0.001 0.003
y[1] (numeric) = 0.0237521642379 0.646796147855
y[1] (closed_form) = 0.0237521642379 0.646796147855
absolute error = 7.159e-32
relative error = 1.106e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.545
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.545
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.545
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = 0.0232440566397 0.645575504877
y[1] (closed_form) = 0.0232440566397 0.645575504877
absolute error = 7.159e-32
relative error = 1.108e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.548
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.548
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.548
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4444 1.551
h = 0.003 0.006
y[1] (numeric) = 0.0230830640406 0.643917847608
y[1] (closed_form) = 0.0230830640406 0.643917847608
absolute error = 7.159e-32
relative error = 1.111e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.552
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.552
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = 0.0216727064022 0.641528590651
y[1] (closed_form) = 0.0216727064022 0.641528590651
absolute error = 7.159e-32
relative error = 1.115e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.558
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.558
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.558
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = 0.021493488343 0.639482453177
y[1] (closed_form) = 0.021493488343 0.639482453177
absolute error = 8.122e-32
relative error = 1.269e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.563
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.563
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.563
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4476 1.565
h = 0.001 0.001
y[1] (numeric) = 0.0213705647942 0.638262097383
y[1] (closed_form) = 0.0213705647942 0.638262097383
absolute error = 8.122e-32
relative error = 1.272e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.566
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.566
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.566
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4486 1.566
h = 0.001 0.003
y[1] (numeric) = 0.0209368809414 0.63788240378
y[1] (closed_form) = 0.0209368809414 0.63788240378
absolute error = 8.105e-32
relative error = 1.270e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.567
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.567
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.567
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = 0.0204520457232 0.636691661501
y[1] (closed_form) = 0.0204520457232 0.636691661501
absolute error = 8.105e-32
relative error = 1.272e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.57
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.57
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.57
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4497 1.573
h = 0.003 0.006
y[1] (numeric) = 0.0203079780368 0.635078517931
y[1] (closed_form) = 0.0203079780368 0.635078517931
absolute error = 8.105e-32
relative error = 1.276e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.574
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.574
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.574
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = 0.0189542823071 0.632744434735
y[1] (closed_form) = 0.0189542823071 0.632744434735
absolute error = 8.105e-32
relative error = 1.280e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.58
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.58
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=889.0MB, alloc=52.3MB, time=10.43
x[1] = 0.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = 0.0187951673356 0.630753073297
y[1] (closed_form) = 0.0187951673356 0.630753073297
absolute error = 8.105e-32
relative error = 1.284e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.585
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.585
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.585
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4529 1.587
h = 0.001 0.001
y[1] (numeric) = 0.0186846379084 0.629565188125
y[1] (closed_form) = 0.0186846379084 0.629565188125
absolute error = 7.120e-32
relative error = 1.130e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.588
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.588
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.588
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = 0.0182656057681 0.629192667238
y[1] (closed_form) = 0.0182656057681 0.629192667238
absolute error = 7.120e-32
relative error = 1.131e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.589
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.589
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.589
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.454 1.592
h = 0.003 0.006
y[1] (numeric) = 0.0181346537464 0.627616712266
y[1] (closed_form) = 0.0181346537464 0.627616712266
absolute error = 6.139e-32
relative error = 9.778e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.593
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.593
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.593
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.457 1.598
h = 0.0001 0.005
y[1] (numeric) = 0.0168267622218 0.625329442568
y[1] (closed_form) = 0.0168267622218 0.625329442568
absolute error = 7.102e-32
relative error = 1.135e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.599
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.599
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.599
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = 0.0166831981345 0.623383837056
y[1] (closed_form) = 0.0166831981345 0.623383837056
absolute error = 6.119e-32
relative error = 9.812e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.604
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.604
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.604
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4572 1.606
h = 0.001 0.001
y[1] (numeric) = 0.0165822840209 0.622223087325
y[1] (closed_form) = 0.0165822840209 0.622223087325
absolute error = 7.102e-32
relative error = 1.141e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.607
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.607
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.607
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4582 1.607
h = 0.001 0.003
y[1] (numeric) = 0.0161752421712 0.621856798306
y[1] (closed_form) = 0.0161752421712 0.621856798306
absolute error = 6.100e-32
relative error = 9.806e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.608
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.608
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.608
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = 0.0157300316963 0.620719388017
y[1] (closed_form) = 0.0157300316963 0.620719388017
absolute error = 6.119e-32
relative error = 9.854e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.611
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.611
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.611
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4593 1.614
h = 0.003 0.006
y[1] (numeric) = 0.0156138956597 0.619184953189
y[1] (closed_form) = 0.0156138956597 0.619184953189
absolute error = 6.100e-32
relative error = 9.849e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.615
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.615
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.615
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = 0.014357412724 0.61694983058
y[1] (closed_form) = 0.014357412724 0.61694983058
absolute error = 6.100e-32
relative error = 9.885e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.62
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.62
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = 0.0142314339098 0.615055321898
y[1] (closed_form) = 0.0142314339098 0.615055321898
absolute error = 6.100e-32
relative error = 9.915e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.625
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.625
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.625
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4625 1.628
h = 0.001 0.001
y[1] (numeric) = 0.0141413899534 0.613924875846
y[1] (closed_form) = 0.0141413899534 0.613924875846
absolute error = 6.100e-32
relative error = 9.933e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.628
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.628
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.628
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4635 1.629
h = 0.001 0.003
y[1] (numeric) = 0.0137477844645 0.613565503909
y[1] (closed_form) = 0.0137477844645 0.613565503909
absolute error = 6.083e-32
relative error = 9.911e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.629
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.629
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.629
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = 0.0133224039584 0.6124553031
y[1] (closed_form) = 0.0133224039584 0.6124553031
absolute error = 7.086e-32
relative error = 1.157e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.632
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.632
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.632
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4646 1.636
h = 0.003 0.006
y[1] (numeric) = 0.013220058297 0.610960886269
y[1] (closed_form) = 0.013220058297 0.610960886269
absolute error = 7.071e-32
relative error = 1.157e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.636
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.636
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.636
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = 0.0120123960809 0.608776369286
y[1] (closed_form) = 0.0120123960809 0.608776369286
absolute error = 7.071e-32
relative error = 1.161e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.642
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.642
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.642
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.0119027777136 0.606931111281
y[1] (closed_form) = 0.0119027777136 0.606931111281
absolute error = 7.071e-32
relative error = 1.165e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.647
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.647
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.647
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4678 1.65
h = 0.001 0.001
y[1] (numeric) = 0.0118228619224 0.605829881119
y[1] (closed_form) = 0.0118228619224 0.605829881119
absolute error = 7.071e-32
relative error = 1.167e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.65
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.65
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.65
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4688 1.651
h = 0.001 0.003
y[1] (numeric) = 0.011442090531 0.605477290597
y[1] (closed_form) = 0.011442090531 0.605477290597
absolute error = 7.071e-32
relative error = 1.168e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.651
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.651
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.651
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.0110354785373 0.604393427175
y[1] (closed_form) = 0.0110354785373 0.604393427175
absolute error = 6.067e-32
relative error = 1.004e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.654
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.654
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.654
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=934.0MB, alloc=52.3MB, time=10.96
x[1] = 0.4699 1.658
h = 0.003 0.006
y[1] (numeric) = 0.0109459719516 0.602937591221
y[1] (closed_form) = 0.0109459719516 0.602937591221
absolute error = 6.067e-32
relative error = 1.006e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.658
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.658
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.658
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.00978469903499 0.600802184289
y[1] (closed_form) = 0.00978469903499 0.600802184289
absolute error = 5.068e-32
relative error = 8.435e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.664
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.664
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.664
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.473 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.00969030502927 0.599004410883
y[1] (closed_form) = 0.00969030502927 0.599004410883
absolute error = 6.057e-32
relative error = 1.011e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.669
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.669
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.669
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4731 1.672
h = 0.001 0.001
y[1] (numeric) = 0.00961982862822 0.597931355628
y[1] (closed_form) = 0.00961982862822 0.597931355628
absolute error = 5.067e-32
relative error = 8.473e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.672
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.672
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.672
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4741 1.673
h = 0.001 0.003
y[1] (numeric) = 0.00925132224523 0.597585409895
y[1] (closed_form) = 0.00925132224523 0.597585409895
absolute error = 5.067e-32
relative error = 8.478e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.673
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.673
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.673
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.00886248411208 0.596527043046
y[1] (closed_form) = 0.00886248411208 0.596527043046
absolute error = 5.067e-32
relative error = 8.493e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.676
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.676
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.676
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4752 1.68
h = 0.003 0.006
y[1] (numeric) = 0.00878493371399 0.595108412883
y[1] (closed_form) = 0.00878493371399 0.595108412883
absolute error = 5.065e-32
relative error = 8.510e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.68
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.68
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.68
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.00766776424498 0.593020665919
y[1] (closed_form) = 0.00766776424498 0.593020665919
absolute error = 5.060e-32
relative error = 8.533e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.686
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.686
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.686
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.00758754022257 0.59126868739
y[1] (closed_form) = 0.00758754022257 0.59126868739
absolute error = 5.060e-32
relative error = 8.558e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.691
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.691
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.691
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4784 1.694
h = 0.001 0.001
y[1] (numeric) = 0.00752586346601 0.590222810714
y[1] (closed_form) = 0.00752586346601 0.590222810714
absolute error = 5.059e-32
relative error = 8.571e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.694
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.694
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.694
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.00716908405861 0.589883372784
y[1] (closed_form) = 0.00716908405861 0.589883372784
absolute error = 5.059e-32
relative error = 8.576e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.695
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.695
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.695
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4795 1.699
h = 0.003 0.006
y[1] (numeric) = 0.00710074440914 0.588495841518
y[1] (closed_form) = 0.00710074440914 0.588495841518
absolute error = 5.057e-32
relative error = 8.593e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.699
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.699
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.699
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.00601926595052 0.586448482608
y[1] (closed_form) = 0.00601926595052 0.586448482608
absolute error = 5.054e-32
relative error = 8.618e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.705
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.705
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.705
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.00594993283347 0.584734778461
y[1] (closed_form) = 0.00594993283347 0.584734778461
absolute error = 6.044e-32
relative error = 1.034e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.71
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.71
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.71
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4827 1.713
