|\^/| 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(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2))));
> end;
exact_soln_y := proc(x)
return c(0.8)*(c(x) + c(2.0))*sqrt(sqrt(c(0.1)*c(x) + c(0.2)))
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,
> array_const_0D1,
> array_const_0D2,
#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_tmp3,
> array_tmp4,
> array_tmp5,
> 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_const_0D1,
array_const_0D2, 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_tmp3, array_tmp4, array_tmp5, 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,
> array_const_0D1,
> array_const_0D2,
#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_tmp3,
> array_tmp4,
> array_tmp5,
> 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_const_0D1,
array_const_0D2, 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_tmp3, array_tmp4, array_tmp5, 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,
> array_const_0D1,
> array_const_0D2,
#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_tmp3,
> array_tmp4,
> array_tmp5,
> 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_const_0D1,
array_const_0D2, 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_tmp3, array_tmp4, array_tmp5, 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,
> array_const_0D1,
> array_const_0D2,
#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_tmp3,
> array_tmp4,
> array_tmp5,
> 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_const_0D1,
array_const_0D2, 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_tmp3, array_tmp4, array_tmp5, 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,
> array_const_0D1,
> array_const_0D2,
#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_tmp3,
> array_tmp4,
> array_tmp5,
> 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_const_0D1,
array_const_0D2, 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_tmp3, array_tmp4, array_tmp5, 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,
> array_const_0D1,
> array_const_0D2,
#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_tmp3,
> array_tmp4,
> array_tmp5,
> 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_const_0D1,
array_const_0D2, 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_tmp3, array_tmp4, array_tmp5, 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,
> array_const_0D1,
> array_const_0D2,
#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_tmp3,
> array_tmp4,
> array_tmp5,
> 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_const_0D1,
array_const_0D2, 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_tmp3, array_tmp4, array_tmp5, 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,
> array_const_0D1,
> array_const_0D2,
#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_tmp3,
> array_tmp4,
> array_tmp5,
> 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 CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> #emit pre sqrt 1 $eq_no = 1
> array_tmp4[1] := sqrt(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[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 CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2;
> #emit pre sqrt ID_FULL iii = 2 $eq_no = 1
> #emit pre sqrt 2 $eq_no = 1
> array_tmp4[2] := 0;
> array_tmp4[2] := (array_tmp3[2]-ats(2,array_tmp4,array_tmp4,2)) / array_tmp4[1] /glob__2;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0;
> array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre sqrt ID_FULL iii = 3 $eq_no = 1
> #emit pre sqrt 3 $eq_no = 1
> array_tmp4[3] := 0;
> array_tmp4[3] := (array_tmp3[3]-ats(3,array_tmp4,array_tmp4,2)) / array_tmp4[1] /glob__2;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0;
> array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre sqrt ID_FULL iii = 4 $eq_no = 1
> #emit pre sqrt 4 $eq_no = 1
> array_tmp4[4] := 0;
> array_tmp4[4] := (array_tmp3[4]-ats(4,array_tmp4,array_tmp4,2)) / array_tmp4[1] /glob__2;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0;
> array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre sqrt ID_FULL iii = 5 $eq_no = 1
> #emit pre sqrt 5 $eq_no = 1
> array_tmp4[5] := 0;
> array_tmp4[5] := (array_tmp3[5]-ats(5,array_tmp4,array_tmp4,2)) / array_tmp4[1] /glob__2;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[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_tmp5[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 sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0;
> array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2;
> #emit sqrt FULL $eq_no = 1
> array_tmp4[kkk] := 0;
> array_tmp4[kkk] := (array_tmp3[kkk] - ats(kkk,array_tmp4,array_tmp4,2)) / array_tmp4[1] / glob__2;
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[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_tmp5[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_const_0D1,
array_const_0D2, 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_tmp3, array_tmp4, array_tmp5, 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_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4[1] := sqrt(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
array_tmp4[2] := 0;
array_tmp4[2] := (array_tmp3[2] - ats(2, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*glob__2);
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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_tmp3[3] := 0;
array_tmp3[3] :=
neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4[3] := 0;
array_tmp4[3] := (array_tmp3[3] - ats(3, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*glob__2);
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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_tmp3[4] := 0;
array_tmp3[4] :=
neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4[4] := 0;
array_tmp4[4] := (array_tmp3[4] - ats(4, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*glob__2);
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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_tmp3[5] := 0;
array_tmp3[5] :=
neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4[5] := 0;
array_tmp4[5] := (array_tmp3[5] - ats(5, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*glob__2);
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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_tmp3[kkk] := 0;
array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/(
array_tmp3[1]*glob__2);
array_tmp4[kkk] := 0;
array_tmp4[kkk] := (
array_tmp3[kkk] - ats(kkk, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*glob__2);
array_tmp5[kkk] := array_tmp4[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_tmp5[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,
> array_const_0D1,
> array_const_0D2,
> #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_tmp3,
> array_tmp4,
> array_tmp5,
> 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 := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #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..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> 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..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 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..(40) ,(0..40+ 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 <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <=40) do # do number 1
> term := 1;
> while (term <= 40) 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_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> 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_const_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> 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;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> 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/sqrt_sqrt_tzeropostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> 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,"glob_min_h := c(0.001);");
> 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(-2.0);");
> 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(0.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> 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,"");
> omniout_str(ALWAYS,"return(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2))));");
> 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_min_h := c(0.001);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-2.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(0.5);
> 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 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> 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,"2017-11-26T16:35:40-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sqrt_sqrt_tzero")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ")
> ;
> 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,"sqrt_sqrt_tzero diffeq.mxt")
> ;
> logitem_str(html_log_file,"sqrt_sqrt_tzero maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> 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_const_0D1,
array_const_0D2, 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_tmp3, array_tmp4, array_tmp5, 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 := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
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 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
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 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 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 <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 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 <= 40 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 <= 40 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 <= 40 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 <= 40 do
term := 1;
while term <= 40 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_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
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_const_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
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;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
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/sqrt_sqrt_tzeropostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1\
* x + 0.2 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
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, "glob_min_h := c(0.001);");
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(-2.0);");
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(0.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
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, "");
omniout_str(ALWAYS, "return(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.\
1) * c(x) + c(0.2))));");
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,");
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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_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-2.0);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(0.5);
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 ) = sqrt ( sqrt ( 0\
.1 * x + 0.2 ) ) ; ");
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, "2017-11-26T16:35:40-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sqrt_sqrt_tzero");
logitem_str(html_log_file, "diff ( y , x , 1 ) = sq\
rt ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
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, "sqrt_sqrt_tzero diffeq.mxt");
logitem_str(html_log_file, "sqrt_sqrt_tzero maple results");
logitem_str(html_log_file, "OK");
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/sqrt_sqrt_tzeropostcpx.cpx#################
diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#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_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-2.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(0.5);
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(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2))));
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) = 1.13686852293 0.067699518624
y[1] (closed_form) = 1.13686852293 0.067699518624
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.628
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 1.13689515458 0.071085844524
y[1] (closed_form) = 1.13689495357 0.0710858559437
absolute error = 2.013e-07
relative error = 1.767e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.262
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=32.1MB, alloc=40.3MB, time=0.41
x[1] = 0.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 1.13693689346 0.0731180867224
y[1] (closed_form) = 1.13693693349 0.0731180808218
absolute error = 4.046e-08
relative error = 3.551e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9908
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 1.13760521473 0.0738040449107
y[1] (closed_form) = 1.13760536965 0.0738039902229
absolute error = 1.643e-07
relative error = 1.441e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.705
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 1.13825602933 0.075844627779
y[1] (closed_form) = 1.13825594625 0.0758446629722
absolute error = 9.023e-08
relative error = 7.910e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.664
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1023 0.116
h = 0.003 0.006
y[1] (numeric) = 1.13828723543 0.0785549389675
y[1] (closed_form) = 1.13828698228 0.0785548402311
absolute error = 2.717e-07
relative error = 2.381e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.53
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = 1.14026227443 0.0826474417242
y[1] (closed_form) = 1.14026192872 0.0826482884106
absolute error = 9.145e-07
relative error = 8.000e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.572
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=77.6MB, alloc=44.3MB, time=0.97
x[1] = 0.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = 1.14027983895 0.0860370352948
y[1] (closed_form) = 1.14027965596 0.086037287927
absolute error = 3.119e-07
relative error = 2.728e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.266
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1055 0.13
h = 0.001 0.001
y[1] (numeric) = 1.14031637936 0.0880709538486
y[1] (closed_form) = 1.1403164367 0.0880711873462
absolute error = 2.404e-07
relative error = 2.102e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.11
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9939
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1065 0.131
h = 0.001 0.003
y[1] (numeric) = 1.14098345327 0.0887591627282
y[1] (closed_form) = 1.14098362486 0.0887593466696
absolute error = 2.516e-07
relative error = 2.198e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.111
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.719
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = 1.14162952484 0.090802997813
y[1] (closed_form) = 1.14162945967 0.0908032732529
absolute error = 2.830e-07
relative error = 2.471e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.112
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.672
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1076 0.138
h = 0.003 0.006
y[1] (numeric) = 1.14165379463 0.0935154980137
y[1] (closed_form) = 1.14165355877 0.0935156411481
absolute error = 2.759e-07
relative error = 2.409e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.112
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.541
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=122.9MB, alloc=44.3MB, time=1.52
x[1] = 0.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = 1.14361987741 0.0976162769036
y[1] (closed_form) = 1.14361955646 0.0976173639111
absolute error = 1.133e-06
relative error = 9.875e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.577
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = 1.14362878454 0.101008593021
y[1] (closed_form) = 1.14362862138 0.10100908616
absolute error = 5.194e-07
relative error = 4.524e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.27
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1108 0.152
h = 0.001 0.001
y[1] (numeric) = 1.14366015174 0.103044223817
y[1] (closed_form) = 1.14366022819 0.10304469603
absolute error = 4.784e-07
relative error = 4.166e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9971
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1118 0.153
h = 0.001 0.003
y[1] (numeric) = 1.14432599856 0.103734687566
y[1] (closed_form) = 1.14432618859 0.10373510947
absolute error = 4.627e-07
relative error = 4.027e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.117
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.735
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = 1.14496736335 0.105781803442
y[1] (closed_form) = 1.14496731791 0.10578231843
absolute error = 5.170e-07
relative error = 4.496e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.119
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.681
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=168.3MB, alloc=44.3MB, time=2.08
x[1] = 0.1129 0.16
h = 0.003 0.006
y[1] (numeric) = 1.14498473028 0.108496540493
y[1] (closed_form) = 1.14498451355 0.108496924802
absolute error = 4.412e-07
relative error = 3.836e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.119
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.552
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = 1.14694194185 0.112605643997
y[1] (closed_form) = 1.14694164744 0.112606970505
absolute error = 1.359e-06
relative error = 0.0001179 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.122
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.582
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.116 0.171
h = 0.0001 0.003
y[1] (numeric) = 1.14694223348 0.116000742036
y[1] (closed_form) = 1.14694209195 0.116001474948
absolute error = 7.465e-07
relative error = 6.475e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.123
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.274
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1161 0.174
h = 0.001 0.001
y[1] (numeric) = 1.14696845325 0.118038120306
y[1] (closed_form) = 1.14696855056 0.118038830522
absolute error = 7.169e-07
relative error = 6.217e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.123
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1171 0.175
h = 0.001 0.003
y[1] (numeric) = 1.14763309317 0.118730842717
y[1] (closed_form) = 1.14763330341 0.118731501888
absolute error = 6.919e-07
relative error = 5.997e-05 %
Correct digits = 6
memory used=213.7MB, alloc=44.3MB, time=2.63
Radius of convergence (given) for eq 1 = 2.124
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.75
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = 1.14826978777 0.120781267149
y[1] (closed_form) = 1.14826976383 0.120782020958
absolute error = 7.542e-07
relative error = 6.532e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.689
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1182 0.182
h = 0.003 0.006
y[1] (numeric) = 1.14828028594 0.123498288021
y[1] (closed_form) = 1.14828009015 0.123498912777
absolute error = 6.547e-07
relative error = 5.669e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.564
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = 1.15022871168 0.12761576283
y[1] (closed_form) = 1.15022844553 0.127617327992
absolute error = 1.588e-06
relative error = 0.0001372 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.588
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = 1.15022043049 0.131013701075
y[1] (closed_form) = 1.15022031236 0.131014672997
absolute error = 9.791e-07
relative error = 8.457e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.278
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=259.0MB, alloc=44.3MB, time=3.19
x[1] = 0.1214 0.196
h = 0.001 0.001
y[1] (numeric) = 1.15024152906 0.133052861386
y[1] (closed_form) = 1.15024164899 0.133053808869
absolute error = 9.550e-07
relative error = 8.248e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.004
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = 1.15090498225 0.133747845876
y[1] (closed_form) = 1.15090521443 0.133748741591
absolute error = 9.253e-07
relative error = 7.986e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.132
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.031
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1225 0.201
h = 0.003 0.006
y[1] (numeric) = 1.15090988519 0.136466758074
y[1] (closed_form) = 1.1509096277 0.136467556324
absolute error = 8.388e-07
relative error = 7.237e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.132
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.574
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = 1.15285071655 0.140591371385
y[1] (closed_form) = 1.15285039497 0.140593108488
absolute error = 1.767e-06
relative error = 0.0001521 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.136
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.592
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = 1.15283505618 0.143991698806
y[1] (closed_form) = 1.15283487844 0.143992842985
absolute error = 1.158e-06
relative error = 9.967e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.136
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.282
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=304.4MB, alloc=44.3MB, time=3.74
x[1] = 0.1257 0.215
h = 0.001 0.001
y[1] (numeric) = 1.15285174618 0.14603235964
y[1] (closed_form) = 1.15285180582 0.146033477887
absolute error = 1.120e-06
relative error = 9.637e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.137
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.007
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1267 0.216
h = 0.001 0.003
y[1] (numeric) = 1.15351416696 0.146729279887
y[1] (closed_form) = 1.15351433828 0.146730345752
absolute error = 1.080e-06
relative error = 9.284e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.138
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.78
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = 1.15414222954 0.148785877305
y[1] (closed_form) = 1.15414216912 0.148787040632
absolute error = 1.165e-06
relative error = 0.0001001 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.706
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1278 0.223
h = 0.003 0.006
y[1] (numeric) = 1.15414001093 0.15150718899
y[1] (closed_form) = 1.15413977768 0.151508226284
absolute error = 1.063e-06
relative error = 9.134e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.587
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = 1.1560722156 0.155640256775
y[1] (closed_form) = 1.15607192545 0.15564223091
absolute error = 1.995e-06
relative error = 0.0001711 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.143
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.598
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=349.8MB, alloc=44.3MB, time=4.30
x[1] = 0.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = 1.1560480632 0.159043530452
y[1] (closed_form) = 1.1560479121 0.159044912175
absolute error = 1.390e-06
relative error = 0.0001191 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.287
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.131 0.237
h = 0.001 0.001
y[1] (numeric) = 1.15605968161 0.161086036189
y[1] (closed_form) = 1.15605976706 0.16108739028
absolute error = 1.357e-06
relative error = 0.0001162 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.01
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.132 0.238
h = 0.001 0.003
y[1] (numeric) = 1.15672095295 0.161785224113
y[1] (closed_form) = 1.15672114939 0.161786525132
absolute error = 1.316e-06
relative error = 0.0001127 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.145
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.797
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.133 0.241
h = 0.0001 0.004
y[1] (numeric) = 1.1573444511 0.163845205494
y[1] (closed_form) = 1.15734441715 0.163846605436
absolute error = 1.400e-06
relative error = 0.0001198 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.716
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1331 0.245
h = 0.003 0.006
y[1] (numeric) = 1.15733546411 0.166568930908
y[1] (closed_form) = 1.15733525686 0.166570206442
absolute error = 1.292e-06
relative error = 0.0001105 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.6
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=395.1MB, alloc=44.3MB, time=4.85
x[1] = 0.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = 1.15925912825 0.170710494784
y[1] (closed_form) = 1.15925887121 0.170712705036
absolute error = 2.225e-06
relative error = 0.0001899 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.603
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = 1.15922652862 0.174116769839
y[1] (closed_form) = 1.15922640586 0.174118388268
absolute error = 1.623e-06
relative error = 0.0001385 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.291
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1363 0.259
h = 0.001 0.001
y[1] (numeric) = 1.1592331029 0.17616115312
y[1] (closed_form) = 1.15923321584 0.176162742245
absolute error = 1.593e-06
relative error = 0.0001359 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.152
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.014
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1373 0.26
h = 0.001 0.003
y[1] (numeric) = 1.15989324477 0.176862611079
y[1] (closed_form) = 1.15989346799 0.176864146456
absolute error = 1.552e-06
relative error = 0.0001322 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.153
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.814
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = 1.160512216 0.178926001069
y[1] (closed_form) = 1.1605122102 0.178927636799
absolute error = 1.636e-06
relative error = 0.0001393 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.154
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.726
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=440.5MB, alloc=44.3MB, time=5.41
x[1] = 0.1384 0.267
h = 0.003 0.006
y[1] (numeric) = 1.16049649698 0.181652183745
y[1] (closed_form) = 1.16049631744 0.18165369669
absolute error = 1.524e-06
relative error = 0.0001297 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.155
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.613
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = 1.16241170691 0.185802283577
y[1] (closed_form) = 1.1624114846 0.185804729007
absolute error = 2.456e-06
relative error = 0.0002086 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.609
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = 1.1623707055 0.189211614004
y[1] (closed_form) = 1.16237061275 0.18921346828
absolute error = 1.857e-06
relative error = 0.0001576 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.296
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1416 0.281
h = 0.001 0.001
y[1] (numeric) = 1.16237226352 0.191257906789
y[1] (closed_form) = 1.16237240559 0.191259730113
absolute error = 1.829e-06
relative error = 0.0001553 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.018
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1426 0.282
h = 0.001 0.003
y[1] (numeric) = 1.16303129577 0.191961636781
y[1] (closed_form) = 1.16303154742 0.191963405699
absolute error = 1.787e-06
relative error = 0.0001516 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.161
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.832
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=486.1MB, alloc=44.3MB, time=5.97
x[1] = 0.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = 1.16364577777 0.194028459222
y[1] (closed_form) = 1.16364580177 0.194030329889
absolute error = 1.871e-06
relative error = 0.0001586 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.162
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.736
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1437 0.289
h = 0.003 0.006
y[1] (numeric) = 1.16362336359 0.196757141787
y[1] (closed_form) = 1.16362321345 0.196758891289
absolute error = 1.756e-06
relative error = 0.0001488 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.626
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = 1.16553020575 0.200915815697
y[1] (closed_form) = 1.16553001979 0.200918495347
absolute error = 2.686e-06
relative error = 0.0002271 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.167
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.615
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = 1.16548084864 0.20432825436
y[1] (closed_form) = 1.16548078755 0.204330343599
absolute error = 2.090e-06
relative error = 0.0001766 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.168
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.301
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1469 0.303
h = 0.001 0.001
y[1] (numeric) = 1.1654774186 0.20637648792
y[1] (closed_form) = 1.16547759144 0.206378544585
absolute error = 2.064e-06
relative error = 0.0001744 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.168
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.022
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=531.4MB, alloc=44.3MB, time=6.52
x[1] = 0.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = 1.166135361 0.207082491592
y[1] (closed_form) = 1.16613564271 0.207084493209
absolute error = 2.021e-06
relative error = 0.0001707 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.169
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.138
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.148 0.308
h = 0.003 0.006
y[1] (numeric) = 1.16610749521 0.209813239216
y[1] (closed_form) = 1.16610729051 0.209815162109
absolute error = 1.934e-06
relative error = 0.0001632 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.638
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151 0.314
h = 0.0001 0.005
y[1] (numeric) = 1.16800710122 0.213979224342
y[1] (closed_form) = 1.16800686663 0.213982075371
absolute error = 2.861e-06
relative error = 0.0002409 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.174
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.621
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = 1.1679505513 0.217394281159
y[1] (closed_form) = 1.16795043758 0.217396542422
absolute error = 2.264e-06
relative error = 0.0001906 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.175
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.305
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1512 0.322
h = 0.001 0.001
y[1] (numeric) = 1.16794282694 0.219444150835
y[1] (closed_form) = 1.16794294637 0.219446378137
absolute error = 2.231e-06
relative error = 0.0001877 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.175
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.025
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=576.6MB, alloc=44.3MB, time=7.07
x[1] = 0.1522 0.323
h = 0.001 0.003
y[1] (numeric) = 1.16859981989 0.220152100006
y[1] (closed_form) = 1.16860004758 0.220154271712
absolute error = 2.184e-06
relative error = 0.0001836 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.176
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.866
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = 1.16920600778 0.222225317744
y[1] (closed_form) = 1.16920601041 0.222227593729
absolute error = 2.276e-06
relative error = 0.0001912 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.756
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1533 0.33
h = 0.003 0.006
y[1] (numeric) = 1.16917120429 0.224958683654
y[1] (closed_form) = 1.16917103208 0.224960841471
absolute error = 2.165e-06
relative error = 0.0001818 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.652
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = 1.17106260311 0.229133310247
y[1] (closed_form) = 1.17106240779 0.229136393676
absolute error = 3.090e-06
relative error = 0.0002589 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.182
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.627
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = 1.17099778416 0.232551571203
y[1] (closed_form) = 1.17099770512 0.232554065746
absolute error = 2.496e-06
relative error = 0.0002091 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.183
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.31
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=622.0MB, alloc=44.3MB, time=7.62
x[1] = 0.1565 0.344
h = 0.001 0.001
y[1] (numeric) = 1.17098512478 0.234603438352
y[1] (closed_form) = 1.17098527794 0.234605897361
absolute error = 2.464e-06
relative error = 0.0002063 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.184