h = 0.001 0.001
y[1] (numeric) = 0.0058950444447 0.583711626229
y[1] (closed_form) = 0.0058950444447 0.583711626229
absolute error = 6.044e-32
relative error = 1.035e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.713
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.713
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.713
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4837 1.714
h = 0.001 0.003
y[1] (numeric) = 0.0055478753409 0.583377811921
y[1] (closed_form) = 0.0055478753409 0.583377811921
absolute error = 6.043e-32
relative error = 1.036e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.714
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.714
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.714
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = 0.00518939055624 0.582364940201
y[1] (closed_form) = 0.00518939055624 0.582364940201
absolute error = 6.042e-32
relative error = 1.037e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.717
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.717
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.717
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4848 1.721
h = 0.003 0.006
y[1] (numeric) = 0.0051315429857 0.581012202526
y[1] (closed_form) = 0.0051315429857 0.581012202526
absolute error = 5.049e-32
relative error = 8.689e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.721
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.721
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.721
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = 0.0040902841857 0.579009900714
y[1] (closed_form) = 0.0040902841857 0.579009900714
absolute error = 5.046e-32
relative error = 8.715e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.727
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.727
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.727
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = 0.00403337311584 0.577339027821
y[1] (closed_form) = 0.00403337311584 0.577339027821
absolute error = 5.045e-32
relative error = 8.738e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.732
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.732
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.732
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=979.0MB, alloc=52.3MB, time=11.48
x[1] = 0.488 1.735
h = 0.001 0.001
y[1] (numeric) = 0.00398622228704 0.576341305667
y[1] (closed_form) = 0.00398622228704 0.576341305667
absolute error = 5.045e-32
relative error = 8.753e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.735
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.735
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.735
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.489 1.736
h = 0.001 0.003
y[1] (numeric) = 0.00364985664359 0.576013739388
y[1] (closed_form) = 0.00364985664359 0.576013739388
absolute error = 5.043e-32
relative error = 8.755e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.736
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.736
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.736
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.49 1.739
h = 0.0001 0.004
y[1] (numeric) = 0.00330663665122 0.575024113648
y[1] (closed_form) = 0.00330663665122 0.575024113648
absolute error = 5.042e-32
relative error = 8.768e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.739
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.739
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4901 1.743
h = 0.003 0.006
y[1] (numeric) = 0.00325856516074 0.573704957088
y[1] (closed_form) = 0.00325856516074 0.573704957088
absolute error = 5.041e-32
relative error = 8.786e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.743
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.743
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = 0.00225560325437 0.57174639013
y[1] (closed_form) = 0.00225560325437 0.57174639013
absolute error = 4.048e-32
relative error = 7.080e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.749
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.749
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.749
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = 0.00221025920152 0.570116858744
y[1] (closed_form) = 0.00221025920152 0.570116858744
absolute error = 5.038e-32
relative error = 8.837e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.754
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.754
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.754
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4933 1.757
h = 0.001 0.001
y[1] (numeric) = 0.00217032595662 0.569143687431
y[1] (closed_form) = 0.00217032595662 0.569143687431
absolute error = 4.048e-32
relative error = 7.112e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.757
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.757
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.757
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4943 1.758
h = 0.001 0.003
y[1] (numeric) = 0.00184430417185 0.568822234054
y[1] (closed_form) = 0.00184430417185 0.568822234054
absolute error = 5.038e-32
relative error = 8.857e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.758
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.758
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.758
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = 0.00151557018286 0.567855125963
y[1] (closed_form) = 0.00151557018286 0.567855125963
absolute error = 5.037e-32
relative error = 8.870e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.761
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.761
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.761
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4954 1.765
h = 0.003 0.006
y[1] (numeric) = 0.00147660883402 0.566568389575
y[1] (closed_form) = 0.00147660883402 0.566568389575
absolute error = 4.046e-32
relative error = 7.142e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.765
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.765
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.765
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = 0.000510131927896 0.56465227769
y[1] (closed_form) = 0.000510131927896 0.56465227769
absolute error = 4.044e-32
relative error = 7.161e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.771
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.771
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.771
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = 0.000475559680243 0.563062661408
y[1] (closed_form) = 0.000475559680243 0.563062661408
absolute error = 5.034e-32
relative error = 8.941e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.776
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.776
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.776
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4986 1.779
h = 0.001 0.001
y[1] (numeric) = 0.000442360021554 0.562113198817
y[1] (closed_form) = 0.000442360021554 0.562113198817
absolute error = 5.034e-32
relative error = 8.956e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.779
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.779
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.779
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4996 1.78
h = 0.001 0.003
y[1] (numeric) = 0.000126246679649 0.561797724439
y[1] (closed_form) = 0.000126246679649 0.561797724439
absolute error = 5.033e-32
relative error = 8.959e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.78
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.78
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = -0.000188733291851 0.560852432283
y[1] (closed_form) = -0.000188733291851 0.560852432283
absolute error = 5.033e-32
relative error = 8.973e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.783
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.783
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.783
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5007 1.787
h = 0.003 0.006
y[1] (numeric) = -0.000219204198635 0.559597004229
y[1] (closed_form) = -0.000219204198635 0.559597004229
absolute error = 6.027e-32
relative error = 1.077e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.787
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.787
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.787
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = -0.00115090451966 0.557722109121
y[1] (closed_form) = -0.00115090451966 0.557722109121
absolute error = 6.025e-32
relative error = 1.080e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.793
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.793
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.793
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = -0.00117544491611 0.556171041885
y[1] (closed_form) = -0.00117544491611 0.556171041885
absolute error = 6.024e-32
relative error = 1.083e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.798
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.798
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.798
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5039 1.801
h = 0.001 0.001
y[1] (numeric) = -0.00120236173071 0.555244481282
y[1] (closed_form) = -0.00120236173071 0.555244481282
absolute error = 6.024e-32
relative error = 1.085e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.801
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.801
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = -0.00150897934636 0.554934853497
y[1] (closed_form) = -0.00150897934636 0.554934853497
absolute error = 6.023e-32
relative error = 1.085e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.802
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.802
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.505 1.806
h = 0.003 0.006
y[1] (numeric) = -0.00153296127341 0.553705611957
y[1] (closed_form) = -0.00153296127341 0.553705611957
absolute error = 5.027e-32
relative error = 9.079e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.806
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.806
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.806
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1024.1MB, alloc=52.3MB, time=12.02
x[1] = 0.508 1.812
h = 0.0001 0.005
y[1] (numeric) = -0.00243649281478 0.551865622548
y[1] (closed_form) = -0.00243649281478 0.551865622548
absolute error = 6.020e-32
relative error = 1.091e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.812
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.812
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.812
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = -0.00245338967754 0.550346795566
y[1] (closed_form) = -0.00245338967754 0.550346795566
absolute error = 6.019e-32
relative error = 1.094e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.817
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.817
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.817
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5082 1.82
h = 0.001 0.001
y[1] (numeric) = -0.0024754961803 0.549439396116
y[1] (closed_form) = -0.0024754961803 0.549439396116
absolute error = 6.019e-32
relative error = 1.095e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.82
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.82
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5092 1.821
h = 0.001 0.003
y[1] (numeric) = -0.00277432190416 0.549134802987
y[1] (closed_form) = -0.00277432190416 0.549134802987
absolute error = 5.023e-32
relative error = 9.147e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.821
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.821
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.821
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = -0.00306575131267 0.548228470031
y[1] (closed_form) = -0.00306575131267 0.548228470031
absolute error = 6.018e-32
relative error = 1.098e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.824
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.824
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.824
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5103 1.828
h = 0.003 0.006
y[1] (numeric) = -0.00308227265922 0.547028584569
y[1] (closed_form) = -0.00308227265922 0.547028584569
absolute error = 6.018e-32
relative error = 1.100e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.828
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.828
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.828
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = -0.00395394058771 0.545227596832
y[1] (closed_form) = -0.00395394058771 0.545227596832
absolute error = 5.019e-32
relative error = 9.206e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.834
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.834
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.834
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = -0.00396203476576 0.543744920464
y[1] (closed_form) = -0.00396203476576 0.543744920464
absolute error = 6.016e-32
relative error = 1.106e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.839
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.839
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.839
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5135 1.842
h = 0.001 0.001
y[1] (numeric) = -0.00397860834911 0.542859005856
y[1] (closed_form) = -0.00397860834911 0.542859005856
absolute error = 6.015e-32
relative error = 1.108e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.842
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.842
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.842
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5145 1.843
h = 0.001 0.003
y[1] (numeric) = -0.00426864904691 0.542560013342
y[1] (closed_form) = -0.00426864904691 0.542560013342
absolute error = 6.015e-32
relative error = 1.109e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.843
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.843
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.843
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = -0.00454818045273 0.54167362037
y[1] (closed_form) = -0.00454818045273 0.54167362037
absolute error = 6.015e-32
relative error = 1.110e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.846
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.846
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.846
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5156 1.85
h = 0.003 0.006
y[1] (numeric) = -0.00455774750228 0.540502107643
y[1] (closed_form) = -0.00455774750228 0.540502107643
absolute error = 6.015e-32
relative error = 1.113e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.85
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.85
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.85
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = -0.00539900072508 0.538738997083
y[1] (closed_form) = -0.00539900072508 0.538738997083
absolute error = 6.013e-32
relative error = 1.116e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.856
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.856
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.856
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = -0.00539889662548 0.537291263102
y[1] (closed_form) = -0.00539889662548 0.537291263102
absolute error = 6.013e-32
relative error = 1.119e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.861
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.861
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.861
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5188 1.864
h = 0.001 0.001
y[1] (numeric) = -0.00541030635273 0.536426119228
y[1] (closed_form) = -0.00541030635273 0.536426119228
absolute error = 6.013e-32
relative error = 1.121e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.864
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.864
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5198 1.865
h = 0.001 0.003
y[1] (numeric) = -0.00569191715338 0.536132600558
y[1] (closed_form) = -0.00569191715338 0.536132600558
absolute error = 6.013e-32
relative error = 1.121e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.865
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.865
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.865
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = -0.00596013021326 0.535265540306
y[1] (closed_form) = -0.00596013021326 0.535265540306
absolute error = 5.014e-32
relative error = 9.368e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.868
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.868
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.868
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5209 1.872
h = 0.003 0.006
y[1] (numeric) = -0.00596321499244 0.534121457696
y[1] (closed_form) = -0.00596321499244 0.534121457696
absolute error = 5.014e-32
relative error = 9.388e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.872
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.872
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.872
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = -0.00677542267078 0.53239513706