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.029
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1575 0.345
h = 0.001 0.003
y[1] (numeric) = 1.17164106437 0.235313663583
y[1] (closed_form) = 1.17164132507 0.235316066386
absolute error = 2.417e-06
relative error = 0.0002022 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.185
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.886
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = 1.17224287137 0.237390378026
y[1] (closed_form) = 1.17224290844 0.23739288641
absolute error = 2.509e-06
relative error = 0.0002097 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.186
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.766
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1586 0.352
h = 0.003 0.006
y[1] (numeric) = 1.17220148028 0.240126361183
y[1] (closed_form) = 1.17220134218 0.240128753006
absolute error = 2.396e-06
relative error = 0.0002002 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.187
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.667
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = 1.17408475845 0.244309662476
y[1] (closed_form) = 1.17408460393 0.244312977291
absolute error = 3.318e-06
relative error = 0.0002767 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.191
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.633
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=667.5MB, alloc=44.3MB, time=8.18
x[1] = 0.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = 1.17401171815 0.247731177181
y[1] (closed_form) = 1.17401167535 0.247733904061
absolute error = 2.727e-06
relative error = 0.0002273 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.316
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1618 0.366
h = 0.001 0.001
y[1] (numeric) = 1.17399415287 0.249785071103
y[1] (closed_form) = 1.17399434132 0.249787760901
absolute error = 2.696e-06
relative error = 0.0002246 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.193
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.033
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1628 0.367
h = 0.001 0.003
y[1] (numeric) = 1.17464905855 0.250497573068
y[1] (closed_form) = 1.17464935381 0.250500206066
absolute error = 2.650e-06
relative error = 0.0002206 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.194
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.905
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = 1.17524652284 0.252577804995
y[1] (closed_form) = 1.1752465959 0.252580544844
absolute error = 2.741e-06
relative error = 0.000228 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.195
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.778
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1639 0.374
h = 0.003 0.006
y[1] (numeric) = 1.17519858271 0.255316444498
y[1] (closed_form) = 1.17519848032 0.255319069385
absolute error = 2.627e-06
relative error = 0.0002184 %
Correct digits = 6
memory used=713.1MB, alloc=52.3MB, time=8.75
Radius of convergence (given) for eq 1 = 2.196
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.682
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = 1.17707382671 0.259508452047
y[1] (closed_form) = 1.17707371449 0.259511997215
absolute error = 3.547e-06
relative error = 0.0002943 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.2
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.64
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.167 0.385
h = 0.0001 0.003
y[1] (numeric) = 1.17699261322 0.26293326897
y[1] (closed_form) = 1.17699260822 0.262936227222
absolute error = 2.958e-06
relative error = 0.0002453 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.201
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.321
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1671 0.388
h = 0.001 0.001
y[1] (numeric) = 1.17697017145 0.264989218271
y[1] (closed_form) = 1.17697039672 0.264992137922
absolute error = 2.928e-06
relative error = 0.0002427 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.202
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.037
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1681 0.389
h = 0.001 0.003
y[1] (numeric) = 1.17762406254 0.265703997318
y[1] (closed_form) = 1.17762439389 0.265706859589
absolute error = 2.881e-06
relative error = 0.0002387 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.203
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.925
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=758.5MB, alloc=52.3MB, time=9.30
x[1] = 0.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = 1.17821722236 0.267787766726
y[1] (closed_form) = 1.17821733296 0.267790737086
absolute error = 2.972e-06
relative error = 0.000246 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.204
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.789
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1692 0.396
h = 0.003 0.006
y[1] (numeric) = 1.17816277215 0.270529100756
y[1] (closed_form) = 1.17816270702 0.270531957749
absolute error = 2.858e-06
relative error = 0.0002364 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.205
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.697
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = 1.18003006834 0.274729844467
y[1] (closed_form) = 1.18002999988 0.274733618939
absolute error = 3.775e-06
relative error = 0.0003116 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.209
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.647
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = 1.17994073025 0.278158010932
y[1] (closed_form) = 1.17994076457 0.278161199573
absolute error = 3.189e-06
relative error = 0.000263 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.21
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.327
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1724 0.41
h = 0.001 0.001
y[1] (numeric) = 1.17991344166 0.28021604353
y[1] (closed_form) = 1.17991370526 0.280219192078
absolute error = 3.160e-06
relative error = 0.0002605 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.211
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.042
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=804.1MB, alloc=52.3MB, time=9.85
x[1] = 0.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = 1.18056633734 0.280933099685
y[1] (closed_form) = 1.18056670628 0.28093619029
absolute error = 3.113e-06
relative error = 0.0002565 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.212
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.258
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1735 0.415
h = 0.003 0.006
y[1] (numeric) = 1.18050658801 0.283676654938
y[1] (closed_form) = 1.1805064752 0.283679684639
absolute error = 3.032e-06
relative error = 0.0002497 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.71
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = 1.18236700753 0.287884847867
y[1] (closed_form) = 1.18236689695 0.287888792645
absolute error = 3.946e-06
relative error = 0.0003243 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.217
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.653
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = 1.18227067466 0.291315838549
y[1] (closed_form) = 1.18227066305 0.29131919843
absolute error = 3.360e-06
relative error = 0.0002759 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.218
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.331
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1767 0.429
h = 0.001 0.001
y[1] (numeric) = 1.18223921276 0.293375628957
y[1] (closed_form) = 1.18223942958 0.293378947469
absolute error = 3.326e-06
relative error = 0.000273 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.219
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.045
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=849.5MB, alloc=52.3MB, time=10.39
x[1] = 0.1777 0.43
h = 0.001 0.003
y[1] (numeric) = 1.18289123977 0.294094633405
y[1] (closed_form) = 1.1828915613 0.294097893495
absolute error = 3.276e-06
relative error = 0.0002688 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.22
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.964
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = 1.18347644928 0.296184985629
y[1] (closed_form) = 1.18347655274 0.29618835604
absolute error = 3.372e-06
relative error = 0.0002764 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.221
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.811
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1788 0.437
h = 0.003 0.006
y[1] (numeric) = 1.18340995697 0.298931355591
y[1] (closed_form) = 1.18340988427 0.298934615577
absolute error = 3.261e-06
relative error = 0.0002672 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.222
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.726
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = 1.18526258867 0.303148337021
y[1] (closed_form) = 1.18526252454 0.303152509127
absolute error = 4.173e-06
relative error = 0.0003411 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.226
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.66
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = 1.18515822219 0.306582762865
y[1] (closed_form) = 1.18515825267 0.306586351277
absolute error = 3.589e-06
relative error = 0.0002931 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.227
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.337
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=894.8MB, alloc=52.3MB, time=10.93
x[1] = 0.182 0.451
h = 0.001 0.001
y[1] (numeric) = 1.18512196897 0.308644687041
y[1] (closed_form) = 1.18512222685 0.308648232643
absolute error = 3.555e-06
relative error = 0.0002903 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.228
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.05
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.183 0.452
h = 0.001 0.003
y[1] (numeric) = 1.1857730359 0.309365968047
y[1] (closed_form) = 1.18577339775 0.309369454694
absolute error = 3.505e-06
relative error = 0.000286 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.229
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.985
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.184 0.455
h = 0.0001 0.004
y[1] (numeric) = 1.18635405035 0.311459911177
y[1] (closed_form) = 1.1863541956 0.311463509291
absolute error = 3.601e-06
relative error = 0.0002936 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.231
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.823
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1841 0.459
h = 0.003 0.006
y[1] (numeric) = 1.18628116073 0.314209080317
y[1] (closed_form) = 1.18628112963 0.314212569577
absolute error = 3.489e-06
relative error = 0.0002843 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.232
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.742
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = 1.18812609049 0.318434875541
y[1] (closed_form) = 1.18812607419 0.318439273885
absolute error = 4.398e-06
relative error = 0.0003576 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.236
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.667
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=940.3MB, alloc=52.3MB, time=11.48
x[1] = 0.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = 1.18801374012 0.321872780623
y[1] (closed_form) = 1.18801381412 0.321876596536
absolute error = 3.817e-06
relative error = 0.0003101 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.237
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.343
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1873 0.473
h = 0.001 0.001
y[1] (numeric) = 1.18797272585 0.32393686452
y[1] (closed_form) = 1.18797302622 0.323940636209
absolute error = 3.784e-06
relative error = 0.0003073 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.238
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.054
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1883 0.474
h = 0.001 0.003
y[1] (numeric) = 1.18862285147 0.324660421234
y[1] (closed_form) = 1.18862325506 0.324664133451
absolute error = 3.734e-06
relative error = 0.0003031 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.239
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.007
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = 1.18919970921 0.326757972331
y[1] (closed_form) = 1.18919989767 0.326761797127
absolute error = 3.829e-06
relative error = 0.0003105 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.241
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.835
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1894 0.481
h = 0.003 0.006
y[1] (numeric) = 1.18912046239 0.329509975308
y[1] (closed_form) = 1.18912047435 0.329513692811
absolute error = 3.718e-06
relative error = 0.0003013 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.242
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.758
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=985.6MB, alloc=52.3MB, time=12.02
x[1] = 0.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = 1.19095777583 0.333744608054
y[1] (closed_form) = 1.19095780873 0.333749231529
absolute error = 4.624e-06
relative error = 0.0003738 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.246
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.674
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = 1.19083749159 0.337186035319
y[1] (closed_form) = 1.19083761053 0.337190077688
absolute error = 4.044e-06
relative error = 0.0003268 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.247
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.349
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1926 0.495
h = 0.001 0.001
y[1] (numeric) = 1.19079174676 0.339252304208
y[1] (closed_form) = 1.19079209102 0.339256300964
absolute error = 4.012e-06
relative error = 0.000324 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.248
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.059
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1936 0.496
h = 0.001 0.003
y[1] (numeric) = 1.19144094967 0.33997813549
y[1] (closed_form) = 1.19144139641 0.339982072273
absolute error = 3.962e-06
relative error = 0.0003198 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.249
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.029
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = 1.192013689 0.342079310871
y[1] (closed_form) = 1.19201392209 0.342083361314
absolute error = 4.057e-06
relative error = 0.0003272 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.251
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.848
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1031.1MB, alloc=52.3MB, time=12.56
x[1] = 0.1947 0.503
h = 0.003 0.006
y[1] (numeric) = 1.19192812535 0.344834181441
y[1] (closed_form) = 1.1919281818 0.344838126143
absolute error = 3.945e-06
relative error = 0.0003179 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.252
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.775
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = 1.19375790779 0.349077673897
y[1] (closed_form) = 1.19375799122 0.349082521388
absolute error = 4.848e-06
relative error = 0.0003898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.256
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.682
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = 1.19362974 0.35252266517
y[1] (closed_form) = 1.19362990528 0.352526932932
absolute error = 4.271e-06
relative error = 0.0003432 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.257
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.355
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1979 0.517
h = 0.001 0.001
y[1] (numeric) = 1.19357929524 0.354591143643
y[1] (closed_form) = 1.19357968476 0.354595364433
absolute error = 4.239e-06
relative error = 0.0003404 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.258
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.064
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = 1.19422759389 0.355319248068
y[1] (closed_form) = 1.19422808514 0.355323408401
absolute error = 4.189e-06
relative error = 0.0003362 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.259
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.392
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1076.6MB, alloc=52.3MB, time=13.10
x[1] = 0.199 0.522
h = 0.003 0.006
y[1] (numeric) = 1.19413688987 0.358076478425
y[1] (closed_form) = 1.1941369052 0.35808059464
absolute error = 4.116e-06
relative error = 0.0003302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.26
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.789
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.202 0.528
h = 0.0001 0.005
y[1] (numeric) = 1.1959601521 0.362327525304
y[1] (closed_form) = 1.19596019958 0.362332541582
absolute error = 5.017e-06
relative error = 0.0004014 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.264
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.688
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = 1.19582519578 0.365775523904
y[1] (closed_form) = 1.19582532152 0.365779961635
absolute error = 4.440e-06
relative error = 0.000355 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.266
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.36
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2022 0.536
h = 0.001 0.001
y[1] (numeric) = 1.1957707034 0.367845868006
y[1] (closed_form) = 1.19577105247 0.367850257604
absolute error = 4.403e-06
relative error = 0.000352 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.266
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.068
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2032 0.537
h = 0.001 0.003
y[1] (numeric) = 1.19641821129 0.36857591725
y[1] (closed_form) = 1.19641866145 0.368580245976
absolute error = 4.352e-06
relative error = 0.0003476 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.268
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.071
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1122.0MB, alloc=52.3MB, time=13.64
x[1] = 0.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = 1.19698334543 0.370683829534
y[1] (closed_form) = 1.1969835847 0.370688273863
absolute error = 4.451e-06
relative error = 0.0003552 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.871
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2043 0.544
h = 0.003 0.006
y[1] (numeric) = 1.19688610068 0.373444048689
y[1] (closed_form) = 1.1968861631 0.373448390138
absolute error = 4.342e-06
relative error = 0.0003463 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.27
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.806
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = 1.19870198958 0.377703993566
y[1] (closed_form) = 1.19870209 0.377709231767
absolute error = 5.239e-06
relative error = 0.0004169 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.275
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.696
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = 1.19855924353 0.381155631636
y[1] (closed_form) = 1.19855941812 0.381160292768
absolute error = 4.664e-06
relative error = 0.0003709 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.276
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.366
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2075 0.558
h = 0.001 0.001
y[1] (numeric) = 1.1985001083 0.383228229664
y[1] (closed_form) = 1.19850050513 0.383232841354
absolute error = 4.629e-06
relative error = 0.0003679 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.277
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.073
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1167.5MB, alloc=52.3MB, time=14.18
x[1] = 0.2085 0.559
h = 0.001 0.003
y[1] (numeric) = 1.19914674582 0.383960548886
y[1] (closed_form) = 1.19914724298 0.383965099248
absolute error = 4.577e-06
relative error = 0.0003635 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.278
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.094
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = 1.19970787068 0.386072128592
y[1] (closed_form) = 1.19970815845 0.386076795548
absolute error = 4.676e-06
relative error = 0.000371 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.28
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.885
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2096 0.566
h = 0.003 0.006
y[1] (numeric) = 1.19960442527 0.388835307451
y[1] (closed_form) = 1.19960453613 0.388839873049
absolute error = 4.567e-06
relative error = 0.0003622 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.281
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.824
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = 1.20141302517 0.393104168253
y[1] (closed_form) = 1.2014131798 0.393109627228
absolute error = 5.461e-06
relative error = 0.000432 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.285
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.704
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = 1.20126254036 0.396559484444
y[1] (closed_form) = 1.20126276512 0.39656436788
absolute error = 4.889e-06
relative error = 0.0003864 %
Correct digits = 5
memory used=1212.9MB, alloc=52.3MB, time=14.73
Radius of convergence (given) for eq 1 = 2.287
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.373
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2128 0.58
h = 0.001 0.001
y[1] (numeric) = 1.20119879327 0.39863435908
y[1] (closed_form) = 1.20119923916 0.398639191793
absolute error = 4.853e-06
relative error = 0.0003835 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.078
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2138 0.581
h = 0.001 0.003
y[1] (numeric) = 1.20184457838 0.399368946083
y[1] (closed_form) = 1.20184512385 0.399373717027
absolute error = 4.802e-06
relative error = 0.0003792 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.289
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.118
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = 1.20240173202 0.401484206766
y[1] (closed_form) = 1.20240206959 0.401489095264
absolute error = 4.900e-06
relative error = 0.0003865 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.291
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.898
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2149 0.588
h = 0.003 0.006
y[1] (numeric) = 1.20229212701 0.404250375652
y[1] (closed_form) = 1.20229228764 0.404255164301
absolute error = 4.791e-06
relative error = 0.0003777 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.292
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.842
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1258.4MB, alloc=52.3MB, time=15.27
x[1] = 0.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = 1.20409352182 0.408528168869
y[1] (closed_form) = 1.20409373188 0.408533847462
absolute error = 5.682e-06
relative error = 0.0004469 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.296
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.712
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.218 0.599
h = 0.0001 0.003
y[1] (numeric) = 1.20393534941 0.411987200742
y[1] (closed_form) = 1.20393562561 0.411992305374
absolute error = 5.112e-06
relative error = 0.0004017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.297
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.379
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2181 0.602
h = 0.001 0.001
y[1] (numeric) = 1.20386702155 0.414064374009
y[1] (closed_form) = 1.20386751776 0.414069426664
absolute error = 5.077e-06
relative error = 0.0003988 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.298
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.083
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2191 0.603
h = 0.001 0.003
y[1] (numeric) = 1.20451197201 0.414801226342
y[1] (closed_form) = 1.20451256706 0.414806216802
absolute error = 5.026e-06
relative error = 0.0003945 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.3
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.142
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = 1.20506519238 0.416920180868
y[1] (closed_form) = 1.20506558103 0.41692528981
absolute error = 5.124e-06
relative error = 0.0004018 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.301
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.912
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1303.8MB, alloc=52.3MB, time=15.81
x[1] = 0.2202 0.61
h = 0.003 0.006
y[1] (numeric) = 1.20494946895 0.419689369229
y[1] (closed_form) = 1.20494968064 0.419694379822
absolute error = 5.015e-06
relative error = 0.000393 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.302
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.86
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = 1.20674374215 0.423976109949
y[1] (closed_form) = 1.20674400882 0.423982006995
absolute error = 5.903e-06
relative error = 0.0004615 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.307
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.72
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = 1.20657793342 0.42743889398
y[1] (closed_form) = 1.20657826232 0.42744421869
absolute error = 5.335e-06
relative error = 0.0004168 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.308
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.386
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2234 0.624
h = 0.001 0.001
y[1] (numeric) = 1.20650505593 0.429518387252
y[1] (closed_form) = 1.20650560373 0.429523658758
absolute error = 5.300e-06
relative error = 0.0004138 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.309
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.088
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = 1.20714918934 0.430257502216
y[1] (closed_form) = 1.20714983521 0.430262711116
absolute error = 5.249e-06
relative error = 0.0004096 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.537
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1349.3MB, alloc=52.3MB, time=16.36
x[1] = 0.2245 0.629
h = 0.003 0.006
y[1] (numeric) = 1.2070284881 0.433029171715
y[1] (closed_form) = 1.20702866489 0.433034352181
absolute error = 5.183e-06
relative error = 0.0004042 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.312
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.876
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = 1.20881659092 0.437323541684
y[1] (closed_form) = 1.20881682746 0.437329605622
absolute error = 6.069e-06
relative error = 0.0004721 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.316
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.727
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = 1.20864420502 0.440789493711
y[1] (closed_form) = 1.20864450041 0.440794986701
absolute error = 5.501e-06
relative error = 0.0004276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.318
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.391
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2277 0.643
h = 0.001 0.001
y[1] (numeric) = 1.20856740839 0.4428709469
y[1] (closed_form) = 1.20856792172 0.442876385637
absolute error = 5.463e-06
relative error = 0.0004244 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.319
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2287 0.644
h = 0.001 0.003
y[1] (numeric) = 1.20921082553 0.443611997666
y[1] (closed_form) = 1.2092114363 0.443617373446
absolute error = 5.410e-06
relative error = 0.0004201 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.32
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.187
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1394.8MB, alloc=52.3MB, time=16.90
x[1] = 0.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = 1.20975678325 0.445737811708
y[1] (closed_form) = 1.2097571904 0.445743307637
absolute error = 5.511e-06
relative error = 0.0004275 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.322
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.938
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2298 0.651
h = 0.003 0.006
y[1] (numeric) = 1.20962974804 0.44851262232
y[1] (closed_form) = 1.20962997824 0.448518022655
absolute error = 5.405e-06
relative error = 0.000419 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.323
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.894
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = 1.21141088314 0.452815965199
y[1] (closed_form) = 1.21141117847 0.452822245416
absolute error = 6.287e-06
relative error = 0.0004861 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.327
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.735
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = 1.21123095625 0.456285735032
y[1] (closed_form) = 1.21123130661 0.456291446008
absolute error = 5.722e-06
relative error = 0.0004421 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.329
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.398
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.233 0.665
h = 0.001 0.001
y[1] (numeric) = 1.21114966787 0.458369546659
y[1] (closed_form) = 1.21115023504 0.458375202206
absolute error = 5.684e-06
relative error = 0.0004389 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.33
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.098
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1440.1MB, alloc=52.3MB, time=17.44
x[1] = 0.234 0.666
h = 0.001 0.003
y[1] (numeric) = 1.21179230022 0.459112854608
y[1] (closed_form) = 1.21179296407 0.459118446813
absolute error = 5.631e-06
relative error = 0.0004346 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.331
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.213
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.235 0.669
h = 0.0001 0.004
y[1] (numeric) = 1.21233443239 0.461242396041
y[1] (closed_form) = 1.21233489412 0.461248109239
absolute error = 5.732e-06
relative error = 0.0004419 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.333
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.952
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2351 0.673
h = 0.003 0.006
y[1] (numeric) = 1.21220139671 0.464020306134
y[1] (closed_form) = 1.21220168154 0.464025925201
absolute error = 5.626e-06
relative error = 0.0004335 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.334
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.913
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = 1.21397564617 0.468332633139
y[1] (closed_form) = 1.2139760014 0.46833912845
absolute error = 6.505e-06
relative error = 0.0004999 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.339
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.744
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = 1.21378822985 0.471806254223
y[1] (closed_form) = 1.21378863637 0.471812182041
absolute error = 5.942e-06
relative error = 0.0004563 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.405
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1485.5MB, alloc=52.3MB, time=17.98
x[1] = 0.2383 0.687
h = 0.001 0.001
y[1] (numeric) = 1.21370248102 0.473892443837
y[1] (closed_form) = 1.21370310319 0.473898315077
absolute error = 5.904e-06
relative error = 0.0004531 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.341
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.103
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2393 0.688
h = 0.001 0.003
y[1] (numeric) = 1.21434434561 0.474638005604
y[1] (closed_form) = 1.21434506371 0.474643813132
absolute error = 5.852e-06
relative error = 0.0004488 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.343
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.238
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = 1.21488268964 0.476771284741
y[1] (closed_form) = 1.21488320711 0.476777214076
absolute error = 5.952e-06
relative error = 0.0004561 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.344
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.966
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2404 0.695
h = 0.003 0.006
y[1] (numeric) = 1.21474369495 0.479552320482
y[1] (closed_form) = 1.21474403559 0.479558157136
absolute error = 5.847e-06
relative error = 0.0004477 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.346
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.933
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = 1.21651114028 0.483873641537
y[1] (closed_form) = 1.21651155652 0.483880350753
absolute error = 6.722e-06
relative error = 0.0005134 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.35
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.752
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1530.9MB, alloc=52.3MB, time=18.53
x[1] = 0.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = 1.21631628616 0.48735114628
y[1] (closed_form) = 1.21631674997 0.48735728979
absolute error = 6.161e-06
relative error = 0.0004702 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.352
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.412
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2436 0.709
h = 0.001 0.001
y[1] (numeric) = 1.21622610816 0.48943973281
y[1] (closed_form) = 1.21622678648 0.489445818617
absolute error = 6.123e-06
relative error = 0.0004671 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.353
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.109
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2446 0.71
h = 0.001 0.003
y[1] (numeric) = 1.21686722185 0.49018754481
y[1] (closed_form) = 1.21686799534 0.49019356655
absolute error = 6.071e-06
relative error = 0.0004628 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.354
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.264
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = 1.21740181497 0.492324571332
y[1] (closed_form) = 1.21740238934 0.492330715665
absolute error = 6.171e-06
relative error = 0.0004699 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.981
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2457 0.717
h = 0.003 0.006
y[1] (numeric) = 1.21725690274 0.495108758065
y[1] (closed_form) = 1.21725730037 0.495114811152
absolute error = 6.066e-06
relative error = 0.0004616 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.357
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.952
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1576.3MB, alloc=52.3MB, time=19.07
x[1] = 0.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = 1.21901762492 0.499439081829
y[1] (closed_form) = 1.21901810322 0.499446003754
absolute error = 6.938e-06
relative error = 0.0005267 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.362
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.761
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = 1.21881538461 0.502920501615
y[1] (closed_form) = 1.21881590684 0.502926859659
absolute error = 6.379e-06
relative error = 0.0004838 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.364
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.419
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2489 0.731
h = 0.001 0.001
y[1] (numeric) = 1.21872080875 0.505011503372
y[1] (closed_form) = 1.21872154432 0.505017802616
absolute error = 6.342e-06
relative error = 0.0004807 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.365
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.114
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = 1.21936118817 0.505761561812
y[1] (closed_form) = 1.21936201818 0.505767796646
absolute error = 6.290e-06
relative error = 0.0004765 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.366
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.694
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.25 0.736
h = 0.003 0.006
y[1] (numeric) = 1.21921146238 0.508548334533
y[1] (closed_form) = 1.21921183094 0.508554555481
absolute error = 6.232e-06
relative error = 0.0004717 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.367
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.969
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1621.7MB, alloc=52.3MB, time=19.62
x[1] = 0.253 0.742
h = 0.0001 0.005
y[1] (numeric) = 1.22096635452 0.512886334738
y[1] (closed_form) = 1.2209668081 0.512893421345
absolute error = 7.101e-06
relative error = 0.0005362 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.372
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.768
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = 1.22075775064 0.516371061675
y[1] (closed_form) = 1.22075824503 0.516377585957
absolute error = 6.543e-06
relative error = 0.0004936 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.374
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.425
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2532 0.75
h = 0.001 0.001
y[1] (numeric) = 1.22065938523 0.518464104701
y[1] (closed_form) = 1.22066009199 0.518470569246
absolute error = 6.503e-06
relative error = 0.0004904 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.119
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2542 0.751
h = 0.001 0.003
y[1] (numeric) = 1.22129911912 0.519216085127
y[1] (closed_form) = 1.22129991966 0.519222484969
absolute error = 6.450e-06
relative error = 0.000486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.376
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.313
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = 1.22182678625 0.521360064674
y[1] (closed_form) = 1.22182739045 0.521366588516
absolute error = 6.552e-06
relative error = 0.0004932 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.378
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.009
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1667.3MB, alloc=52.3MB, time=20.17
x[1] = 0.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = 1.22167093504 0.524150110008
y[1] (closed_form) = 1.22167136269 0.52415654524
absolute error = 6.449e-06
relative error = 0.0004851 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.379
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.379
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2554 0.762
h = 0.003 0.006
y[1] (numeric) = 1.22151378252 0.526940406258
y[1] (closed_form) = 1.22151421016 0.52694684149
absolute error = 6.449e-06
relative error = 0.0004848 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.381
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.991
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = 1.22326063729 0.531288740367
y[1] (closed_form) = 1.22326115585 0.531296036981
absolute error = 7.315e-06
relative error = 0.0005485 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.385
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.778
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = 1.22304333966 0.534777858944
y[1] (closed_form) = 1.22304389481 0.534784595323
absolute error = 6.759e-06
relative error = 0.0005064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.387
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.433
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2586 0.776
h = 0.001 0.001
y[1] (numeric) = 1.222939796 0.536873614706
y[1] (closed_form) = 1.22294056218 0.536880290077
absolute error = 6.719e-06
relative error = 0.0005031 %
Correct digits = 5
memory used=1712.7MB, alloc=52.3MB, time=20.71
Radius of convergence (given) for eq 1 = 2.388
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.125
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2596 0.777
h = 0.001 0.003
y[1] (numeric) = 1.2235786231 0.53762819511
y[1] (closed_form) = 1.22357948221 0.537634805381
absolute error = 6.666e-06
relative error = 0.0004988 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.389
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.343
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = 1.22410187799 0.53977646534
y[1] (closed_form) = 1.22410254247 0.53978320049
absolute error = 6.768e-06
relative error = 0.0005059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.391
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.026
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2607 0.784
h = 0.003 0.006
y[1] (numeric) = 1.22393910916 0.542570074913
y[1] (closed_form) = 1.22393959721 0.542576723094
absolute error = 6.666e-06
relative error = 0.0004979 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.393
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.012
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = 1.22567948251 0.546927434447
y[1] (closed_form) = 1.22568006626 0.546934940169
absolute error = 7.528e-06
relative error = 0.0005609 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.398
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.787
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1758.2MB, alloc=52.3MB, time=21.26
x[1] = 0.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = 1.22545495381 0.550420559681
y[1] (closed_form) = 1.22545557069 0.550427507099
absolute error = 6.975e-06
relative error = 0.0005192 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.399
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.44
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2639 0.798
h = 0.001 0.001
y[1] (numeric) = 1.22534710629 0.552518784083
y[1] (closed_form) = 1.22534793302 0.552525669473
absolute error = 6.935e-06
relative error = 0.0005159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.131
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2649 0.799
h = 0.001 0.003
y[1] (numeric) = 1.22598524863 0.553275598984
y[1] (closed_form) = 1.22598616754 0.553282418973
absolute error = 6.882e-06
relative error = 0.0005116 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.37
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = 1.22650490047 0.555427651282
y[1] (closed_form) = 1.22650562625 0.555434596826
absolute error = 6.983e-06
relative error = 0.0005187 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.404
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.041
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.266 0.806
h = 0.003 0.006
y[1] (numeric) = 1.22633638015 0.558224507937
y[1] (closed_form) = 1.22633692966 0.558231367891
absolute error = 6.882e-06
relative error = 0.0005108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.405
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.032
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1803.6MB, alloc=52.3MB, time=21.80
x[1] = 0.269 0.812
h = 0.0001 0.005
y[1] (numeric) = 1.22807035063 0.562590896734
y[1] (closed_form) = 1.22807100053 0.562598610357
absolute error = 7.741e-06
relative error = 0.0005731 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.797
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = 1.22783864239 0.56608805602
y[1] (closed_form) = 1.227839322 0.566095213299
absolute error = 7.189e-06
relative error = 0.0005317 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.412
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.448
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2692 0.82
h = 0.001 0.001
y[1] (numeric) = 1.2277265222 0.568188764981
y[1] (closed_form) = 1.22772741049 0.568195859238
absolute error = 7.150e-06
relative error = 0.0005285 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.413
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.137
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2702 0.821
h = 0.001 0.003
y[1] (numeric) = 1.22836399561 0.5689478098
y[1] (closed_form) = 1.22836497534 0.568954838368
absolute error = 7.097e-06
relative error = 0.0005242 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.414
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.398
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = 1.22888008062 0.571103650853
y[1] (closed_form) = 1.2288808687 0.571110805623
absolute error = 7.198e-06
relative error = 0.0005312 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.416
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.057
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1849.0MB, alloc=52.3MB, time=22.35
x[1] = 0.2713 0.828
h = 0.003 0.006
y[1] (numeric) = 1.22870585015 0.573903775943
y[1] (closed_form) = 1.22870646215 0.573910846488
absolute error = 7.097e-06
relative error = 0.0005233 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.418
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.053
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = 1.23043349564 0.578279196729
y[1] (closed_form) = 1.23043421264 0.578287117041
absolute error = 7.953e-06
relative error = 0.0005849 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.422
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.806
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = 1.23019465928 0.581780416508
y[1] (closed_form) = 1.23019540263 0.581787782466
absolute error = 7.403e-06
relative error = 0.000544 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.424
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.455
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2745 0.842
h = 0.001 0.001
y[1] (numeric) = 1.23007829755 0.583883625379
y[1] (closed_form) = 1.23007924839 0.583890927345
absolute error = 7.364e-06
relative error = 0.0005408 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.425
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.143
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2755 0.843
h = 0.001 0.003
y[1] (numeric) = 1.23071511767 0.584644895362
y[1] (closed_form) = 1.23071615921 0.584652131363
absolute error = 7.311e-06
relative error = 0.0005365 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.427
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.426
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1894.4MB, alloc=52.3MB, time=22.89
x[1] = 0.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = 1.23122767183 0.586804531302
y[1] (closed_form) = 1.2312285232 0.586811894127
absolute error = 7.412e-06
relative error = 0.0005434 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.429
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.073
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2766 0.85
h = 0.003 0.006
y[1] (numeric) = 1.23104777247 0.589607945423
y[1] (closed_form) = 1.23104844796 0.589615225373
absolute error = 7.311e-06
relative error = 0.0005356 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.43
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.074
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = 1.23276917019 0.59399239984
y[1] (closed_form) = 1.23276995519 0.594000525629
absolute error = 8.164e-06
relative error = 0.0005966 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.435
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.815
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = 1.23252325703 0.59749770562
y[1] (closed_form) = 1.23252406508 0.59750527907
absolute error = 7.616e-06
relative error = 0.0005561 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.437
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.463
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2798 0.864
h = 0.001 0.001
y[1] (numeric) = 1.23240268479 0.599603429189
y[1] (closed_form) = 1.23240369916 0.599610937705
absolute error = 7.577e-06
relative error = 0.0005528 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.438
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.149
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1939.9MB, alloc=52.3MB, time=23.43
x[1] = 0.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = 1.23303886705 0.600366919414
y[1] (closed_form) = 1.23303997138 0.600374361701
absolute error = 7.524e-06
relative error = 0.0005486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.439
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.902
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2809 0.869
h = 0.003 0.006
y[1] (numeric) = 1.23285435703 0.603173029327
y[1] (closed_form) = 1.23285501017 0.603180474253
absolute error = 7.474e-06
relative error = 0.0005445 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.441
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.092
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = 1.23457033058 0.607565186919
y[1] (closed_form) = 1.23457109708 0.607573474334
absolute error = 8.323e-06
relative error = 0.0006049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.446
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.823
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.284 0.88
h = 0.0001 0.003
y[1] (numeric) = 1.23431831787 0.611073946045
y[1] (closed_form) = 1.2343191046 0.611081682839
absolute error = 7.777e-06
relative error = 0.0005646 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.448
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.469
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2841 0.883
h = 0.001 0.001
y[1] (numeric) = 1.23419411598 0.613181795952
y[1] (closed_form) = 1.23419510802 0.613189467004
absolute error = 7.735e-06
relative error = 0.0005613 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.449
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.154
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1985.2MB, alloc=52.3MB, time=23.98
x[1] = 0.2851 0.884
h = 0.001 0.003
y[1] (numeric) = 1.23482973501 0.61394718587
y[1] (closed_form) = 1.23483081639 0.613954790468
absolute error = 7.681e-06
relative error = 0.000557 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.45
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.479
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = 1.23533576866 0.616113856625
y[1] (closed_form) = 1.2353366626 0.616121589154
absolute error = 7.784e-06
relative error = 0.0005639 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.452
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.103
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2862 0.891
h = 0.003 0.006
y[1] (numeric) = 1.23514539054 0.618923376776
y[1] (closed_form) = 1.23514610899 0.618931028905
absolute error = 7.686e-06
relative error = 0.0005563 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.454
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.114
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = 1.23685525819 0.623324569174
y[1] (closed_form) = 1.23685609434 0.623333059821
absolute error = 8.532e-06
relative error = 0.000616 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.459
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.833
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = 1.23659626355 0.626837459932
y[1] (closed_form) = 1.23659711673 0.626845402021
absolute error = 7.988e-06
relative error = 0.0005762 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.461
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.477
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2030.6MB, alloc=52.3MB, time=24.52
x[1] = 0.2894 0.905
h = 0.001 0.001
y[1] (numeric) = 1.23646790852 0.628947850967
y[1] (closed_form) = 1.23646896583 0.628955726415
absolute error = 7.946e-06
relative error = 0.0005728 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.462
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2904 0.906
h = 0.001 0.003
y[1] (numeric) = 1.2371029179 0.629715451723
y[1] (closed_form) = 1.23710406382 0.629723260476
absolute error = 7.892e-06
relative error = 0.0005686 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.463
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.508
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = 1.23760552222 0.63188593238
y[1] (closed_form) = 1.23760648215 0.631893869614
absolute error = 7.995e-06
relative error = 0.0005754 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.465
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.119
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2915 0.913
h = 0.003 0.006
y[1] (numeric) = 1.23740959241 0.63469879691
y[1] (closed_form) = 1.2374103771 0.63470665505
absolute error = 7.897e-06
relative error = 0.0005679 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.467
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.135
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = 1.2391134294 0.639109022815
y[1] (closed_form) = 1.23911433603 0.639117715481
absolute error = 8.740e-06
relative error = 0.0006269 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.472
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.843
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2076.1MB, alloc=52.3MB, time=25.07
x[1] = 0.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = 1.23884750372 0.64262606812
y[1] (closed_form) = 1.23884842425 0.642634214313
absolute error = 8.198e-06
relative error = 0.0005874 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.474
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.485
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2947 0.927
h = 0.001 0.001
y[1] (numeric) = 1.23871502635 0.644739013521
y[1] (closed_form) = 1.23871614981 0.644747092198
absolute error = 8.156e-06
relative error = 0.0005841 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.475
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.166
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2957 0.928
h = 0.001 0.003
y[1] (numeric) = 1.23934944091 0.645508819748
y[1] (closed_form) = 1.23935065226 0.645516831501
absolute error = 8.103e-06
relative error = 0.0005799 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.476
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.537
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = 1.23984865088 0.647683114417
y[1] (closed_form) = 1.23984967772 0.647691255176
absolute error = 8.205e-06
relative error = 0.0005866 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.478
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.136
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2968 0.935
h = 0.003 0.006
y[1] (numeric) = 1.23964721019 0.650499341122
y[1] (closed_form) = 1.23964806204 0.650507404079
absolute error = 8.108e-06
relative error = 0.0005791 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.48
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.157
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2121.5MB, alloc=52.3MB, time=25.62
x[1] = 0.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = 1.24134509105 0.654918598263
y[1] (closed_form) = 1.24134606898 0.654927491737
absolute error = 8.947e-06
relative error = 0.0006375 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.485
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.852
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = 1.24107228509 0.658439820155
y[1] (closed_form) = 1.24107327384 0.658448169262
absolute error = 8.407e-06
relative error = 0.0005984 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.487
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.493
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3 0.949
h = 0.001 0.001
y[1] (numeric) = 1.24093571602 0.660555332639
y[1] (closed_form) = 1.24093690652 0.660563613377
absolute error = 8.366e-06
relative error = 0.0005951 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.488
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.172
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.301 0.95
h = 0.001 0.003
y[1] (numeric) = 1.24156955039 0.661327338828
y[1] (closed_form) = 1.24157082806 0.661335552425
absolute error = 8.312e-06
relative error = 0.0005909 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.489
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.566
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.302 0.953
h = 0.0001 0.004
y[1] (numeric) = 1.24206540076 0.663505451126
y[1] (closed_form) = 1.24206649535 0.663513794232
absolute error = 8.415e-06
relative error = 0.0005976 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.491
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.152
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2166.9MB, alloc=52.3MB, time=26.16
x[1] = 0.3021 0.957
h = 0.003 0.006
y[1] (numeric) = 1.24185848984 0.666325057108
y[1] (closed_form) = 1.24185940972 0.666333323688
absolute error = 8.318e-06
relative error = 0.0005902 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.493
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.18
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = 1.24355048836 0.670753342276
y[1] (closed_form) = 1.24355153839 0.670762435346
absolute error = 9.153e-06
relative error = 0.0006478 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.498
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.862
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = 1.24327085266 0.674278761936
y[1] (closed_form) = 1.24327191048 0.674287312766
absolute error = 8.616e-06
relative error = 0.0006092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.5
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.501
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3053 0.971
h = 0.001 0.001
y[1] (numeric) = 1.24313022243 0.676396853707
y[1] (closed_form) = 1.24313148082 0.676405335339
absolute error = 8.574e-06
relative error = 0.0006059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.501
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.179
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = 1.24376349104 0.677171054212
y[1] (closed_form) = 1.24376483587 0.677179468497
absolute error = 8.521e-06
relative error = 0.0006017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.503
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.081
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2212.4MB, alloc=52.3MB, time=26.70
x[1] = 0.3064 0.976
h = 0.003 0.006
y[1] (numeric) = 1.2435521313 0.679993427548
y[1] (closed_form) = 1.24355303378 0.680001856481
absolute error = 8.477e-06
relative error = 0.0005981 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.199
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = 1.24523901757 0.684429411584
y[1] (closed_form) = 1.24524005367 0.684438663579
absolute error = 9.310e-06
relative error = 0.0006552 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.871
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = 1.24495349306 0.687958380322
y[1] (closed_form) = 1.24495453436 0.687967091886
absolute error = 8.774e-06
relative error = 0.0006168 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.512
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.507
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3096 0.99
h = 0.001 0.001
y[1] (numeric) = 1.24480936056 0.690078653761
y[1] (closed_form) = 1.24481060142 0.690087295418
absolute error = 8.730e-06
relative error = 0.0006134 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.513
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.184
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2257.8MB, alloc=52.3MB, time=27.25
x[1] = 0.3106 0.991
h = 0.001 0.003
y[1] (numeric) = 1.24544212751 0.690854731931
y[1] (closed_form) = 1.24544345421 0.690863306064
absolute error = 8.676e-06
relative error = 0.0006092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.622
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = 1.24593177234 0.69303991689
y[1] (closed_form) = 1.24593291864 0.693048621422
absolute error = 8.780e-06
relative error = 0.0006158 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.516
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.184
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3117 0.998
h = 0.003 0.006
y[1] (numeric) = 1.24571474953 0.695865790091
y[1] (closed_form) = 1.24571572165 0.695874420433
absolute error = 8.685e-06
relative error = 0.0006087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.518
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.221
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = 1.2473958889 0.700310794631
y[1] (closed_form) = 1.24739699853 0.700320243984
absolute error = 9.514e-06
relative error = 0.0006651 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.523
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.881
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = 1.24710362793 0.70384399892
y[1] (closed_form) = 1.24710473984 0.703852910002
absolute error = 8.980e-06
relative error = 0.0006271 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.525
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.516
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2303.2MB, alloc=52.3MB, time=27.79
x[1] = 0.3149 1.012
h = 0.001 0.001
y[1] (numeric) = 1.24695549061 0.705966873384
y[1] (closed_form) = 1.24695680089 0.705975713773
absolute error = 8.937e-06
relative error = 0.0006237 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.526
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.19
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3159 1.013
h = 0.001 0.003
y[1] (numeric) = 1.24758771814 0.706745135192
y[1] (closed_form) = 1.24758911354 0.706753907871
absolute error = 8.883e-06
relative error = 0.0006195 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.528
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.652
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = 1.24807410112 0.708934145932
y[1] (closed_form) = 1.24807531757 0.708943049446
absolute error = 8.986e-06
relative error = 0.0006261 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.53
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.201
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.317 1.02
h = 0.003 0.006
y[1] (numeric) = 1.24785172327 0.711763444101
y[1] (closed_form) = 1.24785276584 0.711772274658
absolute error = 8.892e-06
relative error = 0.000619 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.532
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.244
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32 1.026
h = 0.0001 0.005
y[1] (numeric) = 1.24952718743 0.716217463391
y[1] (closed_form) = 1.24952837132 0.716227108898
absolute error = 9.718e-06
relative error = 0.0006747 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.537
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.891
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2348.7MB, alloc=52.3MB, time=28.34
x[1] = 0.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = 1.24922823994 0.719754922046
y[1] (closed_form) = 1.24922942323 0.719764031457
absolute error = 9.186e-06
relative error = 0.0006371 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.539
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.524
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3202 1.034
h = 0.001 0.001
y[1] (numeric) = 1.24907612794 0.721880408327
y[1] (closed_form) = 1.24907750843 0.721889446281
absolute error = 9.143e-06
relative error = 0.0006337 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.54
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.197
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3212 1.035
h = 0.001 0.003
y[1] (numeric) = 1.24970782988 0.722660847769
y[1] (closed_form) = 1.24970929479 0.722669817837
absolute error = 9.089e-06
relative error = 0.0006296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.541
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.683
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = 1.25019098465 0.724853686124
y[1] (closed_form) = 1.25019227202 0.724862787443
absolute error = 9.192e-06
relative error = 0.0006361 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.544
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.218
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3223 1.042
h = 0.003 0.006
y[1] (numeric) = 1.24996329174 0.727686423809
y[1] (closed_form) = 1.24996440555 0.727695453387
absolute error = 9.098e-06
relative error = 0.000629 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.545
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.267
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2394.1MB, alloc=52.3MB, time=28.88
x[1] = 0.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = 1.25163315163 0.732149451261
y[1] (closed_form) = 1.25163441048 0.732159291719
absolute error = 9.921e-06
relative error = 0.0006842 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.551
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.901
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = 1.2513275673 0.735691182304
y[1] (closed_form) = 1.25132882275 0.735700488857
absolute error = 9.391e-06
relative error = 0.0006469 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.553
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.532
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3255 1.056
h = 0.001 0.001
y[1] (numeric) = 1.25117151062 0.737819290718
y[1] (closed_form) = 1.25117296208 0.737828525071
absolute error = 9.348e-06
relative error = 0.0006436 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.554
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.203
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3265 1.057
h = 0.001 0.003
y[1] (numeric) = 1.25180270059 0.738601901678
y[1] (closed_form) = 1.25180423577 0.73861106798
absolute error = 9.294e-06
relative error = 0.0006394 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.555
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.714
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = 1.25228266048 0.740798569052
y[1] (closed_form) = 1.25228401953 0.740807866999
absolute error = 9.397e-06