y[1] (closed_form) = -0.00677542267078 0.53239513706
absolute error = 5.014e-32
relative error = 9.416e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.878
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.878
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.878
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.524 1.883
h = 0.0001 0.003
y[1] (numeric) = -0.00676768374614 0.530981187249
y[1] (closed_form) = -0.00676768374614 0.530981187249
absolute error = 6.011e-32
relative error = 1.132e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.883
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.883
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.883
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1069.1MB, alloc=52.3MB, time=12.54
x[1] = 0.5241 1.886
h = 0.001 0.001
y[1] (numeric) = -0.00677427397555 0.530136129373
y[1] (closed_form) = -0.00677427397555 0.530136129373
absolute error = 5.014e-32
relative error = 9.457e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.886
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.886
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.886
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5251 1.887
h = 0.001 0.003
y[1] (numeric) = -0.00704779215402 0.529847959945
y[1] (closed_form) = -0.00704779215402 0.529847959945
absolute error = 5.013e-32
relative error = 9.460e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.887
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.887
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.887
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = -0.00730523322473 0.528999647308
y[1] (closed_form) = -0.00730523322473 0.528999647308
absolute error = 5.013e-32
relative error = 9.475e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.89
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.89
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5262 1.894
h = 0.003 0.006
y[1] (numeric) = -0.00730227602133 0.527882091008
y[1] (closed_form) = -0.00730227602133 0.527882091008
absolute error = 5.013e-32
relative error = 9.495e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.894
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.894
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.894
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = -0.00808673266711 0.526191509161
y[1] (closed_form) = -0.00808673266711 0.526191509161
absolute error = 5.012e-32
relative error = 9.523e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.9
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.9
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.9
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = -0.00807188442294 0.524810232959
y[1] (closed_form) = -0.00807188442294 0.524810232959
absolute error = 5.012e-32
relative error = 9.548e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.905
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.905
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.905
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5294 1.908
h = 0.001 0.001
y[1] (numeric) = -0.00807397660781 0.523984604344
y[1] (closed_form) = -0.00807397660781 0.523984604344
absolute error = 5.012e-32
relative error = 9.563e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.908
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.908
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.908
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = -0.00833972263992 0.523701661829
y[1] (closed_form) = -0.00833972263992 0.523701661829
absolute error = 5.012e-32
relative error = 9.568e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.909
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.909
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.909
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5305 1.913
h = 0.003 0.006
y[1] (numeric) = -0.0083321967625 0.522606308415
y[1] (closed_form) = -0.0083321967625 0.522606308415
absolute error = 5.012e-32
relative error = 9.588e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.913
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.913
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.913
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = -0.00909415867936 0.520945985245
y[1] (closed_form) = -0.00909415867936 0.520945985245
absolute error = 5.011e-32
relative error = 9.617e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.919
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.919
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.919
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = -0.0090739568968 0.519592055638
y[1] (closed_form) = -0.0090739568968 0.519592055638
absolute error = 5.010e-32
relative error = 9.641e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.924
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.924
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.924
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5337 1.927
h = 0.001 0.001
y[1] (numeric) = -0.00907263975095 0.518782694365
y[1] (closed_form) = -0.00907263975095 0.518782694365
absolute error = 5.010e-32
relative error = 9.656e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.927
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.927
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.927
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5347 1.928
h = 0.001 0.003
y[1] (numeric) = -0.00933200063041 0.51850424252
y[1] (closed_form) = -0.00933200063041 0.51850424252
absolute error = 6.008e-32
relative error = 1.159e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.928
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.928
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.928
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = -0.00957095451121 0.51768944429
y[1] (closed_form) = -0.00957095451121 0.51768944429
absolute error = 6.008e-32
relative error = 1.160e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.931
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.931
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.931
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5358 1.935
h = 0.003 0.006
y[1] (numeric) = -0.00955811948581 0.516619028074
y[1] (closed_form) = -0.00955811948581 0.516619028074
absolute error = 6.008e-32
relative error = 1.163e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.935
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.935
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.935
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = -0.0102945448644 0.514992566543
y[1] (closed_form) = -0.0102945448644 0.514992566543
absolute error = 6.007e-32
relative error = 1.166e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.941
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.941
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.941
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = -0.0102681079265 0.513669357966
y[1] (closed_form) = -0.0102681079265 0.513669357966
absolute error = 5.004e-32
relative error = 9.740e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.946
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.946
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.946
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.539 1.949
h = 0.001 0.001
y[1] (numeric) = -0.0102628284039 0.51287827075
y[1] (closed_form) = -0.0102628284039 0.51287827075
absolute error = 5.009e-32
relative error = 9.764e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.949
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.949
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.949
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.54 1.95
h = 0.001 0.003
y[1] (numeric) = -0.0105149706895 0.512604821114
y[1] (closed_form) = -0.0105149706895 0.512604821114
absolute error = 5.009e-32
relative error = 9.770e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.95
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.95
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.541 1.953
h = 0.0001 0.004
y[1] (numeric) = -0.010744544523 0.511807206183
y[1] (closed_form) = -0.010744544523 0.511807206183
absolute error = 5.004e-32
relative error = 9.775e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.953
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.953
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.953
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5411 1.957
h = 0.003 0.006
y[1] (numeric) = -0.0107267623986 0.510760924918
y[1] (closed_form) = -0.0107267623986 0.510760924918
absolute error = 5.009e-32
relative error = 9.805e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.957
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.957
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.957
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1114.2MB, alloc=52.3MB, time=13.08
x[1] = 0.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = -0.0114387575625 0.509167371774
y[1] (closed_form) = -0.0114387575625 0.509167371774
absolute error = 5.004e-32
relative error = 9.825e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.963
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.963
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.963
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = -0.0114065174322 0.507873898338
y[1] (closed_form) = -0.0114065174322 0.507873898338
absolute error = 5.004e-32
relative error = 9.850e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.968
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.968
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.968
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5443 1.971
h = 0.001 0.001
y[1] (numeric) = -0.0113975404504 0.507100501754
y[1] (closed_form) = -0.0113975404504 0.507100501754
absolute error = 5.004e-32
relative error = 9.865e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.971
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.971
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.971
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5453 1.972
h = 0.001 0.003
y[1] (numeric) = -0.0116427418046 0.506831939045
y[1] (closed_form) = -0.0116427418046 0.506831939045
absolute error = 5.001e-32
relative error = 9.865e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.973
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.973
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.973
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = -0.0118633728201 0.506051000425
y[1] (closed_form) = -0.0118633728201 0.506051000425
absolute error = 5.001e-32
relative error = 9.880e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.976
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.976
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.976
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5464 1.979
h = 0.003 0.006
y[1] (numeric) = -0.0118409818607 0.505028084104
y[1] (closed_form) = -0.0118409818607 0.505028084104
absolute error = 5.001e-32
relative error = 9.900e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.98
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.98
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.98
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = -0.012529594954 0.503466517889
y[1] (closed_form) = -0.012529594954 0.503466517889
absolute error = 5.001e-32
relative error = 9.930e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.986
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.986
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.986
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = -0.0124919551493 0.502201833276
y[1] (closed_form) = -0.0124919551493 0.502201833276
absolute error = 5.001e-32
relative error = 9.955e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.991
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.991
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.991
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5496 1.993
h = 0.001 0.001
y[1] (numeric) = -0.0124795284155 0.50144556718
y[1] (closed_form) = -0.0124795284155 0.50144556718
absolute error = 4e-32
relative error = 7.974e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.994
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.994
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.994
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5506 1.994
h = 0.001 0.003
y[1] (numeric) = -0.0127180531578 0.501181778591
y[1] (closed_form) = -0.0127180531578 0.501181778591
absolute error = 5e-32
relative error = 9.973e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.995
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.995
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.995
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = -0.0129301545427 0.500417027554
y[1] (closed_form) = -0.0129301545427 0.500417027554
absolute error = 5e-32
relative error = 9.988e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 1.998
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 1.998
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 1.998
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5517 2.001
h = 0.003 0.006
y[1] (numeric) = -0.0129034709136 0.499416736908
y[1] (closed_form) = -0.0129034709136 0.499416736908
absolute error = 4e-32
relative error = 8.007e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.002
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.002
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.002
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = -0.0135696954654 0.497886266895
y[1] (closed_form) = -0.0135696954654 0.497886266895
absolute error = 4e-32
relative error = 8.031e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.008
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.008
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.008
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = -0.0135270330746 0.496649462519
y[1] (closed_form) = -0.0135270330746 0.496649462519
absolute error = 4e-32
relative error = 8.051e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.013
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.013
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.013
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5549 2.015
h = 0.001 0.001
y[1] (numeric) = -0.0135113882951 0.495909788974
y[1] (closed_form) = -0.0135113882951 0.495909788974
absolute error = 4e-32
relative error = 8.063e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.016
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.016
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.016
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = -0.0137434881589 0.495650664192
y[1] (closed_form) = -0.0137434881589 0.495650664192
absolute error = 5e-32
relative error = 1.008e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.017
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.017
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.017
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.556 2.02
h = 0.003 0.006
y[1] (numeric) = -0.0137136050717 0.4946693258
y[1] (closed_form) = -0.0137136050717 0.4946693258
absolute error = 5.001e-32
relative error = 1.011e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.021
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.021
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.021
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.559 2.026
h = 0.0001 0.005
y[1] (numeric) = -0.0143616711825 0.493165183317
y[1] (closed_form) = -0.0143616711825 0.493165183317
absolute error = 4.001e-32
relative error = 8.110e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.027
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.027
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.027
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = -0.0143152867199 0.49195173144
y[1] (closed_form) = -0.0143152867199 0.49195173144
absolute error = 4.001e-32
relative error = 8.130e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.032
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.032
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.032
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5592 2.034
h = 0.001 0.001
y[1] (numeric) = -0.0142972354286 0.491225960503
y[1] (closed_form) = -0.0142972354286 0.491225960503
absolute error = 5.001e-32
relative error = 1.018e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.035
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.035
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.035
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1159.4MB, alloc=52.3MB, time=13.60
x[1] = 0.5602 2.035
h = 0.001 0.003
y[1] (numeric) = -0.0145240512788 0.490970836419
y[1] (closed_form) = -0.0145240512788 0.490970836419
absolute error = 5.001e-32
relative error = 1.018e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.036
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.036
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.036
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = -0.014721484523 0.4902350565
y[1] (closed_form) = -0.014721484523 0.4902350565
absolute error = 5.001e-32