relative error = 0.0006458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.558
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.236
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2439.6MB, alloc=52.3MB, time=29.43
x[1] = 0.3276 1.064
h = 0.003 0.006
y[1] (numeric) = 1.25204969227 0.743634760171
y[1] (closed_form) = 1.2520508781 0.743643987577
absolute error = 9.303e-06
relative error = 0.0006389 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.559
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.291
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = 1.25371401808 0.748106788391
y[1] (closed_form) = 1.25371535258 0.748116822603
absolute error = 1.012e-05
relative error = 0.0006933 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.564
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.912
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = 1.25340184637 0.751652809064
y[1] (closed_form) = 1.25340317471 0.751662311574
absolute error = 9.595e-06
relative error = 0.0006565 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.567
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3308 1.078
h = 0.001 0.001
y[1] (numeric) = 1.25324187482 0.753783549466
y[1] (closed_form) = 1.25324339799 0.753792979054
absolute error = 9.552e-06
relative error = 0.0006531 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.568
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.21
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = 1.25387256625 0.754568325722
y[1] (closed_form) = 1.25387417244 0.754577687104
absolute error = 9.498e-06
relative error = 0.000649 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.569
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.269
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2485.1MB, alloc=52.3MB, time=29.98
x[1] = 0.3319 1.083
h = 0.003 0.006
y[1] (numeric) = 1.25363530784 0.757407342823
y[1] (closed_form) = 1.25363648084 0.757416729784
absolute error = 9.460e-06
relative error = 0.0006459 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.571
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.311
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = 1.25529481863 0.761887047289
y[1] (closed_form) = 1.25529614341 0.761897237587
absolute error = 1.028e-05
relative error = 0.0006998 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.576
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.921
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.335 1.094
h = 0.0001 0.003
y[1] (numeric) = 1.25497696474 0.765436695887
y[1] (closed_form) = 1.254978281 0.765446356356
absolute error = 9.750e-06
relative error = 0.0006633 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.579
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.548
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3351 1.097
h = 0.001 0.001
y[1] (numeric) = 1.25481361568 0.767569663206
y[1] (closed_form) = 1.25481512576 0.767579250136
absolute error = 9.705e-06
relative error = 0.0006598 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.216
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3361 1.098
h = 0.001 0.003
y[1] (numeric) = 1.25544386287 0.768356292489
y[1] (closed_form) = 1.25544545537 0.768365811079
absolute error = 9.651e-06
relative error = 0.0006557 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.581
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.772
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2530.4MB, alloc=52.3MB, time=30.52
x[1] = 0.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = 1.25591791987 0.770560049951
y[1] (closed_form) = 1.25591933886 0.77056970088
absolute error = 9.755e-06
relative error = 0.000662 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.583
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.269
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3372 1.105
h = 0.003 0.006
y[1] (numeric) = 1.25567519921 0.773402640317
y[1] (closed_form) = 1.25567644561 0.773412222903
absolute error = 9.663e-06
relative error = 0.0006553 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.585
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.334
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = 1.25732930458 0.777891330554
y[1] (closed_form) = 1.25733070625 0.777901712392
absolute error = 1.048e-05
relative error = 0.0007086 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.591
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.931
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = 1.25700495441 0.781445299434
y[1] (closed_form) = 1.25700634489 0.781455153669
absolute error = 9.952e-06
relative error = 0.0006724 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.593
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.556
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3404 1.119
h = 0.001 0.001
y[1] (numeric) = 1.25683774544 0.783580916226
y[1] (closed_form) = 1.25683932857 0.78359069624
absolute error = 9.907e-06
relative error = 0.0006689 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.594
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.222
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2575.9MB, alloc=52.3MB, time=31.07
x[1] = 0.3414 1.12
h = 0.001 0.003
y[1] (numeric) = 1.25746751858 0.784369699113
y[1] (closed_form) = 1.25746918346 0.784379410649
absolute error = 9.853e-06
relative error = 0.0006648 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.595
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.804
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = 1.25793847439 0.786577287722
y[1] (closed_form) = 1.25793996712 0.786587131933
absolute error = 9.957e-06
relative error = 0.0006711 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.598
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.287
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3425 1.127
h = 0.003 0.006
y[1] (numeric) = 1.25769059087 0.789423368448
y[1] (closed_form) = 1.2576919114 0.789433145472
absolute error = 9.866e-06
relative error = 0.0006644 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.6
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.358
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = 1.25933935885 0.793921034891
y[1] (closed_form) = 1.25934083803 0.793931607082
absolute error = 1.068e-05
relative error = 0.0007171 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.605
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.942
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = 1.25900856106 0.797479339159
y[1] (closed_form) = 1.25901002645 0.797489385982
absolute error = 1.015e-05
relative error = 0.0006813 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.607
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.565
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2621.3MB, alloc=52.3MB, time=31.61
x[1] = 0.3457 1.141
h = 0.001 0.001
y[1] (numeric) = 1.25883752152 0.799617614005
y[1] (closed_form) = 1.25883917839 0.799627585945
absolute error = 1.011e-05
relative error = 0.0006778 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.608
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.229
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3467 1.142
h = 0.001 0.003
y[1] (numeric) = 1.25946683346 0.800408543991
y[1] (closed_form) = 1.25946857139 0.800418447326
absolute error = 1.005e-05
relative error = 0.0006738 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.61
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.836
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = 1.25993472022 0.802619963597
y[1] (closed_form) = 1.25993628739 0.802629999923
absolute error = 1.016e-05
relative error = 0.00068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.612
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.305
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3478 1.149
h = 0.003 0.006
y[1] (numeric) = 1.25968171278 0.805469546294
y[1] (closed_form) = 1.25968310811 0.805479516574
absolute error = 1.007e-05
relative error = 0.0006733 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.614
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.382
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = 1.26132521059 0.809976178674
y[1] (closed_form) = 1.2613267679 0.809986940035
absolute error = 1.087e-05
relative error = 0.0007254 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.619
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.953
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2666.8MB, alloc=52.3MB, time=32.16
x[1] = 0.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = 1.26098801356 0.81353883272
y[1] (closed_form) = 1.26098955451 0.813549070957
absolute error = 1.035e-05
relative error = 0.0006899 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.622
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.573
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.351 1.163
h = 0.001 0.001
y[1] (numeric) = 1.26081317261 0.815679773775
y[1] (closed_form) = 1.26081490388 0.815689936486
absolute error = 1.031e-05
relative error = 0.0006865 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.623
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.236
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.352 1.164
h = 0.001 0.003
y[1] (numeric) = 1.26144203599 0.81647284427
y[1] (closed_form) = 1.26144384764 0.816482938259
absolute error = 1.026e-05
relative error = 0.0006825 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.624
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.868
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.353 1.167
h = 0.0001 0.004
y[1] (numeric) = 1.26190688554 0.818688094349
y[1] (closed_form) = 1.2619085278 0.818698321626
absolute error = 1.036e-05
relative error = 0.0006886 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.626
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.323
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3531 1.171
h = 0.003 0.006
y[1] (numeric) = 1.26164879286 0.821541190062
y[1] (closed_form) = 1.26165026367 0.821551352419
absolute error = 1.027e-05
relative error = 0.000682 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.628
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.407
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2712.1MB, alloc=52.3MB, time=32.69
x[1] = 0.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = 1.26328708697 0.826056777428
y[1] (closed_form) = 1.263288723 0.826067726781
absolute error = 1.107e-05
relative error = 0.0007335 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.634
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.963
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = 1.26294353877 0.829623794944
y[1] (closed_form) = 1.26294515593 0.829634223424
absolute error = 1.055e-05
relative error = 0.0006984 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.636
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.582
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3563 1.185
h = 0.001 0.001
y[1] (numeric) = 1.26276492538 0.831767409946
y[1] (closed_form) = 1.2627667317 0.831777762279
absolute error = 1.051e-05
relative error = 0.000695 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.637
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = 1.26339335264 0.832562614281
y[1] (closed_form) = 1.26339523867 0.832572897781
absolute error = 1.046e-05
relative error = 0.000691 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.639
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.466
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3574 1.19
h = 0.003 0.006
y[1] (numeric) = 1.26313112426 0.83541858291
y[1] (closed_form) = 1.26313258641 0.835428901893
absolute error = 1.042e-05
relative error = 0.0006882 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.641
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.427
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2757.6MB, alloc=52.3MB, time=33.24
x[1] = 0.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = 1.26476488536 0.839941808233
y[1] (closed_form) = 1.26476651551 0.839952910737
absolute error = 1.122e-05
relative error = 0.0007391 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.646
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.973
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = 1.26441585635 0.84351251724
y[1] (closed_form) = 1.26441746549 0.843523100786
absolute error = 1.071e-05
relative error = 0.0007043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.648
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.59
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3606 1.204
h = 0.001 0.001
y[1] (numeric) = 1.26423398686 0.845658395303
y[1] (closed_form) = 1.26423578416 0.845668902167
absolute error = 1.066e-05
relative error = 0.0007008 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.248
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3616 1.205
h = 0.001 0.003
y[1] (numeric) = 1.26486202323 0.846455425976
y[1] (closed_form) = 1.26486389966 0.846465863913
absolute error = 1.061e-05
relative error = 0.0006968 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.651
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.928
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = 1.26532125933 0.848677765745
y[1] (closed_form) = 1.26532296889 0.848688337488
absolute error = 1.071e-05
relative error = 0.0007029 %
Correct digits = 5
memory used=2803.0MB, alloc=52.3MB, time=33.78
Radius of convergence (given) for eq 1 = 2.654
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.358
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3627 1.212
h = 0.003 0.006
y[1] (numeric) = 1.26505376415 0.85153736638
y[1] (closed_form) = 1.26505530299 0.851547875262
absolute error = 1.062e-05
relative error = 0.0006965 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.655
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.452
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = 1.26668244334 0.856069525351
y[1] (closed_form) = 1.26668415327 0.856080813674
absolute error = 1.142e-05
relative error = 0.0007468 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.661
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.984
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = 1.26632715164 0.859644622065
y[1] (closed_form) = 1.26632883813 0.859655393693
absolute error = 1.090e-05
relative error = 0.0007123 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.663
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.598
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3659 1.226
h = 0.001 0.001
y[1] (numeric) = 1.26614156301 0.861793187744
y[1] (closed_form) = 1.26614343651 0.861803882104
absolute error = 1.086e-05
relative error = 0.0007089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.665
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.255
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2848.4MB, alloc=52.3MB, time=34.32
x[1] = 0.3669 1.227
h = 0.001 0.003
y[1] (numeric) = 1.26676918597 0.862592339782
y[1] (closed_form) = 1.26677113794 0.862602965121
absolute error = 1.080e-05
relative error = 0.0007049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.666
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.961
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = 1.26722547424 0.864818506927
y[1] (closed_form) = 1.26722726068 0.864829266318
absolute error = 1.091e-05
relative error = 0.0007109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.668
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.376
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.368 1.234
h = 0.003 0.006
y[1] (numeric) = 1.26695300298 0.867681649626
y[1] (closed_form) = 1.2669546191 0.867692347237
absolute error = 1.082e-05
relative error = 0.0007045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.477
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.371 1.24
h = 0.0001 0.005
y[1] (numeric) = 1.26857666452 0.872222729467
y[1] (closed_form) = 1.26857845476 0.872234202445
absolute error = 1.161e-05
relative error = 0.0007543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.676
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.995
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = 1.2682151573 0.875802225665
y[1] (closed_form) = 1.26821692173 0.875813184218
absolute error = 1.110e-05
relative error = 0.0007202 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.678
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.607
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2894.0MB, alloc=52.3MB, time=34.86
x[1] = 0.3712 1.248
h = 0.001 0.001
y[1] (numeric) = 1.26802587795 0.877953485561
y[1] (closed_form) = 1.26802782825 0.877964366277
absolute error = 1.105e-05
relative error = 0.0007167 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.68
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.262
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3722 1.249
h = 0.001 0.003
y[1] (numeric) = 1.26865309938 0.878754752082
y[1] (closed_form) = 1.2686551275 0.878765563692
absolute error = 1.100e-05
relative error = 0.0007128 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.681
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.995
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = 1.26910647046 0.880984744739
y[1] (closed_form) = 1.26910833436 0.880995690628
absolute error = 1.110e-05
relative error = 0.0007187 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.683
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.395
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3733 1.256
h = 0.003 0.006
y[1] (numeric) = 1.2688290608 0.883851438482
y[1] (closed_form) = 1.26883075481 0.883862323659
absolute error = 1.102e-05
relative error = 0.0007124 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.685
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.502
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = 1.2704477682 0.888401425826
y[1] (closed_form) = 1.27044963927 0.888413082302
absolute error = 1.181e-05
relative error = 0.0007615 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.691
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.006
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2939.6MB, alloc=52.3MB, time=35.40
x[1] = 0.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = 1.27008009231 0.891985332649
y[1] (closed_form) = 1.27008193525 0.891996476972
absolute error = 1.130e-05
relative error = 0.0007278 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.693
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.616
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3765 1.27
h = 0.001 0.001
y[1] (numeric) = 1.26988715045 0.894139292984
y[1] (closed_form) = 1.26988917811 0.894150358921
absolute error = 1.125e-05
relative error = 0.0007244 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.27
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3775 1.271
h = 0.001 0.003
y[1] (numeric) = 1.27051398205 0.894942667042
y[1] (closed_form) = 1.27051608687 0.894953663795
absolute error = 1.120e-05
relative error = 0.0007205 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.696
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.028
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = 1.27096446623 0.897176483027
y[1] (closed_form) = 1.27096640816 0.89718761427
absolute error = 1.130e-05
relative error = 0.0007263 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.698
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.414
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3786 1.278
h = 0.003 0.006
y[1] (numeric) = 1.27068215561 0.900046736293
y[1] (closed_form) = 1.27068392807 0.900057807876
absolute error = 1.121e-05
relative error = 0.0007201 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.7
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.527
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2985.1MB, alloc=52.3MB, time=35.95
x[1] = 0.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = 1.27229597161 0.904605617203
y[1] (closed_form) = 1.272297924 0.904617456025
absolute error = 1.200e-05
relative error = 0.0007686 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.706
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.017
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = 1.27192217355 0.90819394517
y[1] (closed_form) = 1.27192409555 0.908205274115
absolute error = 1.149e-05
relative error = 0.0007352 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.708
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.625
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3818 1.292
h = 0.001 0.001
y[1] (numeric) = 1.27172559718 0.910350611798
y[1] (closed_form) = 1.27172770275 0.910361861824
absolute error = 1.145e-05
relative error = 0.0007318 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = 1.27235205045 0.911156086387
y[1] (closed_form) = 1.27235423254 0.91116726716
absolute error = 1.139e-05
relative error = 0.0007279 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.711
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.67
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3829 1.297
h = 0.003 0.006
y[1] (numeric) = 1.27206575382 0.914029249024
y[1] (closed_form) = 1.27206752146 0.914040474219
absolute error = 1.136e-05
relative error = 0.0007255 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.713
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.548
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3030.5MB, alloc=52.3MB, time=36.49
x[1] = 0.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = 1.27367530342 0.91859571638
y[1] (closed_form) = 1.27367725345 0.91860770536
absolute error = 1.215e-05
relative error = 0.0007735 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.719
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.027
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.386 1.308
h = 0.0001 0.003
y[1] (numeric) = 1.27329621977 0.922187785699
y[1] (closed_form) = 1.27329813746 0.922199266736
absolute error = 1.164e-05
relative error = 0.0007404 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.721
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.633
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3861 1.311
h = 0.001 0.001
y[1] (numeric) = 1.27309650486 0.924346743382
y[1] (closed_form) = 1.27309860515 0.924358145042
absolute error = 1.159e-05
relative error = 0.0007369 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.723
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.283
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3871 1.312
h = 0.001 0.003
y[1] (numeric) = 1.27372261663 0.92515401606
y[1] (closed_form) = 1.2737247929 0.925165348407
absolute error = 1.154e-05
relative error = 0.000733 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.724
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.091
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = 1.27416776307 0.927394905944
y[1] (closed_form) = 1.27416977887 0.927406373145
absolute error = 1.164e-05
relative error = 0.0007388 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.726
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.449
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3076.0MB, alloc=52.3MB, time=37.03
x[1] = 0.3882 1.319
h = 0.003 0.006
y[1] (numeric) = 1.27387638896 0.930271746206
y[1] (closed_form) = 1.27387823609 0.93028315567
absolute error = 1.156e-05
relative error = 0.0007327 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.728
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.574
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = 1.27548116204 0.934847080487
y[1] (closed_form) = 1.2754831943 0.934859249691
absolute error = 1.234e-05
relative error = 0.0007802 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.734
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.038
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = 1.27509604176 0.938443589463
y[1] (closed_form) = 1.27509803949 0.938455253004
absolute error = 1.183e-05
relative error = 0.0007474 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.736
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.642
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3914 1.333
h = 0.001 0.001
y[1] (numeric) = 1.27489274381 0.940605263707
y[1] (closed_form) = 1.27489492302 0.940616847371
absolute error = 1.179e-05
relative error = 0.000744 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.738
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.29
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3924 1.334
h = 0.001 0.003
y[1] (numeric) = 1.27551849824 0.941414623865
y[1] (closed_form) = 1.27552075278 0.941426138161
absolute error = 1.173e-05
relative error = 0.0007401 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.739
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.125
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3121.5MB, alloc=52.3MB, time=37.58
x[1] = 0.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = 1.27596084275 0.943659329497
y[1] (closed_form) = 1.27596293812 0.943670978812
absolute error = 1.184e-05
relative error = 0.0007458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.469
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3935 1.341
h = 0.003 0.006
y[1] (numeric) = 1.27566467315 0.946539751304
y[1] (closed_form) = 1.27566660029 0.946551343892
absolute error = 1.175e-05
relative error = 0.0007398 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.744
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.6
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = 1.27726473027 0.951123937059
y[1] (closed_form) = 1.27726684521 0.951136285354
absolute error = 1.253e-05
relative error = 0.0007867 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.749
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.049
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = 1.27687361889 0.95472489451
y[1] (closed_form) = 1.27687569716 0.954736739422
absolute error = 1.203e-05
relative error = 0.0007543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.752
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.652
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3967 1.355
h = 0.001 0.001
y[1] (numeric) = 1.2766667653 0.95688929016
y[1] (closed_form) = 1.27666902392 0.956901054712
absolute error = 1.198e-05
relative error = 0.0007508 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.753
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.297
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3167.0MB, alloc=52.3MB, time=38.12
x[1] = 0.3977 1.356
h = 0.001 0.003
y[1] (numeric) = 1.27729217336 0.957700730642
y[1] (closed_form) = 1.27729450668 0.957712425777
absolute error = 1.193e-05
relative error = 0.000747 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.755
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.159
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = 1.27773174501 0.959949248692
y[1] (closed_form) = 1.27773392043 0.959961078997
absolute error = 1.203e-05
relative error = 0.0007527 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.757
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.488
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3988 1.363
h = 0.003 0.006
y[1] (numeric) = 1.27743081627 0.962833258691
y[1] (closed_form) = 1.27743282392 0.962845033264
absolute error = 1.194e-05
relative error = 0.0007467 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.759
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.626
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = 1.27902621724 0.967426279983
y[1] (closed_form) = 1.27902841529 0.967438806241
absolute error = 1.272e-05
relative error = 0.000793 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.765
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.061
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = 1.27862915993 0.971031694164
y[1] (closed_form) = 1.27863131921 0.97104371932
absolute error = 1.222e-05
relative error = 0.0007609 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.767
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.661
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3212.4MB, alloc=52.3MB, time=38.66
x[1] = 0.402 1.377
h = 0.001 0.001
y[1] (numeric) = 1.27841877787 0.973198815729
y[1] (closed_form) = 1.27842111639 0.973210760058
absolute error = 1.217e-05
relative error = 0.0007575 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.769
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.304
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.403 1.378
h = 0.001 0.003
y[1] (numeric) = 1.27904385034 0.974012329333
y[1] (closed_form) = 1.27904626294 0.974024204205
absolute error = 1.212e-05
relative error = 0.0007537 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.194
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.404 1.381
h = 0.0001 0.004
y[1] (numeric) = 1.27948067789 0.976264656203
y[1] (closed_form) = 1.27948293386 0.976276666378
absolute error = 1.222e-05
relative error = 0.0007593 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.772
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.508
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4041 1.385
h = 0.003 0.006
y[1] (numeric) = 1.27917502609 0.979152260595
y[1] (closed_form) = 1.27917711474 0.979164216019
absolute error = 1.214e-05
relative error = 0.0007534 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.775
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.652
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = 1.28076582995 0.983754101021
y[1] (closed_form) = 1.28076811153 0.983766804121
absolute error = 1.291e-05
relative error = 0.0007992 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.78
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.073
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3257.8MB, alloc=52.3MB, time=39.20
x[1] = 0.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = 1.28036287153 0.987363979636
y[1] (closed_form) = 1.2803651123 0.987376183913
absolute error = 1.241e-05
relative error = 0.0007674 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.783
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.67
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4073 1.399
h = 0.001 0.001
y[1] (numeric) = 1.28014898796 0.989533831302
y[1] (closed_form) = 1.28015140685 0.989545954302
absolute error = 1.236e-05
relative error = 0.000764 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.784
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.312
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4083 1.4
h = 0.003 0.006
y[1] (numeric) = 1.28077373545 0.990349410785
y[1] (closed_form) = 1.2807762278 0.990361464294
absolute error = 1.231e-05
relative error = 0.0007602 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.786
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.21
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = 1.28236220995 0.994957054052
y[1] (closed_form) = 1.28236431943 0.994970220462
absolute error = 1.333e-05
relative error = 0.0008215 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.791
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.081
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = 1.28195533074 0.998570155208
y[1] (closed_form) = 1.28195739807 0.998582824413
absolute error = 1.284e-05
relative error = 0.00079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.794
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.677
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3303.2MB, alloc=52.3MB, time=39.75
x[1] = 0.4115 1.414
h = 0.001 0.001
y[1] (numeric) = 1.28173912293 1.00074197454
y[1] (closed_form) = 1.28174136761 1.0007545622
absolute error = 1.279e-05
relative error = 0.0007863 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.795
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.317
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4125 1.415
h = 0.001 0.003
y[1] (numeric) = 1.28236370476 1.00155897877
y[1] (closed_form) = 1.28236602247 1.00157149693
absolute error = 1.273e-05
relative error = 0.0007824 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.797
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.254
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = 1.28279606063 1.00381779317
y[1] (closed_form) = 1.28279822383 1.0038304468
absolute error = 1.284e-05
relative error = 0.0007881 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.799
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.542
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4136 1.422
h = 0.003 0.006
y[1] (numeric) = 1.28248260868 1.00671159438