relative error = 1.020e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.039
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.039
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.039
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5613 2.042
h = 0.003 0.006
y[1] (numeric) = -0.0146878354908 0.489275041961
y[1] (closed_form) = -0.0146878354908 0.489275041961
absolute error = 5.001e-32
relative error = 1.022e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.043
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.043
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.043
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = -0.0153152178252 0.487800406003
y[1] (closed_form) = -0.0153152178252 0.487800406003
absolute error = 5.001e-32
relative error = 1.025e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.049
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.049
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.049
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = -0.0152644385257 0.486613234369
y[1] (closed_form) = -0.0152644385257 0.486613234369
absolute error = 5e-32
relative error = 1.027e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.054
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.054
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.054
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5645 2.056
h = 0.001 0.001
y[1] (numeric) = -0.0152435556834 0.485903108297
y[1] (closed_form) = -0.0152435556834 0.485903108297
absolute error = 5e-32
relative error = 1.029e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.057
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.057
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.057
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5655 2.057
h = 0.001 0.003
y[1] (numeric) = -0.0154643827229 0.485652446734
y[1] (closed_form) = -0.0154643827229 0.485652446734
absolute error = 5e-32
relative error = 1.029e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.058
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.058
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.058
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = -0.0156543436184 0.484931546674
y[1] (closed_form) = -0.0156543436184 0.484931546674
absolute error = 5e-32
relative error = 1.031e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.061
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.061
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.061
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5666 2.064
h = 0.003 0.006
y[1] (numeric) = -0.0156171900859 0.483992197258
y[1] (closed_form) = -0.0156171900859 0.483992197258
absolute error = 5.001e-32
relative error = 1.033e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.065
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.065
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.065
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = -0.0162247438085 0.482546259822
y[1] (closed_form) = -0.0162247438085 0.482546259822
absolute error = 5.001e-32
relative error = 1.036e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.071
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.071
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = -0.0161698813207 0.481384558685
y[1] (closed_form) = -0.0161698813207 0.481384558685
absolute error = 5.001e-32
relative error = 1.038e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.076
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.076
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5698 2.078
h = 0.001 0.001
y[1] (numeric) = -0.0161463589623 0.48068959776
y[1] (closed_form) = -0.0161463589623 0.48068959776
absolute error = 5e-32
relative error = 1.040e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.079
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.079
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5708 2.079
h = 0.001 0.003
y[1] (numeric) = -0.0163614167068 0.48044329567
y[1] (closed_form) = -0.0163614167068 0.48044329567
absolute error = 4e-32
relative error = 8.321e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.08
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.08
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = -0.0165442391434 0.479736850927
y[1] (closed_form) = -0.0165442391434 0.479736850927
absolute error = 5.001e-32
relative error = 1.042e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.083
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.083
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.083
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5719 2.086
h = 0.003 0.006
y[1] (numeric) = -0.0165038258198 0.47881753352
y[1] (closed_form) = -0.0165038258198 0.47881753352
absolute error = 4e-32
relative error = 8.349e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.087
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.087
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = -0.0170923630749 0.477399513387
y[1] (closed_form) = -0.0170923630749 0.477399513387
absolute error = 5e-32
relative error = 1.047e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.093
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.093
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.575 2.097
h = 0.0001 0.003
y[1] (numeric) = -0.0170337090288 0.476262504446
y[1] (closed_form) = -0.0170337090288 0.476262504446
absolute error = 4e-32
relative error = 8.393e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.098
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.098
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5751 2.1
h = 0.001 0.001
y[1] (numeric) = -0.0170077270407 0.475582247476
y[1] (closed_form) = -0.0170077270407 0.475582247476
absolute error = 4e-32
relative error = 8.405e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.101
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.101
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5761 2.101
h = 0.001 0.003
y[1] (numeric) = -0.0172172249145 0.475340204276
y[1] (closed_form) = -0.0172172249145 0.475340204276
absolute error = 4e-32
relative error = 8.410e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.102
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.102
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = -0.0173932251845 0.474647805294
y[1] (closed_form) = -0.0173932251845 0.474647805294
absolute error = 4.001e-32
relative error = 8.424e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.105
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.105
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5772 2.108
h = 0.003 0.006
y[1] (numeric) = -0.0173497811896 0.473747911239
y[1] (closed_form) = -0.0173497811896 0.473747911239
absolute error = 4.001e-32
relative error = 8.440e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.109
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.109
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1204.6MB, alloc=52.3MB, time=14.13
x[1] = 0.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = -0.0179200736294 0.472357053025
y[1] (closed_form) = -0.0179200736294 0.472357053025
absolute error = 5.001e-32
relative error = 1.058e-29 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.116
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.116
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = -0.0178579010078 0.471243987989
y[1] (closed_form) = -0.0178579010078 0.471243987989
absolute error = 4.001e-32
relative error = 8.485e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.121
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.121
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.121
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5804 2.122
h = 0.001 0.001
y[1] (numeric) = -0.0178296279523 0.470577991476
y[1] (closed_form) = -0.0178296279523 0.470577991476
absolute error = 4.001e-32
relative error = 8.497e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.124
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.124
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.124
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = -0.0180337658383 0.470340109025
y[1] (closed_form) = -0.0180337658383 0.470340109025
absolute error = 3.007e-32
relative error = 6.388e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.125
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.125
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.125
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5815 2.127
h = 0.003 0.006
y[1] (numeric) = -0.0179881074331 0.469456497059
y[1] (closed_form) = -0.0179881074331 0.469456497059
absolute error = 4.001e-32
relative error = 8.517e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.129
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.129
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.129
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = -0.0185435958567 0.468088638608
y[1] (closed_form) = -0.0185435958567 0.468088638608
absolute error = 4.001e-32
relative error = 8.541e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.135
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.135
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.135
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = -0.0184788734796 0.466995644202
y[1] (closed_form) = -0.0184788734796 0.466995644202
absolute error = 3.002e-32
relative error = 6.423e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.14
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.14
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.14
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5847 2.141
h = 0.001 0.001
y[1] (numeric) = -0.018448918242 0.466341605149
y[1] (closed_form) = -0.018448918242 0.466341605149
absolute error = 3.007e-32
relative error = 6.442e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.143
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.143
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.143
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5857 2.142
h = 0.001 0.003
y[1] (numeric) = -0.018648643602 0.466107288162
y[1] (closed_form) = -0.018648643602 0.466107288162
absolute error = 3.007e-32
relative error = 6.445e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.144
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.144
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.144
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = -0.0188128918147 0.465440057007
y[1] (closed_form) = -0.0188128918147 0.465440057007
absolute error = 3.002e-32
relative error = 6.444e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.147
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.147
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.147
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5868 2.149
h = 0.003 0.006
y[1] (numeric) = -0.0187645845463 0.464574794817
y[1] (closed_form) = -0.0187645845463 0.464574794817
absolute error = 4.001e-32
relative error = 8.606e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.151
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.151
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = -0.0193031559 0.463232750162
y[1] (closed_form) = -0.0193031559 0.463232750162
absolute error = 3.002e-32
relative error = 6.474e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.157
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.157
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.157
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = -0.019235369417 0.462162379764
y[1] (closed_form) = -0.019235369417 0.462162379764
absolute error = 3.002e-32
relative error = 6.489e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.162
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.162
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.162
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.59 2.163
h = 0.001 0.001
y[1] (numeric) = -0.0192034043795 0.461521818588
y[1] (closed_form) = -0.0192034043795 0.461521818588
absolute error = 3e-32
relative error = 6.495e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.165
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.165
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.165
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.591 2.164
h = 0.001 0.003
y[1] (numeric) = -0.0193981169331 0.461291483992
y[1] (closed_form) = -0.0193981169331 0.461291483992
absolute error = 2.002e-32
relative error = 4.337e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.166
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.166
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.166
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.592 2.167
h = 0.0001 0.004
y[1] (numeric) = -0.0195563555711 0.460637201332
y[1] (closed_form) = -0.0195563555711 0.460637201332
absolute error = 3.002e-32
relative error = 6.510e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.169
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.169
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.169
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5921 2.171
h = 0.003 0.006
y[1] (numeric) = -0.0195055898033 0.45978974444
y[1] (closed_form) = -0.0195055898033 0.45978974444
absolute error = 3.002e-32
relative error = 6.522e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.173
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.173
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.173
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = -0.0200279126766 0.458472827517
y[1] (closed_form) = -0.0200279126766 0.458472827517
absolute error = 3.002e-32
relative error = 6.541e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.179
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.179
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.179
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = -0.0199572887188 0.457424411601
y[1] (closed_form) = -0.0199572887188 0.457424411601
absolute error = 3.002e-32
relative error = 6.556e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.184
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.184
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.184
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5953 2.185
h = 0.001 0.001
y[1] (numeric) = -0.019923454256 0.456796931263
y[1] (closed_form) = -0.019923454256 0.456796931263
absolute error = 3.002e-32
relative error = 6.565e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.187
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.187
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.187
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1249.7MB, alloc=52.3MB, time=14.66
x[1] = 0.5963 2.186
h = 0.001 0.003
y[1] (numeric) = -0.0201133293584 0.456570487824
y[1] (closed_form) = -0.0201133293584 0.456570487824
absolute error = 3.002e-32
relative error = 6.568e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.188
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.188
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.188
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = -0.0202658163194 0.455928796744
y[1] (closed_form) = -0.0202658163194 0.455928796744
absolute error = 3.002e-32
relative error = 6.577e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.191
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.191
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.191
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5974 2.193
h = 0.003 0.006
y[1] (numeric) = -0.0202127704965 0.455098621137
y[1] (closed_form) = -0.0202127704965 0.455098621137
absolute error = 3.002e-32
relative error = 6.589e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.195
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.195
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.195
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = -0.0207194812628 0.453806168295
y[1] (closed_form) = -0.0207194812628 0.453806168295
absolute error = 3.002e-32
relative error = 6.608e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.201
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.201
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.201
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = -0.0206462322039 0.452779062461
y[1] (closed_form) = -0.0206462322039 0.452779062461
absolute error = 4.001e-32
relative error = 8.828e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.206
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.206
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.206
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6006 2.207
h = 0.001 0.001
y[1] (numeric) = -0.0206106600104 0.452164280744
y[1] (closed_form) = -0.0206106600104 0.452164280744
absolute error = 4e-32
relative error = 8.837e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.209
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.209
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.209
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6016 2.208
h = 0.001 0.003
y[1] (numeric) = -0.0207958652973 0.451941639532
y[1] (closed_form) = -0.0207958652973 0.451941639532
absolute error = 3.002e-32
relative error = 6.635e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.21
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.21
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.21
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = -0.0209428454317 0.451312195413
y[1] (closed_form) = -0.0209428454317 0.451312195413
absolute error = 3.002e-32
relative error = 6.644e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.213
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.213
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.213
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6027 2.215
h = 0.003 0.006
y[1] (numeric) = -0.0208876868691 0.45049879664
y[1] (closed_form) = -0.0208876868691 0.45049879664
absolute error = 2.002e-32
relative error = 4.440e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.217
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.217
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.217
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = -0.0213793915032 0.449230165834
y[1] (closed_form) = -0.0213793915032 0.449230165834
absolute error = 2.002e-32
relative error = 4.453e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.224
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.224
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.224
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = -0.0213037164047 0.448223749688
y[1] (closed_form) = -0.0213037164047 0.448223749688
absolute error = 2.002e-32
relative error = 4.463e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.229
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.229
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.229
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6059 2.229
h = 0.001 0.001
y[1] (numeric) = -0.0212665300657 0.447621298549
y[1] (closed_form) = -0.0212665300657 0.447621298549
absolute error = 2.002e-32
relative error = 4.469e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.232
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.232
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.232
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = -0.0214472258576 0.447402372895
y[1] (closed_form) = -0.0214472258576 0.447402372895
absolute error = 1.005e-32
relative error = 2.244e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.233
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.233
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.233
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.607 2.234
h = 0.003 0.006
y[1] (numeric) = -0.0213905667601 0.446603048056
y[1] (closed_form) = -0.0213905667601 0.446603048056
absolute error = 1e-32
relative error = 2.237e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.237
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.237
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.237
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.61 2.24
h = 0.0001 0.005
y[1] (numeric) = -0.0218700916556 0.445354593713
y[1] (closed_form) = -0.0218700916556 0.445354593713
absolute error = 1.005e-32
relative error = 2.254e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.243
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.243
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.243
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = -0.0217927150144 0.444365533219
y[1] (closed_form) = -0.0217927150144 0.444365533219
absolute error = 1.005e-32
relative error = 2.259e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.248
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.248
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.248
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6102 2.248
h = 0.001 0.001
y[1] (numeric) = -0.0217543736023 0.443773428839
y[1] (closed_form) = -0.0217543736023 0.443773428839
absolute error = 1.020e-32
relative error = 2.295e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.251
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.251
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.251
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6112 2.249
h = 0.001 0.003
y[1] (numeric) = -0.0219313537426 0.443557684955
y[1] (closed_form) = -0.0219313537426 0.443557684955
absolute error = 1.020e-32
relative error = 2.296e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.252
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.252
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.252
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = -0.0220688338178 0.442950211743
y[1] (closed_form) = -0.0220688338178 0.442950211743
absolute error = 1.020e-32
relative error = 2.299e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.255
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.255
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.255
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6123 2.256
h = 0.003 0.006
y[1] (numeric) = -0.0220103406697 0.442166772492
y[1] (closed_form) = -0.0220103406697 0.442166772492
absolute error = 1.005e-32
relative error = 2.270e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.259
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.259
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.259
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = -0.0224759047726 0.44094099389
y[1] (closed_form) = -0.0224759047726 0.44094099389
absolute error = 1.020e-32
relative error = 2.310e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.265
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.265
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.265
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1294.8MB, alloc=52.3MB, time=15.18
x[1] = 0.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = -0.0223964332644 0.439971526952
y[1] (closed_form) = -0.0223964332644 0.439971526952
absolute error = 1.020e-32
relative error = 2.315e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.27
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.27
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.27
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6155 2.27
h = 0.001 0.001
y[1] (numeric) = -0.0223566838573 0.43939110265
y[1] (closed_form) = -0.0223566838573 0.43939110265
absolute error = 1.020e-32
relative error = 2.318e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.273
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.273
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.273
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6165 2.271
h = 0.001 0.003
y[1] (numeric) = -0.0225294336656 0.439178917207
y[1] (closed_form) = -0.0225294336656 0.439178917207
absolute error = 1.020e-32
relative error = 2.319e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.274
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.274
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.274
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = -0.0226620382748 0.438582766272
y[1] (closed_form) = -0.0226620382748 0.438582766272
absolute error = 1.020e-32
relative error = 2.322e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.277
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.277
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.277
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6176 2.278
h = 0.003 0.006
y[1] (numeric) = -0.0226018506272 0.437814759599
y[1] (closed_form) = -0.0226018506272 0.437814759599
absolute error = 1.020e-32
relative error = 2.326e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.281
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.281
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.281
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = -0.023053982203 0.436611072568
y[1] (closed_form) = -0.023053982203 0.436611072568
absolute error = 1.020e-32
relative error = 2.332e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.287
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.287
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.287
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = -0.022972581687 0.435660641936
y[1] (closed_form) = -0.022972581687 0.435660641936
absolute error = 1.020e-32
relative error = 2.338e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.292
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.292
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6208 2.292
h = 0.001 0.001
y[1] (numeric) = -0.0229315276127 0.435091566957
y[1] (closed_form) = -0.0229315276127 0.435091566957
absolute error = 1.020e-32
relative error = 2.341e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.295
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.295
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.295
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6218 2.293
h = 0.001 0.003
y[1] (numeric) = -0.0231001885294 0.434882859589
y[1] (closed_form) = -0.0231001885294 0.434882859589
absolute error = 1.044e-32
relative error = 2.397e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.296
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.296
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.296
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = -0.0232281189833 0.434297729525
y[1] (closed_form) = -0.0232281189833 0.434297729525
absolute error = 1.020e-32
relative error = 2.345e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.299
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.299
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.299
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6229 2.3
h = 0.003 0.006
y[1] (numeric) = -0.0231663678039 0.433544718868
y[1] (closed_form) = -0.0231663678039 0.433544718868
absolute error = 1.020e-32
relative error = 2.349e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.303
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.303
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.303
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = -0.0236055707054 0.432362557957
y[1] (closed_form) = -0.0236055707054 0.432362557957
absolute error = 1.044e-32
relative error = 2.411e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.309
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.309
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.309
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.626 2.311
h = 0.0001 0.003
y[1] (numeric) = -0.0235223967754 0.431430626571
y[1] (closed_form) = -0.0235223967754 0.431430626571
absolute error = 1.020e-32
relative error = 2.360e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.314
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.314
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.314
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6261 2.314
h = 0.001 0.001
y[1] (numeric) = -0.0234801350916 0.430872582094
y[1] (closed_form) = -0.0234801350916 0.430872582094
absolute error = 1.020e-32
relative error = 2.363e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.317
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.317
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.317
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6271 2.315
h = 0.001 0.003
y[1] (numeric) = -0.023644842588 0.430667274517
y[1] (closed_form) = -0.023644842588 0.430667274517
absolute error = 1.020e-32
relative error = 2.364e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.318
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.318
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.318
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = -0.0237682904069 0.430092874029
y[1] (closed_form) = -0.0237682904069 0.430092874029
absolute error = 2.010e-32
relative error = 4.666e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.322
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.322
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.322
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6282 2.322
h = 0.003 0.006
y[1] (numeric) = -0.0237050986324 0.429354438568
y[1] (closed_form) = -0.0237050986324 0.429354438568
absolute error = 1.020e-32
relative error = 2.372e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.326
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.326
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.326
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = -0.024131853623 0.428193256359
y[1] (closed_form) = -0.024131853623 0.428193256359
absolute error = 1.020e-32
relative error = 2.378e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.332
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.332
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.332
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = -0.0240470522683 0.427279306488
y[1] (closed_form) = -0.0240470522683 0.427279306488
absolute error = 1.020e-32
relative error = 2.383e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.337
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.337
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.337
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6314 2.336
h = 0.001 0.001
y[1] (numeric) = -0.0240036741624 0.426731985109
y[1] (closed_form) = -0.0240036741624 0.426731985109
absolute error = 1.020e-32
relative error = 2.386e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.34
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.34
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.34
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = -0.0241645580413 0.426530001076
y[1] (closed_form) = -0.0241645580413 0.426530001076
absolute error = 1.020e-32
relative error = 2.387e-30 %
Correct digits = 32
memory used=1340.1MB, alloc=52.3MB, time=15.71
Radius of convergence (given) for eq 1 = 2.341
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.341
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.341
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6325 2.341
h = 0.003 0.006
y[1] (numeric) = -0.02410038602 0.425803801304
y[1] (closed_form) = -0.02410038602 0.425803801304
absolute error = 2e-33
relative error = 4.689e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.345
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.345
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.345
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = -0.0245170358795 0.424660392688
y[1] (closed_form) = -0.0245170358795 0.424660392688
absolute error = 1.005e-32
relative error = 2.363e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.351
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.351
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.351
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = -0.0244311498631 0.423761537448
y[1] (closed_form) = -0.0244311498631 0.423761537448
absolute error = 1.005e-32
relative error = 2.368e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.356
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.356
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.356
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6357 2.355
h = 0.001 0.001
y[1] (numeric) = -0.0243870025443 0.423223220278
y[1] (closed_form) = -0.0243870025443 0.423223220278
absolute error = 1.005e-32
relative error = 2.371e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.359
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.359
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.359
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6367 2.356
h = 0.001 0.003
y[1] (numeric) = -0.0245447333952 0.423024081046
y[1] (closed_form) = -0.0245447333952 0.423024081046
absolute error = 1.005e-32
relative error = 2.372e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.36
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.36
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = -0.0246604386099 0.42246895193
y[1] (closed_form) = -0.0246604386099 0.42246895193
absolute error = 1.005e-32
relative error = 2.375e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.363
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.363
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.363
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6378 2.363
h = 0.003 0.006
y[1] (numeric) = -0.0245950305073 0.421756582648
y[1] (closed_form) = -0.0245950305073 0.421756582648
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.367
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.367
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.367
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = -0.0250000637431 0.420633174768
y[1] (closed_form) = -0.0250000637431 0.420633174768
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.373
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.373
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.373
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = -0.0249127928042 0.419751384791
y[1] (closed_form) = -0.0249127928042 0.419751384791
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.378
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.378
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.378
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.641 2.377
h = 0.001 0.001
y[1] (numeric) = -0.0248676810094 0.41922324652
y[1] (closed_form) = -0.0248676810094 0.41922324652
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.381