y[1] (closed_form) = 1.28248460537 1.00672419486
absolute error = 1.276e-05
relative error = 0.0007825 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.801
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.697
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = 1.2840660062 1.01132839467
y[1] (closed_form) = 1.28406819986 1.01134173604
absolute error = 1.352e-05
relative error = 0.0008272 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.807
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.093
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3348.7MB, alloc=52.3MB, time=40.29
x[1] = 0.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = 1.28365330088 1.01494597095
y[1] (closed_form) = 1.28365545041 1.01495881739
absolute error = 1.303e-05
relative error = 0.0007959 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.686
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4168 1.436
h = 0.001 0.001
y[1] (numeric) = 1.28343363664 1.01712052607
y[1] (closed_form) = 1.28343596241 1.01713329053
absolute error = 1.297e-05
relative error = 0.0007923 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.811
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.324
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4178 1.437
h = 0.001 0.003
y[1] (numeric) = 1.28405791079 1.01793958361
y[1] (closed_form) = 1.284060309 1.01795227856
absolute error = 1.292e-05
relative error = 0.0007884 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.813
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.289
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = 1.28448759816 1.02020219518
y[1] (closed_form) = 1.28448984308 1.02021502569
absolute error = 1.303e-05
relative error = 0.0007941 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.815
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.562
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4189 1.444
h = 0.003 0.006
y[1] (numeric) = 1.28416951877 1.02309960445
y[1] (closed_form) = 1.28417159767 1.02311238276
absolute error = 1.295e-05
relative error = 0.0007885 %
Correct digits = 5
memory used=3394.2MB, alloc=52.3MB, time=40.83
Radius of convergence (given) for eq 1 = 2.817
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.723
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = 1.28574847376 1.0277251762
y[1] (closed_form) = 1.28575075197 1.02773869142
absolute error = 1.371e-05
relative error = 0.0008327 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.823
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.104
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.422 1.455
h = 0.0001 0.003
y[1] (numeric) = 1.28532998615 1.03134723391
y[1] (closed_form) = 1.2853322183 1.03136025647
absolute error = 1.321e-05
relative error = 0.0008017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.825
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.696
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4221 1.458
h = 0.001 0.001
y[1] (numeric) = 1.28510689182 1.03352452816
y[1] (closed_form) = 1.28510929913 1.03353746835
absolute error = 1.316e-05
relative error = 0.0007981 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.827
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.332
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4231 1.459
h = 0.001 0.003
y[1] (numeric) = 1.28573086844 1.03434563169
y[1] (closed_form) = 1.28573334757 1.03435850234
absolute error = 1.311e-05
relative error = 0.0007943 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.828
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.325
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3439.5MB, alloc=52.3MB, time=41.37
x[1] = 0.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = 1.28615791487 1.03661203591
y[1] (closed_form) = 1.28616024195 1.03662504221
absolute error = 1.321e-05
relative error = 0.0007999 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.831
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.582
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4242 1.466
h = 0.003 0.006
y[1] (numeric) = 1.28583524303 1.03951305791
y[1] (closed_form) = 1.28583740455 1.03952601294
absolute error = 1.313e-05
relative error = 0.0007943 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.833
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.75
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = 1.28740981177 1.04414738317
y[1] (closed_form) = 1.28741217491 1.04416107116
absolute error = 1.389e-05
relative error = 0.000838 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.839
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.116
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = 1.28698558535 1.04777392811
y[1] (closed_form) = 1.28698790053 1.04778712571
absolute error = 1.340e-05
relative error = 0.0008074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.841
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.705
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4274 1.48
h = 0.001 0.001
y[1] (numeric) = 1.28675908705 1.04995396457
y[1] (closed_form) = 1.2867615763 1.04996707939
absolute error = 1.335e-05
relative error = 0.0008038 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.843
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.339
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3484.9MB, alloc=52.3MB, time=41.91
x[1] = 0.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = 1.28738277609 1.05077710672
y[1] (closed_form) = 1.28738533657 1.050790152
absolute error = 1.329e-05
relative error = 0.0008 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.844
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.048
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4285 1.485
h = 0.003 0.006
y[1] (numeric) = 1.28705636863 1.05368107932
y[1] (closed_form) = 1.28705853122 1.05369418253
absolute error = 1.328e-05
relative error = 0.0007984 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.847
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.772
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = 1.2886271024 1.0583228733
y[1] (closed_form) = 1.28862946858 1.05833670611
absolute error = 1.403e-05
relative error = 0.0008416 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.852
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.126
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = 1.28819791718 1.06195321732
y[1] (closed_form) = 1.28820023377 1.06196656167
absolute error = 1.354e-05
relative error = 0.0008113 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.855
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.714
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4317 1.499
h = 0.001 0.001
y[1] (numeric) = 1.28796847689 1.06413557628
y[1] (closed_form) = 1.28797096663 1.06414883751
absolute error = 1.349e-05
relative error = 0.0008076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.857
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.346
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3530.4MB, alloc=52.3MB, time=42.45
x[1] = 0.4327 1.5
h = 0.001 0.003
y[1] (numeric) = 1.28859190207 1.06496046403
y[1] (closed_form) = 1.28859446253 1.0649736557
absolute error = 1.344e-05
relative error = 0.0008038 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.858
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.391
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = 1.2890140616 1.06723388201
y[1] (closed_form) = 1.28901647226 1.06724720947
absolute error = 1.354e-05
relative error = 0.0008093 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.86
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.619
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4338 1.507
h = 0.003 0.006
y[1] (numeric) = 1.2886828932 1.07014158381
y[1] (closed_form) = 1.28868513918 1.07015486169
absolute error = 1.347e-05
relative error = 0.0008039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.863
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.799
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = 1.29024934377 1.07479209757
y[1] (closed_form) = 1.29025179553 1.07480610113
absolute error = 1.422e-05
relative error = 0.0008466 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.868
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.138
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = 1.28981449957 1.07842693886
y[1] (closed_form) = 1.28981689992 1.07844045622
absolute error = 1.373e-05
relative error = 0.0008166 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.871
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.723
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3575.9MB, alloc=52.3MB, time=43.00
x[1] = 0.437 1.521
h = 0.001 0.001
y[1] (numeric) = 1.28958170328 1.08061204526
y[1] (closed_form) = 1.28958427571 1.08062547913
absolute error = 1.368e-05
relative error = 0.000813 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.873
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.353
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.438 1.522
h = 0.001 0.003
y[1] (numeric) = 1.29020485905 1.081438958
y[1] (closed_form) = 1.29020750161 1.08145232231
absolute error = 1.362e-05
relative error = 0.0008092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.874
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.427
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.439 1.525
h = 0.0001 0.004
y[1] (numeric) = 1.29062445485 1.08371615479
y[1] (closed_form) = 1.29062694879 1.08372965494
absolute error = 1.373e-05
relative error = 0.0008146 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.877
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.64
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4391 1.529
h = 0.003 0.006
y[1] (numeric) = 1.29028879236 1.08662748095
y[1] (closed_form) = 1.29029112213 1.08664093242
absolute error = 1.365e-05
relative error = 0.0008093 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.879
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.826
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = 1.29185101396 1.09128669549
y[1] (closed_form) = 1.29185355163 1.09130086873
absolute error = 1.440e-05
relative error = 0.0008514 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.884
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.15
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3621.4MB, alloc=52.3MB, time=43.54
x[1] = 0.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = 1.29141055318 1.0949260385
y[1] (closed_form) = 1.29141303766 1.0949397278
absolute error = 1.391e-05
relative error = 0.0008217 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.733
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4423 1.543
h = 0.001 0.001
y[1] (numeric) = 1.29117442638 1.09711389461
y[1] (closed_form) = 1.29117708185 1.09712750006
absolute error = 1.386e-05
relative error = 0.0008181 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.889
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.361
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4433 1.544
h = 0.001 0.003
y[1] (numeric) = 1.29179732221 1.0979428249
y[1] (closed_form) = 1.29180004724 1.0979563608
absolute error = 1.381e-05
relative error = 0.0008144 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.463
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = 1.29221438064 1.10022379515
y[1] (closed_form) = 1.29221695824 1.10023746693
absolute error = 1.391e-05
relative error = 0.0008198 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.893
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.66
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4444 1.551
h = 0.003 0.006
y[1] (numeric) = 1.2918742579 1.10313874888
y[1] (closed_form) = 1.29187667182 1.10315237285
absolute error = 1.384e-05
relative error = 0.0008145 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.895
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.853
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3666.8MB, alloc=52.3MB, time=44.08
x[1] = 0.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = 1.29343230404 1.10780664489
y[1] (closed_form) = 1.29343492792 1.10782098673
absolute error = 1.458e-05
relative error = 0.0008561 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.901
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.162
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = 1.29298626871 1.11145049361
y[1] (closed_form) = 1.29298883766 1.11146435377
absolute error = 1.410e-05
relative error = 0.0008267 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.903
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.743
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4476 1.565
h = 0.001 0.001
y[1] (numeric) = 1.29274683663 1.11364110142
y[1] (closed_form) = 1.29274957552 1.1136548774
absolute error = 1.405e-05
relative error = 0.0008232 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.905
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.369
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4486 1.566
h = 0.001 0.003
y[1] (numeric) = 1.29336948184 1.11447204182
y[1] (closed_form) = 1.29337228971 1.11448574826
absolute error = 1.399e-05
relative error = 0.0008195 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.907
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.499
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = 1.29378402895 1.11675677998
y[1] (closed_form) = 1.29378669056 1.11677062232
absolute error = 1.410e-05
relative error = 0.0008248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.909
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.681
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3712.1MB, alloc=52.3MB, time=44.63
x[1] = 0.4497 1.573
h = 0.003 0.006
y[1] (numeric) = 1.29343947949 1.11967536413
y[1] (closed_form) = 1.29344197791 1.11968915952
absolute error = 1.402e-05
relative error = 0.0008195 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.911
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.881
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = 1.29499340297 1.12435192196
y[1] (closed_form) = 1.29499611336 1.12436643136
absolute error = 1.476e-05
relative error = 0.0008607 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.917
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.175
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = 1.29454183475 1.12800027997
y[1] (closed_form) = 1.29454448851 1.12801430994
absolute error = 1.428e-05
relative error = 0.0008316 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.92
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.753
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4529 1.587
h = 0.001 0.001
y[1] (numeric) = 1.2942991224 1.13019364122
y[1] (closed_form) = 1.29430194505 1.13020758668
absolute error = 1.423e-05
relative error = 0.000828 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.922
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.376
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = 1.29492152615 1.13102658428
y[1] (closed_form) = 1.29492441721 1.13104046021
absolute error = 1.417e-05
relative error = 0.0008244 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.923
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.27
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3757.7MB, alloc=52.3MB, time=45.17
x[1] = 0.454 1.592
h = 0.003 0.006
y[1] (numeric) = 1.29457337549 1.13394813244
y[1] (closed_form) = 1.29457587792 1.13396207293
absolute error = 1.416e-05
relative error = 0.000823 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.925
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.904
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.457 1.598
h = 0.0001 0.005
y[1] (numeric) = 1.29612368922 1.13863208185
y[1] (closed_form) = 1.29612640535 1.13864673305
absolute error = 1.490e-05
relative error = 0.0008637 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.931
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.185
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = 1.29566733777 1.1422842586
y[1] (closed_form) = 1.29566999581 1.14229843228
absolute error = 1.442e-05
relative error = 0.0008349 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.934
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.761
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4572 1.606
h = 0.001 0.001
y[1] (numeric) = 1.29542178892 1.14447995245
y[1] (closed_form) = 1.29542461495 1.14449404133
absolute error = 1.437e-05
relative error = 0.0008313 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.935
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.383
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4582 1.607
h = 0.001 0.003
y[1] (numeric) = 1.29604396829 1.14531461061
y[1] (closed_form) = 1.29604686225 1.14532862999
absolute error = 1.431e-05
relative error = 0.0008276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.937
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.567
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3803.2MB, alloc=52.3MB, time=45.71
x[1] = 0.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = 1.296453866 1.14760631534
y[1] (closed_form) = 1.29645661584 1.14762047064
absolute error = 1.442e-05
relative error = 0.0008328 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.939
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.719
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4593 1.614
h = 0.003 0.006
y[1] (numeric) = 1.29610112431 1.15053160948
y[1] (closed_form) = 1.29610371188 1.15054571941
absolute error = 1.435e-05
relative error = 0.0008277 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.942
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.932
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = 1.29764741201 1.15522418398
y[1] (closed_form) = 1.29765021519 1.1552390008
absolute error = 1.508e-05
relative error = 0.000868 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.947
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.197
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = 1.29718560416 1.15888087603
y[1] (closed_form) = 1.29718834761 1.15889521756
absolute error = 1.460e-05
relative error = 0.0008394 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.771
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4625 1.628
h = 0.001 0.001
y[1] (numeric) = 1.29693682096 1.16107932618
y[1] (closed_form) = 1.29693973137 1.16109358261
absolute error = 1.455e-05
relative error = 0.0008359 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.952
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.391
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3848.7MB, alloc=52.3MB, time=46.26
x[1] = 0.4635 1.629
h = 0.001 0.003
y[1] (numeric) = 1.29755877556 1.1619159732
y[1] (closed_form) = 1.29756175334 1.16193016015
absolute error = 1.450e-05
relative error = 0.0008323 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.953
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.604
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = 1.29796623487 1.16421142921
y[1] (closed_form) = 1.29796906967 1.16422575208
absolute error = 1.460e-05
relative error = 0.0008374 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.956
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.74
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4646 1.636
h = 0.003 0.006
y[1] (numeric) = 1.29760916066 1.16714036047
y[1] (closed_form) = 1.2976118337 1.16715463879
absolute error = 1.453e-05
relative error = 0.0008323 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.958
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.959
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = 1.29915147315 1.1718415396
y[1] (closed_form) = 1.29915436364 1.17185652099
absolute error = 1.526e-05
relative error = 0.0008721 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.964
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.21
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = 1.29868424948 1.17550274932
y[1] (closed_form) = 1.29868707865 1.17551725765
absolute error = 1.478e-05
relative error = 0.0008438 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.967
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.781
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3894.2MB, alloc=52.3MB, time=46.80
x[1] = 0.4678 1.65
h = 0.001 0.001
y[1] (numeric) = 1.2984322563 1.17770395682
y[1] (closed_form) = 1.29843525139 1.17771837977
absolute error = 1.473e-05
relative error = 0.0008403 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.969
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.399
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4688 1.651
h = 0.001 0.003
y[1] (numeric) = 1.29905399484 1.17854258521
y[1] (closed_form) = 1.29905705674 1.1785569387
absolute error = 1.468e-05
relative error = 0.0008367 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.641
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = 1.29945904061 1.18084178625
y[1] (closed_form) = 1.29946196067 1.18085627564
absolute error = 1.478e-05
relative error = 0.0008418 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.972
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.761
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4699 1.658
h = 0.003 0.006
y[1] (numeric) = 1.29909766625 1.18377435621
y[1] (closed_form) = 1.29910042506 1.18378880187
absolute error = 1.471e-05
relative error = 0.0008368 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.975
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.987
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = 1.30063605365 1.18848411923
y[1] (closed_form) = 1.30063903172 1.18849926417
absolute error = 1.543e-05
relative error = 0.0008761 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.981
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.222
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3939.7MB, alloc=52.3MB, time=47.34
x[1] = 0.473 1.669
h = 0.0001 0.003
y[1] (numeric) = 1.30016345437 1.19214984862
y[1] (closed_form) = 1.30016636955 1.19216452272
absolute error = 1.496e-05
relative error = 0.0008481 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.984
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.791
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4731 1.672
h = 0.001 0.001
y[1] (numeric) = 1.29990827535 1.19435381428
y[1] (closed_form) = 1.29991135542 1.19436840271
absolute error = 1.491e-05
relative error = 0.0008446 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.985
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.406
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4741 1.673
h = 0.001 0.003
y[1] (numeric) = 1.30052980637 1.19519441654
y[1] (closed_form) = 1.3005329527 1.19520893556
absolute error = 1.486e-05
relative error = 0.0008411 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.987
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.678
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = 1.30093246319 1.1974973562
y[1] (closed_form) = 1.3009354688 1.1975120111
absolute error = 1.496e-05
relative error = 0.0008461 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.989
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.782
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4752 1.68
h = 0.003 0.006
y[1] (numeric) = 1.30056682074 1.20043356614
y[1] (closed_form) = 1.3005696656 1.2004481781
absolute error = 1.489e-05
relative error = 0.0008411 %
Correct digits = 5
memory used=3985.3MB, alloc=52.3MB, time=47.88
Radius of convergence (given) for eq 1 = 2.991
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.015
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = 1.3021013325 1.20515189207
y[1] (closed_form) = 1.30210439837 1.20516719954
absolute error = 1.561e-05
relative error = 0.0008799 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.997
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.235
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = 1.30162339745 1.20882214275
y[1] (closed_form) = 1.3016263989 1.20883698159
absolute error = 1.514e-05
relative error = 0.0008523 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4784 1.694
h = 0.001 0.001
y[1] (numeric) = 1.30136505648 1.21102886715
y[1] (closed_form) = 1.30136822181 1.21104362006
absolute error = 1.509e-05
relative error = 0.0008488 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.002
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.414
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = 1.30198638838 1.21187143579
y[1] (closed_form) = 1.30198961944 1.21188611932
absolute error = 1.503e-05
relative error = 0.0008453 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.003
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.498
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4030.7MB, alloc=52.3MB, time=48.42
x[1] = 0.4795 1.699
h = 0.003 0.006
y[1] (numeric) = 1.30161727336 1.21481061666
y[1] (closed_form) = 1.3016201249 1.21482537065
absolute error = 1.503e-05
relative error = 0.000844 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.006
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.039
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = 1.30314838653 1.21953625091
y[1] (closed_form) = 1.30315146059 1.2195516972
absolute error = 1.575e-05
relative error = 0.0008824 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.012
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.245
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = 1.30266583636 1.22321033145
y[1] (closed_form) = 1.30266884468 1.223225311
absolute error = 1.528e-05
relative error = 0.000855 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.015
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.809
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4827 1.713
h = 0.001 0.001
y[1] (numeric) = 1.30240475979 1.22541939351
y[1] (closed_form) = 1.30240793113 1.22543428689
absolute error = 1.523e-05
relative error = 0.0008515 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.016
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.421
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4837 1.714
h = 0.001 0.003
y[1] (numeric) = 1.30302590361 1.22626364651
y[1] (closed_form) = 1.30302914021 1.22627847054
absolute error = 1.517e-05
relative error = 0.000848 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.018
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.748
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4076.2MB, alloc=52.3MB, time=48.97
x[1] = 0.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = 1.30342413521 1.22857349748
y[1] (closed_form) = 1.30342723313 1.22858845733
absolute error = 1.528e-05
relative error = 0.0008529 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.02
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.822
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4848 1.721
h = 0.003 0.006
y[1] (numeric) = 1.30305059173 1.23151643299
y[1] (closed_form) = 1.30305352985 1.23153135138
absolute error = 1.520e-05
relative error = 0.000848 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.023
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.067
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = 1.30457791977 1.23625059109
y[1] (closed_form) = 1.30458108206 1.23626619803
absolute error = 1.592e-05
relative error = 0.000886 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.028
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.258
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = 1.30409010693 1.23992919542
y[1] (closed_form) = 1.30409320203 1.23994433781
absolute error = 1.546e-05
relative error = 0.0008589 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.031
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.819
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.488 1.735
h = 0.001 0.001
y[1] (numeric) = 1.30382591229 1.24214101701
y[1] (closed_form) = 1.30382916939 1.242156073
absolute error = 1.540e-05
relative error = 0.0008554 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.033
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.429
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4121.7MB, alloc=52.3MB, time=49.51
x[1] = 0.489 1.736
h = 0.001 0.003
y[1] (numeric) = 1.30444687232 1.24298722255
y[1] (closed_form) = 1.30445019415 1.24300220924
absolute error = 1.535e-05
relative error = 0.0008519 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.035
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.786
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.49 1.739
h = 0.0001 0.004
y[1] (numeric) = 1.30484278373 1.24530079323
y[1] (closed_form) = 1.30484596797 1.24531591568
absolute error = 1.545e-05
relative error = 0.0008568 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.037
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.843
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4901 1.743
h = 0.003 0.006
y[1] (numeric) = 1.30446506218 1.24824737112
y[1] (closed_form) = 1.30446808714 1.24826245287
absolute error = 1.538e-05
relative error = 0.000852 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.04
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.096
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = 1.30598865264 1.25299003144
y[1] (closed_form) = 1.30599190338 1.25300579805
absolute error = 1.610e-05
relative error = 0.0008895 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.045
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.27
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = 1.30549561592 1.25667316014
y[1] (closed_form) = 1.30549879803 1.25668846439
absolute error = 1.563e-05
relative error = 0.0008626 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.048
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.83
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4167.2MB, alloc=52.3MB, time=50.05
x[1] = 0.4933 1.757
h = 0.001 0.001
y[1] (numeric) = 1.30522832644 1.25888774127
y[1] (closed_form) = 1.30523166957 1.25890295887
absolute error = 1.558e-05
relative error = 0.0008592 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.05
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.437
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4943 1.758
h = 0.001 0.003
y[1] (numeric) = 1.30584911066 1.25973589185
y[1] (closed_form) = 1.305852518 1.2597510402
absolute error = 1.553e-05
relative error = 0.0008557 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.052
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.824
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = 1.30624272533 1.26205317524
y[1] (closed_form) = 1.30624599614 1.2620684593
absolute error = 1.563e-05
relative error = 0.0008605 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.054
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.864
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4954 1.765
h = 0.003 0.006
y[1] (numeric) = 1.30586085662 1.2650033957
y[1] (closed_form) = 1.30586396866 1.26501863981
absolute error = 1.556e-05
relative error = 0.0008557 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.057
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.124
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = 1.3073807564 1.26975453643
y[1] (closed_form) = 1.30738409578 1.2697704617
absolute error = 1.627e-05
relative error = 0.0008928 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.062
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.283
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4212.6MB, alloc=52.3MB, time=50.60
x[1] = 0.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = 1.30688253419 1.27344218975
y[1] (closed_form) = 1.30688580354 1.27345765485
absolute error = 1.581e-05
relative error = 0.0008663 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.065
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.84
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4986 1.779
h = 0.001 0.001
y[1] (numeric) = 1.30661217291 1.27565953018
y[1] (closed_form) = 1.30661560229 1.27567490842
absolute error = 1.576e-05
relative error = 0.0008628 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.067
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.445
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4996 1.78
h = 0.001 0.003
y[1] (numeric) = 1.30723278917 1.27650961832
y[1] (closed_form) = 1.30723628224 1.27652492736
absolute error = 1.570e-05
relative error = 0.0008594 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.069
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.862
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = 1.30762413024 1.27883060732