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.381
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.381
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.642 2.378
h = 0.001 0.003
y[1] (numeric) = -0.0250218147935 0.419027292809
y[1] (closed_form) = -0.0250218147935 0.419027292809
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.382
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.382
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.382
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.643 2.381
h = 0.0001 0.004
y[1] (numeric) = -0.0251335328784 0.418482110373
y[1] (closed_form) = -0.0251335328784 0.418482110373
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.385
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.385
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.385
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6431 2.385
h = 0.003 0.006
y[1] (numeric) = -0.0250669915349 0.417783192248
y[1] (closed_form) = -0.0250669915349 0.417783192248
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.389
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.389
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.389
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = -0.0254608296455 0.416679285984
y[1] (closed_form) = -0.0254608296455 0.416679285984
absolute error = 1e-32
relative error = 2.395e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.395
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.395
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.395
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = -0.025372295748 0.415814094475
y[1] (closed_form) = -0.025372295748 0.415814094475
absolute error = 1e-32
relative error = 2.400e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.4
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.4
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.4
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6463 2.399
h = 0.001 0.001
y[1] (numeric) = -0.025326295956 0.415295857816
y[1] (closed_form) = -0.025326295956 0.415295857816
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.403
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.403
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.403
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6473 2.4
h = 0.001 0.003
y[1] (numeric) = -0.0254769477909 0.415103018996
y[1] (closed_form) = -0.0254769477909 0.415103018996
absolute error = 1e-33
relative error = 2.405e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.405
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.405
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.405
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = -0.025584837424 0.414567527511
y[1] (closed_form) = -0.025584837424 0.414567527511
absolute error = 1e-33
relative error = 2.408e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.408
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.408
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.408
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6484 2.407
h = 0.003 0.006
y[1] (numeric) = -0.0255172594375 0.413881694516
y[1] (closed_form) = -0.0255172594375 0.413881694516
absolute error = 1e-33
relative error = 2.412e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.412
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.412
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.412
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = -0.0259003052158 0.412796806378
y[1] (closed_form) = -0.0259003052158 0.412796806378
absolute error = 1e-33
relative error = 2.418e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.418
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.418
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.418
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1385.2MB, alloc=52.3MB, time=16.24
x[1] = 0.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = -0.0258106228602 0.411947762877
y[1] (closed_form) = -0.0258106228602 0.411947762877
absolute error = 1e-33
relative error = 2.423e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.423
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.423
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.423
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6516 2.421
h = 0.001 0.001
y[1] (numeric) = -0.0257638069754 0.411439160208
y[1] (closed_form) = -0.0257638069754 0.411439160208
absolute error = 1e-33
relative error = 2.426e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.426
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.426
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.426
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6526 2.422
h = 0.001 0.003
y[1] (numeric) = -0.0259110873162 0.411249367496
y[1] (closed_form) = -0.0259110873162 0.411249367496
absolute error = 1.005e-32
relative error = 2.439e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.427
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.427
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.427
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = -0.0260152997468 0.410723319571
y[1] (closed_form) = -0.0260152997468 0.410723319571
absolute error = 1e-32
relative error = 2.430e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.43
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.43
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.43
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6537 2.429
h = 0.003 0.006
y[1] (numeric) = -0.0259467758632 0.410050218423
y[1] (closed_form) = -0.0259467758632 0.410050218423
absolute error = 1e-32
relative error = 2.434e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.434
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.434
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.434
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = -0.0263194143712 0.408983879987
y[1] (closed_form) = -0.0263194143712 0.408983879987
absolute error = 1e-32
relative error = 2.440e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.44
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.44
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.44
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = -0.026228691062 0.408150549689
y[1] (closed_form) = -0.026228691062 0.408150549689
absolute error = 1e-32
relative error = 2.445e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.445
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.445
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.445
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6569 2.443
h = 0.001 0.001
y[1] (numeric) = -0.0261811266979 0.407651322645
y[1] (closed_form) = -0.0261811266979 0.407651322645
absolute error = 1e-32
relative error = 2.448e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.448
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.448
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.448
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = -0.0263251415634 0.407464509062
y[1] (closed_form) = -0.0263251415634 0.407464509062
absolute error = 1e-33
relative error = 2.449e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.449
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.449
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.449
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.658 2.448
h = 0.003 0.006
y[1] (numeric) = -0.026256018112 0.406802103406
y[1] (closed_form) = -0.026256018112 0.406802103406
absolute error = 1e-33
relative error = 2.453e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.453
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.453
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.453
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661 2.454
h = 0.0001 0.005
y[1] (numeric) = -0.0266202075153 0.405751485978
y[1] (closed_form) = -0.0266202075153 0.405751485978
absolute error = 1e-33
relative error = 2.459e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.459
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.459
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.459
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = -0.0265288496605 0.404931355152
y[1] (closed_form) = -0.0265288496605 0.404931355152
absolute error = 1.005e-32
relative error = 2.477e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.464
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.464
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.464
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6612 2.462
h = 0.001 0.001
y[1] (numeric) = -0.0264807997512 0.404440006125
y[1] (closed_form) = -0.0264807997512 0.404440006125
absolute error = 1e-33
relative error = 2.467e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.467
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.467
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.467
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6622 2.463
h = 0.001 0.003
y[1] (numeric) = -0.0266221199052 0.40425574184
y[1] (closed_form) = -0.0266221199052 0.40425574184
absolute error = 1e-32
relative error = 2.468e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.468
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.468
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.468
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = -0.0267199745877 0.403746674837
y[1] (closed_form) = -0.0267199745877 0.403746674837
absolute error = 1e-32
relative error = 2.471e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.471
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.471
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.471
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6633 2.47
h = 0.003 0.006
y[1] (numeric) = -0.0266500558756 0.403096374848
y[1] (closed_form) = -0.0266500558756 0.403096374848
absolute error = 1e-32
relative error = 2.475e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.475
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.475
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.475
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = -0.0270045052495 0.402063469619
y[1] (closed_form) = -0.0270045052495 0.402063469619
absolute error = 1.005e-32
relative error = 2.494e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.482
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.482
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.482
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = -0.0269122845645 0.401258281277
y[1] (closed_form) = -0.0269122845645 0.401258281277
absolute error = 1.005e-32
relative error = 2.499e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.487
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.487
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.487
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6665 2.484
h = 0.001 0.001
y[1] (numeric) = -0.0268635986259 0.40077584977
y[1] (closed_form) = -0.0268635986259 0.40077584977
absolute error = 1.005e-32
relative error = 2.502e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.49
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.49
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.49
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6675 2.485
h = 0.001 0.003
y[1] (numeric) = -0.0270018387446 0.400594443465
y[1] (closed_form) = -0.0270018387446 0.400594443465
absolute error = 1.005e-32
relative error = 2.503e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.491
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.491
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.491
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = -0.0270964087409 0.40009415399
y[1] (closed_form) = -0.0270964087409 0.40009415399
absolute error = 1.005e-32
relative error = 2.506e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.494
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.494
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.494
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1430.2MB, alloc=52.3MB, time=16.76
x[1] = 0.6686 2.492
h = 0.003 0.006
y[1] (numeric) = -0.0270257708325 0.399455640063
y[1] (closed_form) = -0.0270257708325 0.399455640063
absolute error = 1.005e-32
relative error = 2.510e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.498
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.498
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.498
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = -0.0273708195571 0.398440018961
y[1] (closed_form) = -0.0273708195571 0.398440018961
absolute error = 1.020e-32
relative error = 2.553e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.504
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.504
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.504
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = -0.0272778260035 0.397649379654
y[1] (closed_form) = -0.0272778260035 0.397649379654
absolute error = 1.005e-32
relative error = 2.521e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.509
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.509
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.509
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6718 2.506
h = 0.001 0.001
y[1] (numeric) = -0.0272285608699 0.397175631781
y[1] (closed_form) = -0.0272285608699 0.397175631781
absolute error = 2.002e-32
relative error = 5.030e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.512
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.512
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.512
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6728 2.507
h = 0.001 0.003
y[1] (numeric) = -0.0273638154371 0.396997021417
y[1] (closed_form) = -0.0273638154371 0.396997021417
absolute error = 1.005e-32
relative error = 2.525e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.513
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.513
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.513
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = -0.0274552269542 0.396505291456
y[1] (closed_form) = -0.0274552269542 0.396505291456
absolute error = 1.005e-32
relative error = 2.529e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.516
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.516
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.516
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6739 2.514
h = 0.003 0.006
y[1] (numeric) = -0.0273839413334 0.395878254814
y[1] (closed_form) = -0.0273839413334 0.395878254814
absolute error = 2.002e-32
relative error = 5.046e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.52
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.52
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.52
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = -0.0277199143066 0.394879502841
y[1] (closed_form) = -0.0277199143066 0.394879502841
absolute error = 2.002e-32
relative error = 5.059e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.526
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.526
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.526
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.677 2.525
h = 0.0001 0.003
y[1] (numeric) = -0.0276262323719 0.394103032424
y[1] (closed_form) = -0.0276262323719 0.394103032424
absolute error = 2.002e-32
relative error = 5.069e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.531
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.531
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.531
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6771 2.528
h = 0.001 0.001
y[1] (numeric) = -0.0275764415105 0.393637742171
y[1] (closed_form) = -0.0275764415105 0.393637742171
absolute error = 2.002e-32
relative error = 5.075e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.534
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.534
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.534
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6781 2.529
h = 0.001 0.003
y[1] (numeric) = -0.0277088013333 0.393461867332
y[1] (closed_form) = -0.0277088013333 0.393461867332
absolute error = 1e-32
relative error = 2.535e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.535
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.535
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.535
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = -0.0277971748823 0.392978485774
y[1] (closed_form) = -0.0277971748823 0.392978485774
absolute error = 1e-32
relative error = 2.538e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.538
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.538
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.538
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6792 2.536
h = 0.003 0.006
y[1] (numeric) = -0.0277253087312 0.392362628027
y[1] (closed_form) = -0.0277253087312 0.392362628027
absolute error = 1e-32
relative error = 2.542e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.542
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.542
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.542
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = -0.0280525170957 0.391380342795
y[1] (closed_form) = -0.0280525170957 0.391380342795
absolute error = 1e-32