y[1] (closed_form) = 1.30762748785 1.27884605199
absolute error = 1.581e-05
relative error = 0.0008641 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.071
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.886
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5007 1.787
h = 0.003 0.006
y[1] (numeric) = 1.30723814496 1.28178447024
y[1] (closed_form) = 1.30724134432 1.2817998757
absolute error = 1.573e-05
relative error = 0.0008594 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.074
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.153
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4258.1MB, alloc=52.3MB, time=51.14
x[1] = 0.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = 1.30875440033 1.28654406938
y[1] (closed_form) = 1.30875782855 1.28656015235
absolute error = 1.644e-05
relative error = 0.000896 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.08
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.296
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = 1.30825103065 1.29023624725
y[1] (closed_form) = 1.30825438747 1.29025187221
absolute error = 1.598e-05
relative error = 0.0008698 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.083
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.85
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5039 1.801
h = 0.001 0.001
y[1] (numeric) = 1.30797762037 1.29245634658
y[1] (closed_form) = 1.30798113624 1.29247188447
absolute error = 1.593e-05
relative error = 0.0008663 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.084
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.453
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = 1.30859807636 1.2933083648
y[1] (closed_form) = 1.3086016554 1.29332383354
absolute error = 1.588e-05
relative error = 0.000863 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.086
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.73
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.505 1.806
h = 0.003 0.006
y[1] (numeric) = 1.30820874136 1.29626519993
y[1] (closed_form) = 1.3082119498 1.29628074439
absolute error = 1.587e-05
relative error = 0.0008618 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.088
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.177
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4303.6MB, alloc=52.3MB, time=51.68
x[1] = 0.508 1.812
h = 0.0001 0.005
y[1] (numeric) = 1.3097217959 1.30103201936
y[1] (closed_form) = 1.30972523451 1.30104823821
absolute error = 1.658e-05
relative error = 0.0008981 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.094
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.307
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = 1.30921397172 1.3047280308
y[1] (closed_form) = 1.30921733777 1.30474379349
absolute error = 1.612e-05
relative error = 0.000872 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.097
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.859
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5082 1.82
h = 0.001 0.001
y[1] (numeric) = 1.3089379222 1.30695046849
y[1] (closed_form) = 1.30894144645 1.30696614391
absolute error = 1.607e-05
relative error = 0.0008686 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.099
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.46
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5092 1.821
h = 0.001 0.003
y[1] (numeric) = 1.30955822343 1.30780414027
y[1] (closed_form) = 1.30956181041 1.3078197466
absolute error = 1.601e-05
relative error = 0.0008652 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.933
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = 1.30994535059 1.31013197871
y[1] (closed_form) = 1.30994880407 1.31014772054
absolute error = 1.612e-05
relative error = 0.0008699 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.926
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4349.1MB, alloc=52.3MB, time=52.23
x[1] = 0.5103 1.828
h = 0.003 0.006
y[1] (numeric) = 1.30955174239 1.31309257011
y[1] (closed_form) = 1.30955503857 1.31310827408
absolute error = 1.605e-05
relative error = 0.0008653 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.105
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.206
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = 1.31106123719 1.3178678071
y[1] (closed_form) = 1.31106476497 1.31788418183
absolute error = 1.675e-05
relative error = 0.0009011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.111
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.319
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = 1.31054833532 1.32156834254
y[1] (closed_form) = 1.31055178923 1.32158426327
absolute error = 1.629e-05
relative error = 0.0008753 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.114
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.869
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5135 1.842
h = 0.001 0.001
y[1] (numeric) = 1.31026927863 1.32379353814
y[1] (closed_form) = 1.31027288978 1.32380937141
absolute error = 1.624e-05
relative error = 0.0008719 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.116
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.468
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5145 1.843
h = 0.001 0.003
y[1] (numeric) = 1.31088943365 1.3246491262
y[1] (closed_form) = 1.31089310703 1.32466489045
absolute error = 1.619e-05
relative error = 0.0008685 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.118
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.971
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4394.5MB, alloc=52.3MB, time=52.77
x[1] = 0.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = 1.31127435198 1.32698064947
y[1] (closed_form) = 1.31127789289 1.32699654911
absolute error = 1.629e-05
relative error = 0.0008731 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.12
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.948
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5156 1.85
h = 0.003 0.006
y[1] (numeric) = 1.31087671311 1.32994488203
y[1] (closed_form) = 1.31088009724 1.32996074453
absolute error = 1.622e-05
relative error = 0.0008686 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.123
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.235
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = 1.31238269264 1.3347285141
y[1] (closed_form) = 1.31238630975 1.33474504377
absolute error = 1.692e-05
relative error = 0.000904 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.129
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.332
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = 1.31186475006 1.33843357259
y[1] (closed_form) = 1.31186829201 1.33844965039
absolute error = 1.646e-05
relative error = 0.0008784 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.132
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.88
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5188 1.864
h = 0.001 0.001
y[1] (numeric) = 1.31158270835 1.34066152518
y[1] (closed_form) = 1.3115864066 1.34067751534
absolute error = 1.641e-05
relative error = 0.0008751 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.134
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.476
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4440.1MB, alloc=52.3MB, time=53.32
x[1] = 0.5198 1.865
h = 0.001 0.003
y[1] (numeric) = 1.31220272448 1.34151902205
y[1] (closed_form) = 1.31220648445 1.34153494326
absolute error = 1.636e-05
relative error = 0.0008717 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.135
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.01
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = 1.31258545606 1.34385422258
y[1] (closed_form) = 1.31258908458 1.34387027908
absolute error = 1.646e-05
relative error = 0.0008763 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.137
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.97
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5209 1.872
h = 0.003 0.006
y[1] (numeric) = 1.31218381597 1.34682209526
y[1] (closed_form) = 1.31218728823 1.34683811532
absolute error = 1.639e-05
relative error = 0.0008717 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.14
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.264
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = 1.31368632409 1.35161409978
y[1] (closed_form) = 1.31369003068 1.35163078343
absolute error = 1.709e-05
relative error = 0.0009067 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.146
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.345
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.524 1.883
h = 0.0001 0.003
y[1] (numeric) = 1.31316337739 1.35532368006
y[1] (closed_form) = 1.31316700758 1.35533991398
absolute error = 1.663e-05
relative error = 0.0008815 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.149
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.89
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4485.5MB, alloc=52.3MB, time=53.86
x[1] = 0.5241 1.886
h = 0.001 0.001
y[1] (numeric) = 1.31287837262 1.35755438855
y[1] (closed_form) = 1.31288215815 1.35757053465
absolute error = 1.658e-05
relative error = 0.0008781 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.485
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5251 1.887
h = 0.001 0.003
y[1] (numeric) = 1.31349825702 1.35841378679
y[1] (closed_form) = 1.31350210379 1.35842986401
absolute error = 1.653e-05
relative error = 0.0008748 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.152
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.049
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = 1.31387882364 1.36075265689
y[1] (closed_form) = 1.31388253997 1.3607688693
absolute error = 1.663e-05
relative error = 0.0008793 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.155
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.992
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5262 1.894
h = 0.003 0.006
y[1] (numeric) = 1.3134732115 1.36372416842
y[1] (closed_form) = 1.31347677209 1.36374034508
absolute error = 1.656e-05
relative error = 0.0008748 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.157
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.293
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = 1.31497229145 1.36852452265
y[1] (closed_form) = 1.31497608767 1.36854135934
absolute error = 1.726e-05
relative error = 0.0009094 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.358
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4531.1MB, alloc=52.3MB, time=54.41
x[1] = 0.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = 1.31444437688 1.37223862319
y[1] (closed_form) = 1.31444809548 1.37225501227
absolute error = 1.681e-05
relative error = 0.0008844 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.166
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.901
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5294 1.908
h = 0.001 0.001
y[1] (numeric) = 1.31415643076 1.37447208631
y[1] (closed_form) = 1.31416030376 1.3744883874
absolute error = 1.675e-05
relative error = 0.0008811 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.168
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.493
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = 1.31477619051 1.3753333785
y[1] (closed_form) = 1.31478012425 1.3753496108
absolute error = 1.670e-05
relative error = 0.0008778 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.17
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.968
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5305 1.913
h = 0.003 0.006
y[1] (numeric) = 1.31436734576 1.37830785867
y[1] (closed_form) = 1.31437091761 1.37832417133
absolute error = 1.670e-05
relative error = 0.0008768 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.172
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.318
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = 1.31586340995 1.38311534158
y[1] (closed_form) = 1.31586721855 1.38313231126
absolute error = 1.739e-05
relative error = 0.000911 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.369
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4576.6MB, alloc=52.3MB, time=54.95
x[1] = 0.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = 1.31533119414 1.38683327297
y[1] (closed_form) = 1.31533492407 1.38684979685
absolute error = 1.694e-05
relative error = 0.0008862 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.181
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.909
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5337 1.927
h = 0.001 0.001
y[1] (numeric) = 1.31504070063 1.38906907136
y[1] (closed_form) = 1.31504458416 1.3890855071
absolute error = 1.689e-05
relative error = 0.0008829 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.183
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.5
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5347 1.928
h = 0.001 0.003
y[1] (numeric) = 1.31566033619 1.38993198649
y[1] (closed_form) = 1.31566428005 1.3899483535
absolute error = 1.684e-05
relative error = 0.0008797 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.185
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.121
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = 1.31603688791 1.39227763884
y[1] (closed_form) = 1.31604070318 1.39229414082
absolute error = 1.694e-05
relative error = 0.0008841 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.187
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.033
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5358 1.935
h = 0.003 0.006
y[1] (numeric) = 1.31562391801 1.39525587079
y[1] (closed_form) = 1.31562757851 1.39527233827
absolute error = 1.687e-05
relative error = 0.0008797 %
Correct digits = 5
memory used=4622.1MB, alloc=52.3MB, time=55.50
Radius of convergence (given) for eq 1 = 3.19
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.348
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = 1.3171166332 1.40007166124
y[1] (closed_form) = 1.31712053168 1.40008878224
absolute error = 1.756e-05
relative error = 0.0009135 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.196
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.382
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = 1.31657951603 1.40379410974
y[1] (closed_form) = 1.31658333467 1.40381078703
absolute error = 1.711e-05
relative error = 0.000889 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.199
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.92
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.539 1.949
h = 0.001 0.001
y[1] (numeric) = 1.31628612102 1.40603266023
y[1] (closed_form) = 1.31629009233 1.40604924924
absolute error = 1.706e-05
relative error = 0.0008856 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.201
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.508
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.54 1.95
h = 0.001 0.003
y[1] (numeric) = 1.31690564479 1.40689745563
y[1] (closed_form) = 1.31690967596 1.40691397598
absolute error = 1.701e-05
relative error = 0.0008824 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.202
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.16
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4667.7MB, alloc=52.3MB, time=56.04
x[1] = 0.541 1.953
h = 0.0001 0.004
y[1] (numeric) = 1.31728009251 1.40924675528
y[1] (closed_form) = 1.31728399606 1.40926341049
absolute error = 1.711e-05
relative error = 0.0008868 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.205
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.055
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5411 1.957
h = 0.003 0.006
y[1] (numeric) = 1.31686323239 1.41222862159
y[1] (closed_form) = 1.3168669817 1.41224524296
absolute error = 1.704e-05
relative error = 0.0008824 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.207
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.377
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = 1.31835264013 1.41705269649
y[1] (closed_form) = 1.31835662861 1.41706996788
absolute error = 1.773e-05
relative error = 0.0009158 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.396
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = 1.31781065682 1.4207796598
y[1] (closed_form) = 1.31781456432 1.42079648958
absolute error = 1.728e-05
relative error = 0.0008916 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.217
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.931
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5443 1.971
h = 0.001 0.001
y[1] (numeric) = 1.3175143814 1.4230209607
y[1] (closed_form) = 1.31751844065 1.42303770205
absolute error = 1.723e-05
relative error = 0.0008883 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.218
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.516
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4713.1MB, alloc=52.3MB, time=56.59
x[1] = 0.5453 1.972
h = 0.001 0.003
y[1] (numeric) = 1.31813380008 1.42388762897
y[1] (closed_form) = 1.31813791872 1.42390430176
absolute error = 1.717e-05
relative error = 0.0008851 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.22
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.2
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = 1.31850616456 1.4262405679
y[1] (closed_form) = 1.31851015655 1.42625737539
absolute error = 1.728e-05
relative error = 0.0008894 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.222
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.077
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5464 1.979
h = 0.003 0.006
y[1] (numeric) = 1.31808544228 1.42922606648
y[1] (closed_form) = 1.31808928055 1.42924284079
absolute error = 1.721e-05
relative error = 0.0008851 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.225
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.407
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = 1.31957158355 1.43405840264
y[1] (closed_form) = 1.31957566214 1.43407582351
absolute error = 1.789e-05
relative error = 0.0009181 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.231
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.409
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = 1.31902476895 1.43778987822
y[1] (closed_form) = 1.31902876546 1.43780685955
absolute error = 1.745e-05
relative error = 0.0008941 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.234
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.941
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4758.5MB, alloc=52.3MB, time=57.14
x[1] = 0.5496 1.993
h = 0.001 0.001
y[1] (numeric) = 1.318725634 1.44003392766
y[1] (closed_form) = 1.31872978134 1.44005082044
absolute error = 1.739e-05
relative error = 0.0008908 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.236
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.525
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5506 1.994
h = 0.001 0.003
y[1] (numeric) = 1.31934495418 1.44090246146
y[1] (closed_form) = 1.31934916044 1.44091928576
absolute error = 1.734e-05
relative error = 0.0008877 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.238
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.239
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = 1.31971525592 1.44325903152
y[1] (closed_form) = 1.31971933649 1.4432759904
absolute error = 1.744e-05
relative error = 0.0008919 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.24
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.1
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5517 2.001
h = 0.003 0.006
y[1] (numeric) = 1.31929069923 1.44624816011
y[1] (closed_form) = 1.3192946266 1.44626508642
absolute error = 1.738e-05
relative error = 0.0008876 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.243
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.436
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = 1.32077361445 1.45108873423
y[1] (closed_form) = 1.32077778326 1.45110630369
absolute error = 1.806e-05
relative error = 0.0009203 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.249
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.422
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4804.0MB, alloc=52.3MB, time=57.68
x[1] = 0.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = 1.32022200308 1.45482471929
y[1] (closed_form) = 1.32022608871 1.45484185128
absolute error = 1.761e-05
relative error = 0.0008965 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.252
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.952
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5549 2.015
h = 0.001 0.001
y[1] (numeric) = 1.31992002927 1.4570715153
y[1] (closed_form) = 1.31992426482 1.4570885586
absolute error = 1.756e-05
relative error = 0.0008933 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.254
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.533
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = 1.3205392574 1.45794190727
y[1] (closed_form) = 1.32054355141 1.45795888219
absolute error = 1.751e-05
relative error = 0.0008901 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.255
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.21
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.556 2.02
h = 0.003 0.006
y[1] (numeric) = 1.32011157966 1.46093399673
y[1] (closed_form) = 1.32011552025 1.46095105614
absolute error = 1.751e-05
relative error = 0.0008892 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.258
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.462
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.559 2.026
h = 0.0001 0.005
y[1] (numeric) = 1.32159165218 1.46578160534
y[1] (closed_form) = 1.32159583518 1.46579930497
absolute error = 1.819e-05
relative error = 0.0009215 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.264
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.433
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4849.5MB, alloc=52.3MB, time=58.23
x[1] = 0.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = 1.32103588561 1.46952141302
y[1] (closed_form) = 1.32103998449 1.46953867693
absolute error = 1.774e-05
relative error = 0.000898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.267
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.961
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5592 2.034
h = 0.001 0.001
y[1] (numeric) = 1.3207314519 1.47177053798
y[1] (closed_form) = 1.32073569993 1.4717877131
absolute error = 1.769e-05
relative error = 0.0008947 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5602 2.035
h = 0.001 0.003
y[1] (numeric) = 1.32135058386 1.47264252257
y[1] (closed_form) = 1.32135488995 1.47265962937
absolute error = 1.764e-05
relative error = 0.0008916 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.27
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.313
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = 1.32171705798 1.47500580345
y[1] (closed_form) = 1.32172124015 1.47502304456
absolute error = 1.774e-05
relative error = 0.0008958 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.273
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.141
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5613 2.042
h = 0.003 0.006
y[1] (numeric) = 1.32128539611 1.47800163499
y[1] (closed_form) = 1.32128942604 1.47801884471
absolute error = 1.768e-05
relative error = 0.0008916 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.276
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.492
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4895.0MB, alloc=52.3MB, time=58.78
x[1] = 0.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = 1.32276231656 1.48285743851
y[1] (closed_form) = 1.32276658995 1.48287528506
absolute error = 1.835e-05
relative error = 0.0009235 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.282
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.447
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = 1.32220181654 1.48660175028
y[1] (closed_form) = 1.32220600477 1.48661916316
absolute error = 1.791e-05
relative error = 0.0009002 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.285
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.972
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5645 2.056
h = 0.001 0.001
y[1] (numeric) = 1.32189458187 1.48885361797
y[1] (closed_form) = 1.32189891838 1.48887094195
absolute error = 1.786e-05
relative error = 0.000897 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.287
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.549
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5655 2.057
h = 0.001 0.003
y[1] (numeric) = 1.32251363358 1.48972744722
y[1] (closed_form) = 1.32251802769 1.48974470298
absolute error = 1.781e-05
relative error = 0.0008939 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.353
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = 1.3228781023 1.49209433582
y[1] (closed_form) = 1.32288237341 1.49211172573
absolute error = 1.791e-05
relative error = 0.000898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.291
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.164
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4940.6MB, alloc=52.3MB, time=59.33
x[1] = 0.5666 2.064
h = 0.003 0.006
y[1] (numeric) = 1.32244268392 1.49509379013
y[1] (closed_form) = 1.32244680332 1.49511114926
absolute error = 1.784e-05
relative error = 0.0008938 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.294
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.522
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = 1.32391649113 1.49995776507
y[1] (closed_form) = 1.32392085499 1.49997575766
absolute error = 1.851e-05
relative error = 0.0009254 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.3
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.46
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = 1.32335129117 1.50370657749
y[1] (closed_form) = 1.32335556887 1.50372413845
absolute error = 1.807e-05
relative error = 0.0009023 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.303
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.982
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5698 2.078
h = 0.001 0.001
y[1] (numeric) = 1.32304127562 1.50596118553
y[1] (closed_form) = 1.3230457007 1.50597865748
absolute error = 1.802e-05
relative error = 0.0008991 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.305
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.557
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5708 2.079
h = 0.001 0.003
y[1] (numeric) = 1.32366025319 1.50683685217
y[1] (closed_form) = 1.32366473543 1.506854256
absolute error = 1.797e-05
relative error = 0.000896 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.306
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.393
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4986.0MB, alloc=52.3MB, time=59.87
x[1] = 0.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = 1.32402273603 1.50920734008
y[1] (closed_form) = 1.3240270962 1.50922487791
absolute error = 1.807e-05
relative error = 0.0009001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.309
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.187
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5719 2.086
h = 0.003 0.006
y[1] (numeric) = 1.32358358783 1.5122104142
y[1] (closed_form) = 1.32358779681 1.51222792184
absolute error = 1.801e-05
relative error = 0.000896 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.312
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.552
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = 1.32505432008 1.51708253698
y[1] (closed_form) = 1.32505877449 1.51710067474
absolute error = 1.868e-05
relative error = 0.0009272 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.318
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.473
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.575 2.097
h = 0.0001 0.003
y[1] (numeric) = 1.32448445336 1.52083584642
y[1] (closed_form) = 1.32448882061 1.52085355456
absolute error = 1.824e-05
relative error = 0.0009044 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.321
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.993
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5751 2.1
h = 0.001 0.001
y[1] (numeric) = 1.32417167677 1.52309319231
y[1] (closed_form) = 1.32417619054 1.52311081136
absolute error = 1.819e-05
relative error = 0.0009012 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.323
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.566
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5031.5MB, alloc=52.3MB, time=60.42
x[1] = 0.5761 2.101
h = 0.001 0.003
y[1] (numeric) = 1.32479058624 1.52397068909
y[1] (closed_form) = 1.32479515672 1.52398824012
absolute error = 1.814e-05
relative error = 0.0008981 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.324
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.433
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = 1.32515110248 1.52634476785
y[1] (closed_form) = 1.3251555518 1.5263624527
absolute error = 1.824e-05
relative error = 0.0009022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.327
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.21
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5772 2.108
h = 0.003 0.006
y[1] (numeric) = 1.32470825086 1.52935145862
y[1] (closed_form) = 1.32471254951 1.52936911388
absolute error = 1.817e-05
relative error = 0.0008981 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.33
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.582
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = 1.32617594589 1.53423170564
y[1] (closed_form) = 1.32618049092 1.53424998771
absolute error = 1.884e-05
relative error = 0.0009289 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.336
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.487
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = 1.32560144524 1.53798950824
y[1] (closed_form) = 1.32560590215 1.5380073627
absolute error = 1.840e-05
relative error = 0.0009063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.339
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.004
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5076.9MB, alloc=52.3MB, time=60.96
x[1] = 0.5804 2.122
h = 0.001 0.001
y[1] (numeric) = 1.32528592727 1.54024958937
y[1] (closed_form) = 1.32529052983 1.54026735465
absolute error = 1.835e-05
relative error = 0.0009032 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.341
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.574
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = 1.32590477454 1.54112890906
y[1] (closed_form) = 1.32590943337 1.54114660642
absolute error = 1.830e-05
relative error = 0.0009002 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.342
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.456
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5815 2.127
h = 0.003 0.006
y[1] (numeric) = 1.32545890803 1.54413854939
y[1] (closed_form) = 1.32546322166 1.54415633488
absolute error = 1.830e-05
relative error = 0.0008993 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.345
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.608
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = 1.32692392216 1.54902573496
y[1] (closed_form) = 1.326928483 1.54904414443
absolute error = 1.897e-05
relative error = 0.0009299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.351
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.498
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = 1.32634540535 1.5527873472
y[1] (closed_form) = 1.32634987724 1.55280533079
absolute error = 1.853e-05
relative error = 0.0009074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.354
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.013
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5122.4MB, alloc=52.3MB, time=61.50
x[1] = 0.5847 2.141
h = 0.001 0.001
y[1] (numeric) = 1.32602751073 1.55504974822
y[1] (closed_form) = 1.32603212752 1.55506764254
absolute error = 1.848e-05
relative error = 0.0009043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.581
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5857 2.142
h = 0.001 0.003
y[1] (numeric) = 1.32664628751 1.5559306306
y[1] (closed_form) = 1.3266509602 1.55594845709
absolute error = 1.843e-05
relative error = 0.0009013 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.358
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.508
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = 1.32700315231 1.55831134547
y[1] (closed_form) = 1.3270077055 1.55832930547
absolute error = 1.853e-05
relative error = 0.0009052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.36
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.252