relative error = 2.549e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.549
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.549
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.549
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = -0.0279582261282 0.390617673882
y[1] (closed_form) = -0.0279582261282 0.390617673882
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.554
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.554
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.554
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6824 2.55
h = 0.001 0.001
y[1] (numeric) = -0.0279079598422 0.390160622794
y[1] (closed_form) = -0.0279079598422 0.390160622794
absolute error = 1e-32
relative error = 2.557e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.557
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.557
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.557
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = -0.0280375122223 0.389987424641
y[1] (closed_form) = -0.0280375122223 0.389987424641
absolute error = 1e-32
relative error = 2.558e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.558
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.558
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.558
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6835 2.555
h = 0.003 0.006
y[1] (numeric) = -0.0279653255871 0.389380963896
y[1] (closed_form) = -0.0279653255871 0.389380963896
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.562
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.562
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.562
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = -0.0282854186809 0.388412639366
y[1] (closed_form) = -0.0282854186809 0.388412639366
absolute error = 1e-33
relative error = 2.568e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.568
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.568
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.568
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = -0.0281908220002 0.387661571557
y[1] (closed_form) = -0.0281908220002 0.387661571557
absolute error = 1e-32
relative error = 2.573e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.573
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.573
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.573
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1475.4MB, alloc=52.3MB, time=17.29
x[1] = 0.6867 2.569
h = 0.001 0.001
y[1] (numeric) = -0.0281402792287 0.387211447983
y[1] (closed_form) = -0.0281402792287 0.387211447983
absolute error = 1e-32
relative error = 2.576e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.576
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.576
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.576
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6877 2.57
h = 0.001 0.003
y[1] (numeric) = -0.0282675133672 0.387040539977
y[1] (closed_form) = -0.0282675133672 0.387040539977
absolute error = 1e-32
relative error = 2.577e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.577
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.577
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.577
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = -0.0283506302401 0.386572186581
y[1] (closed_form) = -0.0283506302401 0.386572186581
absolute error = 1e-32
relative error = 2.580e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.58
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.58
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.58
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6888 2.577
h = 0.003 0.006
y[1] (numeric) = -0.0282779742361 0.385976375035
y[1] (closed_form) = -0.0282779742361 0.385976375035
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.584
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.584
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.584
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = -0.0285898429345 0.385023797184
y[1] (closed_form) = -0.0285898429345 0.385023797184
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.59
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.59
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.59
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = -0.0284947682054 0.384285878664
y[1] (closed_form) = -0.0284947682054 0.384285878664
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.595
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.595
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.595
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.692 2.591
h = 0.001 0.001
y[1] (numeric) = -0.0284438334288 0.383843606323
y[1] (closed_form) = -0.0284438334288 0.383843606323
absolute error = 1e-33
relative error = 2.598e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.598
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.598
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.598
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.693 2.592
h = 0.001 0.003
y[1] (numeric) = -0.0285684131342 0.383675268621
y[1] (closed_form) = -0.0285684131342 0.383675268621
absolute error = 1e-32
relative error = 2.599e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.599
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.599
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.599
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.694 2.595
h = 0.0001 0.004
y[1] (numeric) = -0.0286488056623 0.383214694297
y[1] (closed_form) = -0.0286488056623 0.383214694297
absolute error = 1e-32
relative error = 2.602e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.602
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.602
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.602
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6941 2.599
h = 0.003 0.006
y[1] (numeric) = -0.0285757366576 0.382629261068
y[1] (closed_form) = -0.0285757366576 0.382629261068
absolute error = 1.005e-32
relative error = 2.619e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.606
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.606
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.606
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = -0.0288796565386 0.381692061304
y[1] (closed_form) = -0.0288796565386 0.381692061304
absolute error = 1.005e-32
relative error = 2.625e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.612
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.612
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.612
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = -0.0287841701964 0.380966958482
y[1] (closed_form) = -0.0287841701964 0.380966958482
absolute error = 1.005e-32
relative error = 2.630e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.617
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.617
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.617
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6973 2.613
h = 0.001 0.001
y[1] (numeric) = -0.0287328857528 0.380532338936
y[1] (closed_form) = -0.0287328857528 0.380532338936
absolute error = 1.005e-32
relative error = 2.634e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.62
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.62
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.62
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6983 2.614
h = 0.001 0.003
y[1] (numeric) = -0.0288548891828 0.380366517014
y[1] (closed_form) = -0.0288548891828 0.380366517014
absolute error = 1e-33
relative error = 2.622e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.622
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.622
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.622
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = -0.0289326585897 0.379913535018
y[1] (closed_form) = -0.0289326585897 0.379913535018
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.625
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.625
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.625
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6994 2.621
h = 0.003 0.006
y[1] (numeric) = -0.0288592295643 0.379338218094
y[1] (closed_form) = -0.0288592295643 0.379338218094
absolute error = 1e-33
relative error = 2.629e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.629
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.629
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.629
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = -0.0291554648845 0.378416038792
y[1] (closed_form) = -0.0291554648845 0.378416038792
absolute error = 1e-33
relative error = 2.635e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.635
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.635
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.635
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = -0.029059629319 0.377703428975
y[1] (closed_form) = -0.029059629319 0.377703428975
absolute error = 2e-33
relative error = 5.280e-31 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.64
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.64
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.64
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7026 2.635
h = 0.001 0.001
y[1] (numeric) = -0.0290080350482 0.377276270246
y[1] (closed_form) = -0.0290080350482 0.377276270246
absolute error = 1.005e-32
relative error = 2.656e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.643
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.643
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.643
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7036 2.636
h = 0.001 0.003
y[1] (numeric) = -0.0291275374348 0.377112910993
y[1] (closed_form) = -0.0291275374348 0.377112910993
absolute error = 1e-33
relative error = 2.644e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.644
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.644
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.644
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = -0.029202780534 0.376667340319
y[1] (closed_form) = -0.029202780534 0.376667340319
absolute error = 1.020e-32
relative error = 2.699e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.647
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.647
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.647
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1520.5MB, alloc=52.3MB, time=17.81
x[1] = 0.7047 2.643
h = 0.003 0.006
y[1] (numeric) = -0.0291290412815 0.376101886209
y[1] (closed_form) = -0.0291290412815 0.376101886209
absolute error = 1e-33
relative error = 2.651e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.651
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.651
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.651
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = -0.0294178455243 0.375194380326
y[1] (closed_form) = -0.0294178455243 0.375194380326
absolute error = 1e-33
relative error = 2.657e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.657
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.657
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.657
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = -0.0293217193211 0.374493951291
y[1] (closed_form) = -0.0293217193211 0.374493951291
absolute error = 1e-33
relative error = 2.662e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.662
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.662
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.662
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7079 2.657
h = 0.001 0.001
y[1] (numeric) = -0.0292698527116 0.374074067603
y[1] (closed_form) = -0.0292698527116 0.374074067603
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.665
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.665
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.665
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = -0.029386926493 0.373913119284
y[1] (closed_form) = -0.029386926493 0.373913119284
absolute error = 1e-33
relative error = 2.666e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.666
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.666
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.666
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.709 2.662
h = 0.003 0.006
y[1] (numeric) = -0.0293130713156 0.373355960967
y[1] (closed_form) = -0.0293130713156 0.373355960967
absolute error = 1e-33
relative error = 2.670e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.67
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.67
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.67
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.712 2.668
h = 0.0001 0.005
y[1] (numeric) = -0.0295958436267 0.372460899982
y[1] (closed_form) = -0.0295958436267 0.372460899982
absolute error = 1e-33
relative error = 2.676e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.676
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.676
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.676
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = -0.0294996516517 0.371770716006
y[1] (closed_form) = -0.0294996516517 0.371770716006
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.681
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.681
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.681
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7122 2.676
h = 0.001 0.001
y[1] (numeric) = -0.0294476627079 0.371356952905
y[1] (closed_form) = -0.0294476627079 0.371356952905
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.684
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.684
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.684
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7132 2.677
h = 0.001 0.003
y[1] (numeric) = -0.029562729897 0.371198067234
y[1] (closed_form) = -0.029562729897 0.371198067234
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.685
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.685
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.685
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = -0.0296335990583 0.370765851896
y[1] (closed_form) = -0.0296335990583 0.370765851896
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.689
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.689
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.689
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7143 2.684
h = 0.003 0.006
y[1] (numeric) = -0.0295595156702 0.370218105735
y[1] (closed_form) = -0.0295595156702 0.370218105735
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.693
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.693
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.693
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = -0.0298352978014 0.369337096575
y[1] (closed_form) = -0.0298352978014 0.369337096575
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.699
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.699
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.699
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = -0.0297389113996 0.368658538279
y[1] (closed_form) = -0.0297389113996 0.368658538279
absolute error = 1e-33
relative error = 2.704e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.704
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.704
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.704
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7175 2.698
h = 0.001 0.001
y[1] (numeric) = -0.0296867120332 0.368251719842
y[1] (closed_form) = -0.0296867120332 0.368251719842
absolute error = 1e-33
relative error = 2.707e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.707
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.707
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.707
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7185 2.699
h = 0.001 0.003
y[1] (numeric) = -0.0297994778136 0.368095151574
y[1] (closed_form) = -0.0297994778136 0.368095151574
absolute error = 1e-33
relative error = 2.708e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.708
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.708
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.708
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = -0.0298680732647 0.367669858593
y[1] (closed_form) = -0.0298680732647 0.367669858593
absolute error = 1e-33
relative error = 2.711e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.711
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.711
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.711
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7196 2.706
h = 0.003 0.006
y[1] (numeric) = -0.0297938034359 0.367131293705
y[1] (closed_form) = -0.0297938034359 0.367131293705
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.715
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.715
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.715
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = -0.0300628209237 0.366264017722
y[1] (closed_form) = -0.0300628209237 0.366264017722
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.721
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.721
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.721
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = -0.0299662891089 0.365596800668
y[1] (closed_form) = -0.0299662891089 0.365596800668
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.726
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.726
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.726
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7228 2.72
h = 0.001 0.001
y[1] (numeric) = -0.0299139108794 0.365196757594
y[1] (closed_form) = -0.0299139108794 0.365196757594
absolute error = 1e-33
relative error = 2.729e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.729
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.729
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.729
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1565.8MB, alloc=52.3MB, time=18.34
x[1] = 0.7238 2.721
h = 0.001 0.003
y[1] (numeric) = -0.0300244403774 0.365042458744
y[1] (closed_form) = -0.0300244403774 0.365042458744
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.73
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.73
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.73
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = -0.0300908439366 0.364623927417
y[1] (closed_form) = -0.0300908439366 0.364623927417
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.733
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.733
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.733
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7249 2.728
h = 0.003 0.006
y[1] (numeric) = -0.0300164269134 0.36409432023
y[1] (closed_form) = -0.0300164269134 0.36409432023
absolute error = 1e-33
relative error = 2.737e-31 %
Correct digits = 33
Radius of convergence (given) for eq 1 = 2.737
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.737
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.737
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = -0.0302788963635 0.363240468002
y[1] (closed_form) = -0.0302788963635 0.363240468002
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.743
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.743
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.743
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.728 2.739
h = 0.0001 0.003
y[1] (numeric) = -0.0301822651393 0.362584316739
y[1] (closed_form) = -0.0301822651393 0.362584316739
absolute error = 1e-32
relative error = 2.748e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.748
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.748
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.748
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7281 2.742
h = 0.001 0.001
y[1] (numeric) = -0.0301297377393 0.362190885055
y[1] (closed_form) = -0.0301297377393 0.362190885055
absolute error = 1e-32
relative error = 2.751e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.751
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.751
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.751
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7291 2.743
h = 0.001 0.003
y[1] (numeric) = -0.0302380937338 0.362038808868
y[1] (closed_form) = -0.0302380937338 0.362038808868
absolute error = 1e-32
relative error = 2.753e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.753
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.753
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.753
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = -0.030302383774 0.361626883282
y[1] (closed_form) = -0.030302383774 0.361626883282
absolute error = 1e-32
relative error = 2.756e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.756
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.756
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.756
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7302 2.75
h = 0.003 0.006
y[1] (numeric) = -0.0302278564262 0.361106017255
y[1] (closed_form) = -0.0302278564262 0.361106017255
absolute error = 1.005e-32
relative error = 2.773e-30 %
Correct digits = 32
Radius of convergence (given) for eq 1 = 2.76
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.76
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.76
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = -0.0304839859308 0.360265288273
y[1] (closed_form) = -0.0304839859308 0.360265288273
absolute error = 2.002e-32
relative error = 5.539e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.766
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.766
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.766
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = -0.0303872984666 0.35961993599
y[1] (closed_form) = -0.0303872984666 0.35961993599
absolute error = 2.002e-32
relative error = 5.549e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.771
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.771
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.771
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7334 2.764
h = 0.001 0.001
y[1] (numeric) = -0.0303346498294 0.359232956849
y[1] (closed_form) = -0.0303346498294 0.359232956849
absolute error = 2.002e-32
relative error = 5.555e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.774
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.774
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.774
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = -0.0304408928534 0.359083057763
y[1] (closed_form) = -0.0304408928534 0.359083057763
absolute error = 2.002e-32
relative error = 5.557e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.775
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.775
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.775
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7345 2.769
h = 0.003 0.006
y[1] (numeric) = -0.0303663990938 0.358569548361
y[1] (closed_form) = -0.0303663990938 0.358569548361
absolute error = 2e-32
relative error = 5.558e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.779
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.779
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.779
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = -0.0306173834223 0.357739953671
y[1] (closed_form) = -0.0306173834223 0.357739953671
absolute error = 2.002e-32
relative error = 5.577e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.785
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.785
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.785
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = -0.0305208045424 0.357103689511
y[1] (closed_form) = -0.0305208045424 0.357103689511
absolute error = 2.002e-32
relative error = 5.587e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.79
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.79
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.79
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7377 2.783
h = 0.001 0.001
y[1] (numeric) = -0.030468147027 0.356722142095
y[1] (closed_form) = -0.030468147027 0.356722142095
absolute error = 2.002e-32
relative error = 5.593e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.793
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.793
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.793
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7387 2.784
h = 0.001 0.003
y[1] (numeric) = -0.0305726433229 0.356574105617
y[1] (closed_form) = -0.0305726433229 0.356574105617
absolute error = 2.002e-32
relative error = 5.595e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.794
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.794
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.794
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = -0.0306332725963 0.356174095644
y[1] (closed_form) = -0.0306332725963 0.356174095644
absolute error = 2e-32
relative error = 5.595e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.797
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.797
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.797
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7398 2.791
h = 0.003 0.006
y[1] (numeric) = -0.0305587288662 0.355668941891
y[1] (closed_form) = -0.0305587288662 0.355668941891
absolute error = 2e-32
relative error = 5.603e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.801
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.801
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.801
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = -0.0308037357939 0.354851931694
y[1] (closed_form) = -0.0308037357939 0.354851931694
absolute error = 2e-32
relative error = 5.615e-30 %
Correct digits = 31
memory used=1611.0MB, alloc=52.3MB, time=18.87
Radius of convergence (given) for eq 1 = 2.808
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.808
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.808
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = -0.0307071710679 0.354225991487
y[1] (closed_form) = -0.0307071710679 0.354225991487
absolute error = 2.002e-32
relative error = 5.632e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.813
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.813
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.813
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.743 2.805
h = 0.001 0.001
y[1] (numeric) = -0.030654438195 0.353850613732
y[1] (closed_form) = -0.030654438195 0.353850613732
absolute error = 2.002e-32
relative error = 5.638e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.816
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.816
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.816
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.744 2.806
h = 0.001 0.003
y[1] (numeric) = -0.030756927998 0.353704671977
y[1] (closed_form) = -0.030756927998 0.353704671977
absolute error = 2.002e-32
relative error = 5.640e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.817
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.817
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.817
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.745 2.809
h = 0.0001 0.004
y[1] (numeric) = -0.0308156487147 0.353310845876
y[1] (closed_form) = -0.0308156487147 0.353310845876
absolute error = 2e-32
relative error = 5.639e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.82
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.82
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.82
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7451 2.813
h = 0.003 0.006
y[1] (numeric) = -0.0307410858931 0.352813849928
y[1] (closed_form) = -0.0307410858931 0.352813849928
absolute error = 3e-32
relative error = 8.471e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.824
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.824
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.824
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = -0.0309803013596 0.352009147653
y[1] (closed_form) = -0.0309803013596 0.352009147653
absolute error = 3e-32
relative error = 8.490e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.83
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.83
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.83
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = -0.0308837868187 0.351393287575
y[1] (closed_form) = -0.0308837868187 0.351393287575
absolute error = 3.002e-32
relative error = 8.509e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.835
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.835
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.835
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7483 2.827
h = 0.001 0.001
y[1] (numeric) = -0.0308310020797 0.351023934271
y[1] (closed_form) = -0.0308310020797 0.351023934271
absolute error = 2.002e-32
relative error = 5.683e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.838
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.838
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.838
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7493 2.828
h = 0.001 0.003
y[1] (numeric) = -0.0309315400289 0.350880044933
y[1] (closed_form) = -0.0309315400289 0.350880044933
absolute error = 2.010e-32
relative error = 5.706e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.839
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.839
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.839
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = -0.0309884188009 0.350492263785
y[1] (closed_form) = -0.0309884188009 0.350492263785
absolute error = 2.002e-32
relative error = 5.691e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.842
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.842
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.842
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7504 2.835
h = 0.003 0.006
y[1] (numeric) = -0.0309138658758 0.350003233857
y[1] (closed_form) = -0.0309138658758 0.350003233857
absolute error = 3.007e-32
relative error = 8.557e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.846
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.846
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = -0.0311474687158 0.349210570724
y[1] (closed_form) = -0.0311474687158 0.349210570724
absolute error = 3.002e-32
relative error = 8.562e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.852
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.852
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.852
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = -0.0310510381382 0.348604554403
y[1] (closed_form) = -0.0310510381382 0.348604554403
absolute error = 3.007e-32
relative error = 8.591e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.857
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.857
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.857
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7536 2.849
h = 0.001 0.001
y[1] (numeric) = -0.0309982236209 0.348241084763
y[1] (closed_form) = -0.0309982236209 0.348241084763
absolute error = 2.010e-32
relative error = 5.749e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.86
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.86
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.86
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7546 2.85
h = 0.001 0.003
y[1] (numeric) = -0.0310968624565 0.348099206603
y[1] (closed_form) = -0.0310968624565 0.348099206603
absolute error = 3.007e-32
relative error = 8.603e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.861
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.861
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.861
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = -0.0311519631814 0.34771733551
y[1] (closed_form) = -0.0311519631814 0.34771733551
absolute error = 2.010e-32
relative error = 5.757e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.864
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.864
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.864
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7557 2.857
h = 0.003 0.006
y[1] (numeric) = -0.0310774473579 0.347236085653
y[1] (closed_form) = -0.0310774473579 0.347236085653
absolute error = 3.007e-32
relative error = 8.624e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.868
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.868
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.868
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = -0.0313056096219 0.346455200416
y[1] (closed_form) = -0.0313056096219 0.346455200416
absolute error = 2.022e-32
relative error = 5.814e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.875
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.875
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.875
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = -0.0312092946624 0.345858798655
y[1] (closed_form) = -0.0312092946624 0.345858798655
absolute error = 2.022e-32
relative error = 5.824e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.88
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.88
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.88
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7589 2.871
h = 0.001 0.001
y[1] (numeric) = -0.0311564711303 0.345501076149
y[1] (closed_form) = -0.0311564711303 0.345501076149
absolute error = 3.015e-32
relative error = 8.691e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.883
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.883
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.883
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1656.0MB, alloc=52.3MB, time=19.39
x[1] = 0.7599 2.872
h = 0.001 0.003
y[1] (numeric) = -0.0312532617736 0.345361168964
y[1] (closed_form) = -0.0312532617736 0.345361168964
absolute error = 3.007e-32
relative error = 8.670e-30 %
Correct digits = 31
Radius of convergence (given) for eq 1 = 2.884
Order of pole (given) = 0 0
Radius of convergence (ratio test) for eq 1 = 2.884
Order of pole (ratio test) = 1 0
Radius of convergence (three term test) for eq 1 = 2.884
Order of pole (three term test) = 1 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = y * y ;
Iterations = 754
Total Elapsed Time = 19 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 19 Seconds
> quit
memory used=1659.2MB, alloc=52.3MB, time=19.43