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5868 2.149
h = 0.003 0.006
y[1] (numeric) = 1.32655343587 1.56132471372
y[1] (closed_form) = 1.32655783936 1.5613426452
absolute error = 1.846e-05
relative error = 0.0009012 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.363
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.638
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = 1.32801548191 1.5662199799
y[1] (closed_form) = 1.32802013349 1.56623853209
absolute error = 1.913e-05
relative error = 0.0009314 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.369
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.512
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5168.0MB, alloc=52.3MB, time=62.05
x[1] = 0.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = 1.32743239142 1.569986078
y[1] (closed_form) = 1.32743695312 1.57000420629
absolute error = 1.869e-05
relative error = 0.0009092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.372
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.024
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.59 2.163
h = 0.001 0.001
y[1] (numeric) = 1.32711179148 1.57225120931
y[1] (closed_form) = 1.32711649723 1.57226924827
absolute error = 1.864e-05
relative error = 0.0009061 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.374
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.59
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.591 2.164
h = 0.001 0.003
y[1] (numeric) = 1.32773051685 1.57313390131
y[1] (closed_form) = 1.32773527807 1.57315187254
absolute error = 1.859e-05
relative error = 0.0009031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.376
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.549
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.592 2.167
h = 0.0001 0.004
y[1] (numeric) = 1.32808546896 1.57551818272
y[1] (closed_form) = 1.32809011157 1.57553628727
absolute error = 1.869e-05
relative error = 0.000907 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.379
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.275
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5921 2.171
h = 0.003 0.006
y[1] (numeric) = 1.3276321232 1.57853515808
y[1] (closed_form) = 1.32763661662 1.57855323468
absolute error = 1.863e-05
relative error = 0.0009031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.381
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.669
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5213.6MB, alloc=52.3MB, time=62.59
x[1] = 0.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = 1.32909123742 1.58343848114
y[1] (closed_form) = 1.32909597978 1.58345717521
absolute error = 1.929e-05
relative error = 0.0009329 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.387
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.525
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = 1.32850360512 1.5872090607
y[1] (closed_form) = 1.32850825671 1.58722733284
absolute error = 1.885e-05
relative error = 0.0009109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.391
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.035
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5953 2.185
h = 0.001 0.001
y[1] (numeric) = 1.32818031892 1.58947691937
y[1] (closed_form) = 1.32818511371 1.58949510211
absolute error = 1.880e-05
relative error = 0.0009078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.393
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.598
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5963 2.186
h = 0.001 0.003
y[1] (numeric) = 1.32879899849 1.59036141384
y[1] (closed_form) = 1.32880384833 1.59037952895
absolute error = 1.875e-05
relative error = 0.0009049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.394
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.589
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = 1.32915205627 1.59274925311
y[1] (closed_form) = 1.32915678837 1.59276750136
absolute error = 1.885e-05
relative error = 0.0009087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.397
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.298
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5259.1MB, alloc=52.3MB, time=63.14
x[1] = 0.5974 2.193
h = 0.003 0.006
y[1] (numeric) = 1.32869510656 1.59576983185
y[1] (closed_form) = 1.32869968999 1.59578805271
absolute error = 1.879e-05
relative error = 0.0009048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.399
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.699
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = 1.33015132472 1.60068118802
y[1] (closed_form) = 1.33015615791 1.60070002313
absolute error = 1.945e-05
relative error = 0.0009343 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.406
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.539
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = 1.32955918215 1.60445624446
y[1] (closed_form) = 1.32956392369 1.6044746596
absolute error = 1.902e-05
relative error = 0.0009126 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.409
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.046
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6006 2.207
h = 0.001 0.001
y[1] (numeric) = 1.32923322856 1.60672682745
y[1] (closed_form) = 1.32923811247 1.60674515313
absolute error = 1.897e-05
relative error = 0.0009095 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.411
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.607
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6016 2.208
h = 0.001 0.003
y[1] (numeric) = 1.32985186785 1.60761311726
y[1] (closed_form) = 1.32985680638 1.60763137543
absolute error = 1.891e-05
relative error = 0.0009066 %
Correct digits = 5
memory used=5304.7MB, alloc=52.3MB, time=63.69
Radius of convergence (given) for eq 1 = 3.412
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.63
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = 1.33020304942 1.61000450567
y[1] (closed_form) = 1.33020787108 1.6100228968
absolute error = 1.901e-05
relative error = 0.0009104 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.415
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.321
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6027 2.215
h = 0.003 0.006
y[1] (numeric) = 1.32974252087 1.61302868393
y[1] (closed_form) = 1.32974719437 1.6130470482
absolute error = 1.895e-05
relative error = 0.0009065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.418
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.73
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = 1.33119587821 1.61794804944
y[1] (closed_form) = 1.33120080227 1.61796702476
absolute error = 1.960e-05
relative error = 0.0009356 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.424
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.552
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = 1.33059925661 1.62172757799
y[1] (closed_form) = 1.33060408816 1.6217461353
absolute error = 1.918e-05
relative error = 0.0009141 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.427
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.057
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5350.1MB, alloc=52.3MB, time=64.23
x[1] = 0.6059 2.229
h = 0.001 0.001
y[1] (numeric) = 1.3302706543 1.62400088216
y[1] (closed_form) = 1.33027562739 1.62401934995
absolute error = 1.913e-05
relative error = 0.000911 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.429
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.616
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = 1.3308892587 1.62488896023
y[1] (closed_form) = 1.33089428599 1.62490736062
absolute error = 1.907e-05
relative error = 0.0009082 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.431
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.706
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.607 2.234
h = 0.003 0.006
y[1] (numeric) = 1.33042581619 1.62791607368
y[1] (closed_form) = 1.33043050627 1.6279345654
absolute error = 1.908e-05
relative error = 0.0009074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.433
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.756
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.61 2.24
h = 0.0001 0.005
y[1] (numeric) = 1.33187664389 1.63284228077
y[1] (closed_form) = 1.33188158522 1.63286138082
absolute error = 1.973e-05
relative error = 0.0009363 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.439
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.564
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = 1.33127613843 1.63662560199
y[1] (closed_form) = 1.3312809865 1.63664428569
absolute error = 1.930e-05
relative error = 0.0009149 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.443
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.066
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5395.5MB, alloc=52.3MB, time=64.78
x[1] = 0.6102 2.248
h = 0.001 0.001
y[1] (numeric) = 1.33094523864 1.63890121463
y[1] (closed_form) = 1.33095022754 1.63891980875
absolute error = 1.925e-05
relative error = 0.0009119 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.445
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.623
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6112 2.249
h = 0.001 0.003
y[1] (numeric) = 1.33156379607 1.63979082598
y[1] (closed_form) = 1.33156883883 1.63980935279
absolute error = 1.920e-05
relative error = 0.000909 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.446
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.706
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = 1.33191149189 1.64218877332
y[1] (closed_form) = 1.33191641936 1.64220743274
absolute error = 1.930e-05
relative error = 0.0009127 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.449
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.364
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6123 2.256
h = 0.003 0.006
y[1] (numeric) = 1.33144432711 1.64521959674
y[1] (closed_form) = 1.33144910737 1.6452382303
absolute error = 1.924e-05
relative error = 0.0009089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.452
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.787
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = 1.33289235859 1.65015376927
y[1] (closed_form) = 1.33289739084 1.65017300801
absolute error = 1.989e-05
relative error = 0.0009375 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.458
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.578
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5441.0MB, alloc=52.3MB, time=65.32
x[1] = 0.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = 1.33228743138 1.65394155369
y[1] (closed_form) = 1.33229236957 1.653960378
absolute error = 1.946e-05
relative error = 0.0009163 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.461
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.077
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6155 2.27
h = 0.001 0.001
y[1] (numeric) = 1.33195391715 1.65621988162
y[1] (closed_form) = 1.33195899534 1.65623861632
absolute error = 1.941e-05
relative error = 0.0009133 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.463
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.632
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6165 2.271
h = 0.001 0.003
y[1] (numeric) = 1.33257244957 1.65711126818
y[1] (closed_form) = 1.33257758121 1.65712993568
absolute error = 1.936e-05
relative error = 0.0009104 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.465
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.747
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = 1.33291831987 1.65951273971
y[1] (closed_form) = 1.33292333706 1.65953153961
absolute error = 1.946e-05
relative error = 0.0009141 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.467
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.387
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6176 2.278
h = 0.003 0.006
y[1] (numeric) = 1.33244764669 1.66254715113
y[1] (closed_form) = 1.33245251719 1.6625659257
absolute error = 1.940e-05
relative error = 0.0009103 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.818
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5486.5MB, alloc=52.3MB, time=65.86
x[1] = 0.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = 1.33389291582 1.66748926527
y[1] (closed_form) = 1.33389803903 1.6675086419
absolute error = 2.004e-05
relative error = 0.0009386 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.476
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.592
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = 1.33328359717 1.67128150767
y[1] (closed_form) = 1.33328862551 1.67130047178
absolute error = 1.962e-05
relative error = 0.0009177 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.48
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.088
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6208 2.292
h = 0.001 0.001
y[1] (numeric) = 1.3329474866 1.67356254749
y[1] (closed_form) = 1.33295265414 1.67358142195
absolute error = 1.957e-05
relative error = 0.0009146 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.482
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.64
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6218 2.293
h = 0.001 0.003
y[1] (numeric) = 1.33356599914 1.67445570224
y[1] (closed_form) = 1.33357121973 1.67447450963
absolute error = 1.952e-05
relative error = 0.0009118 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.483
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.788
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = 1.33391006119 1.67686068909
y[1] (closed_form) = 1.33391516816 1.67687962867
absolute error = 1.962e-05
relative error = 0.0009155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.486
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.411
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5532.0MB, alloc=52.3MB, time=66.41
x[1] = 0.6229 2.3
h = 0.003 0.006
y[1] (numeric) = 1.33343590372 1.67989868415
y[1] (closed_form) = 1.33344086451 1.67991759891
absolute error = 1.955e-05
relative error = 0.0009117 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.488
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.849
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = 1.33487844391 1.68484871608
y[1] (closed_form) = 1.33488365808 1.68486822979
absolute error = 2.020e-05
relative error = 0.0009396 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.495
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.605
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.626 2.311
h = 0.0001 0.003
y[1] (numeric) = 1.33426476379 1.68864541109
y[1] (closed_form) = 1.33426988232 1.68866451419
absolute error = 1.978e-05
relative error = 0.0009189 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.498
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.1
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6261 2.314
h = 0.001 0.001
y[1] (numeric) = 1.33392607483 1.6909291593
y[1] (closed_form) = 1.33393133176 1.69094817272
absolute error = 1.973e-05
relative error = 0.0009159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.5
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.649
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6271 2.315
h = 0.001 0.003
y[1] (numeric) = 1.33454457253 1.69182407528
y[1] (closed_form) = 1.3345498821 1.69184302174
absolute error = 1.968e-05
relative error = 0.0009131 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.502
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.83
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5577.5MB, alloc=52.3MB, time=66.96
x[1] = 0.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = 1.33488684336 1.69423256855
y[1] (closed_form) = 1.33489204013 1.694251647
absolute error = 1.977e-05
relative error = 0.0009167 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.434
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6282 2.322
h = 0.003 0.006
y[1] (numeric) = 1.33440922546 1.69727414276
y[1] (closed_form) = 1.33441427656 1.6972931969
absolute error = 1.971e-05
relative error = 0.000913 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.507
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.88
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = 1.33584906963 1.70223206865
y[1] (closed_form) = 1.33585437478 1.70225171866
absolute error = 2.035e-05
relative error = 0.0009406 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.513
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.619
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = 1.33523105773 1.70603321076
y[1] (closed_form) = 1.33523626648 1.70605245205
absolute error = 1.993e-05
relative error = 0.0009201 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.517
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.111
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6314 2.336
h = 0.001 0.001
y[1] (numeric) = 1.33488980811 1.70831966378
y[1] (closed_form) = 1.33489515446 1.70833881536
absolute error = 1.988e-05
relative error = 0.0009171 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.519
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.658
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5623.0MB, alloc=52.3MB, time=67.50
x[1] = 0.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = 1.33550829591 1.70921633405
y[1] (closed_form) = 1.33551369451 1.70923541879
absolute error = 1.983e-05
relative error = 0.0009144 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.959
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6325 2.341
h = 0.003 0.006
y[1] (numeric) = 1.33502786001 1.71226082655
y[1] (closed_form) = 1.33503292911 1.71228000543
absolute error = 1.984e-05
relative error = 0.0009137 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.523
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.906
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = 1.33646531593 1.71722549664
y[1] (closed_form) = 1.33647063966 1.71724526877
absolute error = 2.048e-05
relative error = 0.000941 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.529
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.631
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = 1.33584354601 1.72103041102
y[1] (closed_form) = 1.33584877268 1.72104977603
absolute error = 2.006e-05
relative error = 0.0009207 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.532
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.12
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6357 2.355
h = 0.001 0.001
y[1] (numeric) = 1.33550007417 1.7233191591
y[1] (closed_form) = 1.33550543776 1.72333843437
absolute error = 2.001e-05
relative error = 0.0009177 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.535
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.665
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5668.4MB, alloc=52.3MB, time=68.04
x[1] = 0.6367 2.356
h = 0.001 0.003
y[1] (numeric) = 1.33611853655 1.72421733383
y[1] (closed_form) = 1.33612395206 1.72423654236
absolute error = 1.996e-05
relative error = 0.0009149 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.536
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.907
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = 1.33645747743 1.72663230708
y[1] (closed_form) = 1.33646278164 1.72665164722
absolute error = 2.005e-05
relative error = 0.0009185 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.539
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.478
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6378 2.363
h = 0.003 0.006
y[1] (numeric) = 1.33597344063 1.72968048838
y[1] (closed_form) = 1.33597860011 1.72969980513
absolute error = 1.999e-05
relative error = 0.0009148 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.541
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.937
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = 1.33740826089 1.73465300851
y[1] (closed_form) = 1.33741367561 1.73467291548
absolute error = 2.063e-05
relative error = 0.0009419 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.548
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.645
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = 1.33678221366 1.7384623597
y[1] (closed_form) = 1.33678753059 1.73848186142
absolute error = 2.021e-05
relative error = 0.0009217 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.551
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.131
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5713.9MB, alloc=52.3MB, time=68.59
x[1] = 0.641 2.377
h = 0.001 0.001
y[1] (numeric) = 1.33643621372 1.74075380592
y[1] (closed_form) = 1.3364416668 1.74077321789
absolute error = 2.016e-05
relative error = 0.0009188 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.553
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.674
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.642 2.378
h = 0.001 0.003
y[1] (numeric) = 1.33705467523 1.74165372216
y[1] (closed_form) = 1.33706017984 1.74167306752
absolute error = 2.011e-05
relative error = 0.000916 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.555
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.948
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.643 2.381
h = 0.0001 0.004
y[1] (numeric) = 1.33739187256 1.74407217643
y[1] (closed_form) = 1.33739726667 1.74409165317
absolute error = 2.021e-05
relative error = 0.0009195 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.557
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.501
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6431 2.385
h = 0.003 0.006
y[1] (numeric) = 1.33690444228 1.74712392373
y[1] (closed_form) = 1.33690969217 1.74714337756
absolute error = 2.015e-05
relative error = 0.0009159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.56
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.969
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = 1.33833665854 1.75210427009
y[1] (closed_form) = 1.33834216424 1.75212431114
absolute error = 2.078e-05
relative error = 0.0009427 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.566
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.659
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5759.3MB, alloc=52.3MB, time=69.13
x[1] = 0.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = 1.33770636278 1.7559180522
y[1] (closed_form) = 1.33771177 1.75593768985
absolute error = 2.037e-05
relative error = 0.0009227 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.57
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.143
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6463 2.399
h = 0.001 0.001
y[1] (numeric) = 1.33735785196 1.75821219276
y[1] (closed_form) = 1.33736339455 1.75823174064
absolute error = 2.032e-05
relative error = 0.0009198 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.572
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.683
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6473 2.4
h = 0.001 0.003
y[1] (numeric) = 1.3379763173 1.75911384366
y[1] (closed_form) = 1.33798191104 1.75913332505
absolute error = 2.027e-05
relative error = 0.0009171 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.573
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.99
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = 1.3383117873 1.76153576994
y[1] (closed_form) = 1.33831727132 1.7615553825
absolute error = 2.036e-05
relative error = 0.0009205 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.576
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.525
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6484 2.407
h = 0.003 0.006
y[1] (numeric) = 1.33782098645 1.76459107834
y[1] (closed_form) = 1.33782632676 1.76461066846
absolute error = 2.030e-05
relative error = 0.0009169 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.579
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5804.9MB, alloc=52.3MB, time=69.68
x[1] = 0.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = 1.3392506299 1.76957922717
y[1] (closed_form) = 1.33925622659 1.76959940153
absolute error = 2.094e-05
relative error = 0.0009434 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.585
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.673
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = 1.33861611413 1.77339743416
y[1] (closed_form) = 1.33862161164 1.77341720696
absolute error = 2.052e-05
relative error = 0.0009237 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.588
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.154
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6516 2.421
h = 0.001 0.001
y[1] (numeric) = 1.33826510946 1.77569426517
y[1] (closed_form) = 1.33827074157 1.77571394819
absolute error = 2.047e-05
relative error = 0.0009207 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.591
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.692
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6526 2.422
h = 0.001 0.003
y[1] (numeric) = 1.33888358323 1.77659764393
y[1] (closed_form) = 1.33888926612 1.77661726058
absolute error = 2.042e-05
relative error = 0.000918 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.592
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.032
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = 1.33921734192 1.77902303321
y[1] (closed_form) = 1.33922291586 1.77904278082
absolute error = 2.052e-05
relative error = 0.0009215 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.595
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.548
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5850.6MB, alloc=52.3MB, time=70.22
x[1] = 0.6537 2.429
h = 0.003 0.006
y[1] (numeric) = 1.33872319317 1.78208189771
y[1] (closed_form) = 1.33872862391 1.78210162334
absolute error = 2.046e-05
relative error = 0.0009179 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.598
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.031
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = 1.34015029459 1.78707782526
y[1] (closed_form) = 1.34015598224 1.78709813217
absolute error = 2.109e-05
relative error = 0.0009441 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.604
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.687
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = 1.339511587 1.79090045097
y[1] (closed_form) = 1.33951717481 1.79092035816
absolute error = 2.068e-05
relative error = 0.0009245 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.607
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.165
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6569 2.443
h = 0.001 0.001
y[1] (numeric) = 1.33915810533 1.7931999685
y[1] (closed_form) = 1.33916382697 1.7932197859
absolute error = 2.063e-05
relative error = 0.0009216 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.609
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.701
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = 1.33977659205 1.79410506832
y[1] (closed_form) = 1.3397823641 1.79412481949
absolute error = 2.058e-05
relative error = 0.000919 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.611
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.22
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5896.1MB, alloc=52.3MB, time=70.77
x[1] = 0.658 2.448
h = 0.003 0.006
y[1] (numeric) = 1.33927971651 1.79716683205
y[1] (closed_form) = 1.33928516651 1.7971866798
absolute error = 2.058e-05
relative error = 0.0009183 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.614
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.058
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661 2.454
h = 0.0001 0.005
y[1] (numeric) = 1.34070456186 1.80216940649
y[1] (closed_form) = 1.34071026927 1.80218983297
absolute error = 2.121e-05
relative error = 0.0009442 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.699
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = 1.34006221593 1.8059957812
y[1] (closed_form) = 1.34006782291 1.80601580952
absolute error = 2.080e-05
relative error = 0.0009248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.623
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.175
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6612 2.462
h = 0.001 0.001
y[1] (numeric) = 1.33970658356 1.80829757873
y[1] (closed_form) = 1.33971232372 1.80831751727
absolute error = 2.075e-05
relative error = 0.0009219 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.625
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.708
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6622 2.463
h = 0.001 0.003
y[1] (numeric) = 1.34032506459 1.80920415482
y[1] (closed_form) = 1.34033085485 1.80922402722
absolute error = 2.070e-05
relative error = 0.0009193 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.627
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.11
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5941.7MB, alloc=52.3MB, time=71.31
x[1] = 0.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = 1.34065563988 1.81163594396
y[1] (closed_form) = 1.34066132261 1.8116559469
absolute error = 2.079e-05
relative error = 0.0009227 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.63
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.593
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6633 2.47
h = 0.003 0.006
y[1] (numeric) = 1.3401552788 1.81470137266
y[1] (closed_form) = 1.34016081925 1.81472135448
absolute error = 2.074e-05
relative error = 0.0009192 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.632
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.09
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = 1.34157763853 1.81971168205
y[1] (closed_form) = 1.34158343688 1.8197322397
absolute error = 2.136e-05
relative error = 0.0009448 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.639
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.713
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = 1.34093115256 1.82354246407
y[1] (closed_form) = 1.34093684984 1.82356262536
absolute error = 2.095e-05
relative error = 0.0009256 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.642
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.186
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6665 2.484
h = 0.001 0.001
y[1] (numeric) = 1.34057307413 1.82584694079
y[1] (closed_form) = 1.34057890385 1.82586701229
absolute error = 2.090e-05
relative error = 0.0009227 %
Correct digits = 5
memory used=5987.3MB, alloc=52.3MB, time=71.85
Radius of convergence (given) for eq 1 = 3.644
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.717
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6675 2.485
h = 0.001 0.003
y[1] (numeric) = 1.34119157638 1.82675522547
y[1] (closed_form) = 1.34119745582 1.82677523097
absolute error = 2.085e-05
relative error = 0.0009201 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.646
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.152
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = 1.34152048518 1.82919045193
y[1] (closed_form) = 1.34152625786 1.82921058774
absolute error = 2.095e-05
relative error = 0.0009234 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.648
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.616
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6686 2.492
h = 0.003 0.006
y[1] (numeric) = 1.34101683983 1.83225942219
y[1] (closed_form) = 1.34102247073 1.83227953733
absolute error = 2.089e-05
relative error = 0.00092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.651
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.121
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = 1.34243674352 1.83727744287
y[1] (closed_form) = 1.34244263277 1.83729813095
absolute error = 2.151e-05
relative error = 0.0009453 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.658
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.727
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6032.8MB, alloc=52.3MB, time=72.40
x[1] = 0.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = 1.34178614487 1.84111262573
y[1] (closed_form) = 1.34179193245 1.84113291924
absolute error = 2.110e-05
relative error = 0.0009263 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.661
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.197
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6718 2.506
h = 0.001 0.001
y[1] (numeric) = 1.34142563672 1.8434197775
y[1] (closed_form) = 1.341431556 1.84343998123
absolute error = 2.105e-05
relative error = 0.0009234 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.663
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.726
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6728 2.507
h = 0.001 0.003
y[1] (numeric) = 1.34204416449 1.84432976409
y[1] (closed_form) = 1.34205013313 1.84434990195
absolute error = 2.100e-05
relative error = 0.0009208 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.665
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.194
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = 1.34237142206 1.84676841881
y[1] (closed_form) = 1.34237728468 1.84678868674
absolute error = 2.110e-05
relative error = 0.0009241 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.667
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.64
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6739 2.514
h = 0.003 0.006
y[1] (numeric) = 1.34186451421 1.84984092529
y[1] (closed_form) = 1.34187023554 1.84986117299
absolute error = 2.104e-05
relative error = 0.0009207 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.153
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6078.3MB, alloc=52.3MB, time=72.94
x[1] = 0.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = 1.34328199101 1.85486663364
y[1] (closed_form) = 1.34328797115 1.85488745141
absolute error = 2.166e-05
relative error = 0.0009458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.676
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.741
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.677 2.525
h = 0.0001 0.003
y[1] (numeric) = 1.34262730678 1.85870621075
y[1] (closed_form) = 1.34263318463 1.85872663573
absolute error = 2.125e-05
relative error = 0.0009269 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.68
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.209
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6771 2.528
h = 0.001 0.001
y[1] (numeric) = 1.34226438509 1.86101603337
y[1] (closed_form) = 1.34227039391 1.8610363686
absolute error = 2.120e-05
relative error = 0.0009241 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.682
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.735
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6781 2.529
h = 0.001 0.003
y[1] (numeric) = 1.34288294258 1.86192771523
y[1] (closed_form) = 1.3428890004 1.86194798471
absolute error = 2.116e-05
relative error = 0.0009215 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.683
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.237
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = 1.34320856399 1.86436978913
y[1] (closed_form) = 1.34321451652 1.86439018844
absolute error = 2.125e-05
relative error = 0.0009248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.686
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.664
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6123.8MB, alloc=52.3MB, time=73.48
x[1] = 0.6792 2.536
h = 0.003 0.006
y[1] (numeric) = 1.34269841518 1.86744582641
y[1] (closed_form) = 1.34270422692 1.86746620593
absolute error = 2.119e-05
relative error = 0.0009214 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.689
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.185
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = 1.34411349384 1.87247919884
y[1] (closed_form) = 1.34411956484 1.87250014558
absolute error = 2.181e-05
relative error = 0.0009462 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.755
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = 1.34345475083 1.87632316353
y[1] (closed_form) = 1.34346071895 1.87634371925
absolute error = 2.140e-05
relative error = 0.0009275 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.699
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.22
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6824 2.55
h = 0.001 0.001
y[1] (numeric) = 1.34308943162 1.87863565276
y[1] (closed_form) = 1.34309552997 1.87865611875
absolute error = 2.136e-05
relative error = 0.0009247 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.701
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.744
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = 1.34370802296 1.87954902327
y[1] (closed_form) = 1.34371416997 1.87956942364
absolute error = 2.131e-05
relative error = 0.0009222 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.702
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.48
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6169.2MB, alloc=52.3MB, time=74.02
x[1] = 0.6835 2.555
h = 0.003 0.006
y[1] (numeric) = 1.34319523402 1.88262793895
y[1] (closed_form) = 1.34320106619 1.88264843803
absolute error = 2.131e-05
relative error = 0.0009215 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.705
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.212
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = 1.34460818027 1.88766786142
y[1] (closed_form) = 1.34461427207 1.88768892529
absolute error = 2.193e-05
relative error = 0.0009461 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.712
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.767
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = 1.34394591269 1.89151554945
y[1] (closed_form) = 1.3439519011 1.89153622381
absolute error = 2.152e-05
relative error = 0.0009276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.23
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6867 2.569
h = 0.001 0.001
y[1] (numeric) = 1.34357851076 1.89383030226
y[1] (closed_form) = 1.34358462879 1.89385088689
absolute error = 2.147e-05
relative error = 0.0009248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.717
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.751
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6877 2.57
h = 0.001 0.003
y[1] (numeric) = 1.34419711448 1.8947451215
y[1] (closed_form) = 1.34420328086 1.89476564063
absolute error = 2.143e-05
relative error = 0.0009223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.719
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.315
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6214.7MB, alloc=52.3MB, time=74.56
x[1] = 0.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = 1.34451969034 1.89719351445
y[1] (closed_form) = 1.34452575279 1.89721416297
absolute error = 2.152e-05
relative error = 0.0009255 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.721
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.709
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6888 2.577
h = 0.003 0.006
y[1] (numeric) = 1.34400352554 1.90027606902
y[1] (closed_form) = 1.3440094481 1.90029669854
absolute error = 2.146e-05
relative error = 0.0009221 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.724
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.244
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = 1.3454141264 1.90532361213
y[1] (closed_form) = 1.34542030899 1.90534480364
absolute error = 2.207e-05
relative error = 0.0009464 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.731
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.781
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = 1.34474784925 1.90917567538
y[1] (closed_form) = 1.3447539279 1.90919647912
absolute error = 2.167e-05
relative error = 0.0009281 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.734
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.241
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.692 2.591
h = 0.001 0.001
y[1] (numeric) = 1.34437807919 1.91149308693
y[1] (closed_form) = 1.34438428673 1.91151380097
absolute error = 2.162e-05
relative error = 0.0009253 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.736
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.76
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6260.0MB, alloc=52.3MB, time=75.11
x[1] = 0.693 2.592
h = 0.001 0.003
y[1] (numeric) = 1.34499672433 1.91240958266
y[1] (closed_form) = 1.34500297988 1.91243023133
absolute error = 2.158e-05
relative error = 0.0009228 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.738
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.358
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.694 2.595
h = 0.0001 0.004
y[1] (numeric) = 1.3453177062 1.91486136897
y[1] (closed_form) = 1.34532385852 1.91488214679
absolute error = 2.167e-05
relative error = 0.000926 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.741
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.733
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6941 2.599
h = 0.003 0.006
y[1] (numeric) = 1.3447983609 1.91794743865
y[1] (closed_form) = 1.34480437383 1.9179681979
absolute error = 2.161e-05
relative error = 0.0009226 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.743
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.276
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = 1.34620664402 1.92300257897
y[1] (closed_form) = 1.34621291736 1.92302389741
absolute error = 2.222e-05
relative error = 0.0009467 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.75
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.795
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = 1.34553638332 1.92685901048
y[1] (closed_form) = 1.34554255216 1.92687994289
absolute error = 2.182e-05
relative error = 0.0009285 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.753
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.253
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6305.5MB, alloc=52.3MB, time=75.65
x[1] = 0.6973 2.613
h = 0.001 0.001
y[1] (numeric) = 1.34516426066 1.92917907637
y[1] (closed_form) = 1.34517055768 1.92919991911
absolute error = 2.177e-05
relative error = 0.0009258 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.755
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.769
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6983 2.614
h = 0.001 0.003
y[1] (numeric) = 1.34578295114 1.93009724208
y[1] (closed_form) = 1.34578929583 1.93011801958
absolute error = 2.172e-05
relative error = 0.0009233 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.757
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.401
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = 1.34610235336 1.93255241265
y[1] (closed_form) = 1.34610859554 1.93257331907
absolute error = 2.182e-05
relative error = 0.0009264 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.76
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.757
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6994 2.621
h = 0.003 0.006
y[1] (numeric) = 1.34557984825 1.93564199176
y[1] (closed_form) = 1.34558595152 1.93566288
absolute error = 2.176e-05
relative error = 0.0009231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.762
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.308
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = 1.3469858409 1.94070470587
y[1] (closed_form) = 1.34699220493 1.94072615055
absolute error = 2.237e-05
relative error = 0.0009469 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.769
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.81
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6351.0MB, alloc=52.3MB, time=76.21
x[1] = 0.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = 1.34631162239 1.94456549862
y[1] (closed_form) = 1.34631788139 1.94458655899
absolute error = 2.197e-05
relative error = 0.0009289 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.772
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.264
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7026 2.635
h = 0.001 0.001
y[1] (numeric) = 1.34593716249 1.9468882144
y[1] (closed_form) = 1.34594354898 1.94690918513
absolute error = 2.192e-05
relative error = 0.0009262 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.775
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.778
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7036 2.636
h = 0.001 0.003
y[1] (numeric) = 1.34655590217 1.94780804361
y[1] (closed_form) = 1.34656233598 1.94782894923
absolute error = 2.187e-05
relative error = 0.0009237 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.776
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.443
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = 1.34687373891 1.95026658936
y[1] (closed_form) = 1.34688007091 1.95028762366
absolute error = 2.197e-05
relative error = 0.0009268 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.779
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.781
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7047 2.643
h = 0.003 0.006
y[1] (numeric) = 1.34634809447 1.95335967212
y[1] (closed_form) = 1.34635428804 1.95338068864
absolute error = 2.191e-05
relative error = 0.0009235 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.782
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.34
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6396.5MB, alloc=52.3MB, time=76.75
x[1] = 0.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = 1.34775182353 1.95842993668
y[1] (closed_form) = 1.3477582782 1.95845150691
absolute error = 2.252e-05
relative error = 0.0009471 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.788
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.824
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = 1.34707367268 1.96229508355
y[1] (closed_form) = 1.34708002182 1.96231627118
absolute error = 2.212e-05
relative error = 0.0009293 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.792
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.276
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7079 2.657
h = 0.001 0.001
y[1] (numeric) = 1.34669689076 1.96462044472
y[1] (closed_form) = 1.34670336668 1.96464154275
absolute error = 2.207e-05
relative error = 0.0009266 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.794
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.787
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = 1.3473156834 1.96554193099
y[1] (closed_form) = 1.34732220632 1.96556296405
absolute error = 2.202e-05
relative error = 0.0009241 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.795
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.74
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.709 2.662
h = 0.003 0.006
y[1] (numeric) = 1.34678748119 1.96863786986
y[1] (closed_form) = 1.34679369622 1.96865900347
absolute error = 2.203e-05
relative error = 0.0009235 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.798
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.367
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6442.1MB, alloc=52.3MB, time=77.30
x[1] = 0.712 2.668
h = 0.0001 0.005
y[1] (numeric) = 1.34818919352 1.97371458841
y[1] (closed_form) = 1.34819566995 1.97373627339
absolute error = 2.263e-05
relative error = 0.0009468 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.804
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.836
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = 1.34750762629 1.97758343098
y[1] (closed_form) = 1.34751399674 1.97760473481
absolute error = 2.224e-05
relative error = 0.0009292 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.808
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.286
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7122 2.676
h = 0.001 0.001
y[1] (numeric) = 1.34712882627 1.97991103817
y[1] (closed_form) = 1.3471353229 1.97993225243
absolute error = 2.219e-05
relative error = 0.0009265 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.795
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7132 2.677
h = 0.001 0.003
y[1] (numeric) = 1.34774764785 1.98083394635
y[1] (closed_form) = 1.34775419118 1.98085509574
absolute error = 2.214e-05
relative error = 0.000924 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.812
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.523
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = 1.34806256877 1.98329873006
y[1] (closed_form) = 1.34806901158 1.98332000768
absolute error = 2.223e-05
relative error = 0.0009271 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.814
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.826
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6487.5MB, alloc=52.3MB, time=77.84
x[1] = 0.7143 2.684
h = 0.003 0.006
y[1] (numeric) = 1.34753109495 1.9863982799
y[1] (closed_form) = 1.34753740022 1.98641954048
absolute error = 2.218e-05
relative error = 0.0009239 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.817
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.4
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = 1.34893059303 1.99148250592
y[1] (closed_form) = 1.34893716001 1.99150431518
absolute error = 2.278e-05
relative error = 0.0009469 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.851
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = 1.34824514026 1.99535568948
y[1] (closed_form) = 1.34825160076 1.99537711927
absolute error = 2.238e-05
relative error = 0.0009294 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.297
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7175 2.698
h = 0.001 0.001
y[1] (numeric) = 1.34786404615 1.99768593376
y[1] (closed_form) = 1.34787063215 1.99770727402
absolute error = 2.233e-05
relative error = 0.0009267 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.804
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7185 2.699
h = 0.001 0.003
y[1] (numeric) = 1.34848292761 1.99861048715
y[1] (closed_form) = 1.34848956 1.99863176269
absolute error = 2.229e-05
relative error = 0.0009243 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.566
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6533.1MB, alloc=52.3MB, time=78.38
x[1] = 0.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = 1.34879632275 2.00107862021
y[1] (closed_form) = 1.34880285528 2.00110002372
absolute error = 2.238e-05
relative error = 0.0009273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.851
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7196 2.706
h = 0.003 0.006
y[1] (numeric) = 1.34826176706 2.00418165709
y[1] (closed_form) = 1.34826816254 2.00420304395
absolute error = 2.232e-05
relative error = 0.0009241 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.432
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = 1.34965907675 2.00927336741
y[1] (closed_form) = 1.34966573422 2.00929530027
absolute error = 2.292e-05
relative error = 0.0009469 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.865
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = 1.34896976315 2.01315088463
y[1] (closed_form) = 1.34897631367 2.0131724397
absolute error = 2.253e-05
relative error = 0.0009296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.309
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7228 2.72
h = 0.001 0.001
y[1] (numeric) = 1.3485863897 2.01548376137
y[1] (closed_form) = 1.34859306504 2.01550522696
absolute error = 2.248e-05
relative error = 0.000927 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.813
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6578.5MB, alloc=52.3MB, time=78.92
x[1] = 0.7238 2.721
h = 0.001 0.003
y[1] (numeric) = 1.34920533465 2.01640995364
y[1] (closed_form) = 1.34921205605 2.01643135464
absolute error = 2.243e-05
relative error = 0.0009246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.609
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = 1.3495172175 2.01888142697
y[1] (closed_form) = 1.34952383971 2.01890295568
absolute error = 2.252e-05
relative error = 0.0009275 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.853
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.875
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7249 2.728
h = 0.003 0.006
y[1] (numeric) = 1.3489795996 2.02198794489
y[1] (closed_form) = 1.34898608524 2.02200945734
absolute error = 2.247e-05
relative error = 0.0009244 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.856
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.464
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = 1.3503747464 2.02708711639
y[1] (closed_form) = 1.3503814943 2.02710917218
absolute error = 2.306e-05
relative error = 0.0009469 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.862
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.879
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.728 2.739
h = 0.0001 0.003
y[1] (numeric) = 1.34968159646 2.03096895987
y[1] (closed_form) = 1.34968823694 2.03099063954
absolute error = 2.267e-05
relative error = 0.0009298 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.866
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.32
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6624.1MB, alloc=52.3MB, time=79.47
x[1] = 0.7281 2.742
h = 0.001 0.001
y[1] (numeric) = 1.34929595828 2.03330446443
y[1] (closed_form) = 1.34930272291 2.03332605467
absolute error = 2.263e-05
relative error = 0.0009271 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.868
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.822
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7291 2.743
h = 0.001 0.003
y[1] (numeric) = 1.34991497022 2.03423228927
y[1] (closed_form) = 1.34992178059 2.03425381506
absolute error = 2.258e-05
relative error = 0.0009248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.869
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.652
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = 1.35022535412 2.03670709379
y[1] (closed_form) = 1.35023206597 2.03672874704
absolute error = 2.267e-05
relative error = 0.0009277 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.9
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7302 2.75
h = 0.003 0.006
y[1] (numeric) = 1.34968469347 2.03981708671
y[1] (closed_form) = 1.34969126922 2.03983872406
absolute error = 2.261e-05
relative error = 0.0009246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.497
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = 1.35107770253 2.04492369635
y[1] (closed_form) = 1.35108454079 2.04494587441
absolute error = 2.321e-05
memory used=6669.5MB, alloc=52.3MB, time=80.01
relative error = 0.0009469 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.881
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.894
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = 1.35038074046 2.04880985863
y[1] (closed_form) = 1.35038747085 2.04883166222
absolute error = 2.282e-05
relative error = 0.0009299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.885
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.332
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7334 2.764
h = 0.001 0.001
y[1] (numeric) = 1.349992852 2.0511479863
y[1] (closed_form) = 1.34999970588 2.05116970052
absolute error = 2.277e-05
relative error = 0.0009273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.831
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = 1.3506119344 2.05207743746
y[1] (closed_form) = 1.35061883369 2.05209908736
absolute error = 2.272e-05
relative error = 0.0009249 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.889
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7345 2.769
h = 0.003 0.006
y[1] (numeric) = 1.35006879427 2.05519026301
y[1] (closed_form) = 1.35007539238 2.05521201504
absolute error = 2.273e-05
relative error = 0.0009244 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.892
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.524
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6714.9MB, alloc=52.3MB, time=80.56
x[1] = 0.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = 1.35145989489 2.06030323167
y[1] (closed_form) = 1.35146675575 2.06032552218
absolute error = 2.332e-05
relative error = 0.0009465 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.898
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.906
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = 1.35075961934 2.06419306039
y[1] (closed_form) = 1.35076637193 2.06421497782
absolute error = 2.293e-05
relative error = 0.0009297 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.902
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.342
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7377 2.783
h = 0.001 0.001
y[1] (numeric) = 1.3503697742 2.06653341559
y[1] (closed_form) = 1.35037664971 2.0665552437
absolute error = 2.289e-05
relative error = 0.000927 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.904
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.839
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7387 2.784
h = 0.001 0.003
y[1] (numeric) = 1.35098890069 2.06746426253
y[1] (closed_form) = 1.35099582135 2.06748602644
absolute error = 2.284e-05
relative error = 0.0009247 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.905
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.732
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = 1.3512964909 2.06994522402
y[1] (closed_form) = 1.35130331426 2.06996711493
absolute error = 2.293e-05
relative error = 0.0009276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.908
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.945
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6760.2MB, alloc=52.3MB, time=81.10
x[1] = 0.7398 2.791
h = 0.003 0.006
y[1] (numeric) = 1.35075017829 2.07306163111
y[1] (closed_form) = 1.35075686642 2.0730835068
absolute error = 2.288e-05
relative error = 0.0009245 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.911
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.557
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = 1.35213918735 2.07818199549
y[1] (closed_form) = 1.35214613845 2.07820440706
absolute error = 2.346e-05
relative error = 0.0009464 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.92
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = 1.35143514416 2.08207612924
y[1] (closed_form) = 1.35144198656 2.08209816937
absolute error = 2.308e-05
relative error = 0.0009297 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.921
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.353
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.743 2.805
h = 0.001 0.001
y[1] (numeric) = 1.35104307529 2.08441909891
y[1] (closed_form) = 1.35105003995 2.08444104976
absolute error = 2.303e-05
relative error = 0.0009271 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.923
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.848
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.744 2.806
h = 0.001 0.003
y[1] (numeric) = 1.35166227856 2.08535156064
y[1] (closed_form) = 1.35166928807 2.08537344744
absolute error = 2.298e-05
relative error = 0.0009248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.925
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.776
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6805.7MB, alloc=52.3MB, time=81.64
x[1] = 0.745 2.809
h = 0.0001 0.004
y[1] (numeric) = 1.35196840719 2.08783582757
y[1] (closed_form) = 1.35197532004 2.08785784111
absolute error = 2.307e-05
relative error = 0.0009276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.928
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.97
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7451 2.813
h = 0.003 0.006
y[1] (numeric) = 1.35141910646 2.09095569231
y[1] (closed_form) = 1.35142588455 2.09097769098
absolute error = 2.302e-05
relative error = 0.0009246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.93
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.59
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = 1.35280604815 2.09608342955
y[1] (closed_form) = 1.35281308942 2.09610596154
absolute error = 2.361e-05
relative error = 0.0009463 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.937
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.935
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = 1.35209826083 2.0999818607
y[1] (closed_form) = 1.35210519299 2.10000402286
absolute error = 2.322e-05
relative error = 0.0009297 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.941
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.365
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7483 2.827
h = 0.001 0.001
y[1] (numeric) = 1.35170398226 2.10232744003
y[1] (closed_form) = 1.35171103603 2.10234951298
absolute error = 2.317e-05
relative error = 0.0009271 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.943
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.858
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6851.1MB, alloc=52.3MB, time=82.18
x[1] = 0.7493 2.828
h = 0.001 0.003
y[1] (numeric) = 1.3523232656 2.1032615104
y[1] (closed_form) = 1.3523303639 2.10328351943
absolute error = 2.313e-05
relative error = 0.0009248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.944
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.819
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = 1.35262794536 2.10574907374
y[1] (closed_form) = 1.35263494764 2.10577120925
absolute error = 2.322e-05
relative error = 0.0009276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.947
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.994
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7504 2.835
h = 0.003 0.006
y[1] (numeric) = 1.3520756752 2.10887238988
y[1] (closed_form) = 1.35208254319 2.10889451087
absolute error = 2.316e-05
relative error = 0.0009246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.622
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = 1.35346057339 2.11400747721
y[1] (closed_form) = 1.35346770475 2.11403012898
absolute error = 2.375e-05
relative error = 0.0009461 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.956
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.949
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = 1.35274906521 2.11791019807
y[1] (closed_form) = 1.35275608705 2.11793248161
absolute error = 2.336e-05
relative error = 0.0009297 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.96
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.377
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6896.6MB, alloc=52.3MB, time=82.73
x[1] = 0.7536 2.849
h = 0.001 0.001
y[1] (numeric) = 1.35235259081 2.12025838225
y[1] (closed_form) = 1.35235973362 2.12028057664
absolute error = 2.332e-05
relative error = 0.0009271 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.962
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.867
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7546 2.85
h = 0.001 0.003
y[1] (numeric) = 1.35297195744 2.12119405512
y[1] (closed_form) = 1.35297914448 2.12121618574
absolute error = 2.327e-05
relative error = 0.0009248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.964
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.863
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = 1.35327520089 2.12368490585
y[1] (closed_form) = 1.35328229253 2.12370716269
absolute error = 2.336e-05
relative error = 0.0009276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.966
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.019
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7557 2.857
h = 0.003 0.006
y[1] (numeric) = 1.35271997981 2.12681166712
y[1] (closed_form) = 1.35272693762 2.12683390979
absolute error = 2.331e-05
relative error = 0.0009246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.969
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.655
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = 1.35410285804 2.13195408184
y[1] (closed_form) = 1.3541100794 2.13197685275
absolute error = 2.389e-05
relative error = 0.0009458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.976
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.964
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6942.1MB, alloc=52.3MB, time=83.28
x[1] = 0.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = 1.35338765202 2.13586108467
y[1] (closed_form) = 1.35339476348 2.13588348895
absolute error = 2.351e-05
relative error = 0.0009296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.979
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.389
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7589 2.871
h = 0.001 0.001
y[1] (numeric) = 1.35298899553 2.13821186884
y[1] (closed_form) = 1.35299622733 2.13823418404
absolute error = 2.346e-05
relative error = 0.0009271 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.982
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.876
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7599 2.872
h = 0.001 0.003
y[1] (numeric) = 1.35360844861 2.13914913814
y[1] (closed_form) = 1.35361572433 2.13917138969
absolute error = 2.341e-05
relative error = 0.0009248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.983
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.907
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ;
Iterations = 754
Total Elapsed Time = 1 Minutes 23 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 1 Minutes 23 Seconds
> quit
memory used=6975.0MB, alloc=52.3MB, time=83.65