|\^/| 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_tonepostcpx.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 := 0.5 + 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 := 0.5 + 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,"2017-11-26T16:34:16-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sqrt_sqrt_tone")
> ;
> 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_tone diffeq.mxt")
> ;
> logitem_str(html_log_file,"sqrt_sqrt_tone 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_tonepostcpx.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 := 0.5 + 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,");
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omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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 := 0.5 + 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, "2017-11-26T16:34:16-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sqrt_sqrt_tone");
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_tone diffeq.mxt");
logitem_str(html_log_file, "sqrt_sqrt_tone 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_tonepostcpx.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 := 0.5 + 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] = 0.5 0.1
h = 0.0001 0.005
y[1] (numeric) = 1.41386007082 0.0707142122923
y[1] (closed_form) = 1.41386007082 0.0707142122923
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.502
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.127
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5001 0.105
h = 0.0001 0.003
y[1] (numeric) = 1.4138947441 0.0742510362896
y[1] (closed_form) = 1.41389456764 0.0742510452758
absolute error = 1.767e-07
relative error = 1.248e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.502
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.502
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=31.9MB, alloc=40.3MB, time=0.42
x[1] = 0.5002 0.108
h = 0.001 0.001
y[1] (numeric) = 1.41394267415 0.0763735157229
y[1] (closed_form) = 1.41394270931 0.0763735108062
absolute error = 3.551e-08
relative error = 2.508e-06 %
Correct digits = 8
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 = 1.179
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5012 0.109
h = 0.001 0.003
y[1] (numeric) = 1.41464218668 0.0770885062371
y[1] (closed_form) = 1.41464232295 0.0770884591282
absolute error = 1.442e-07
relative error = 1.018e-05 %
Correct digits = 7
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 = 5.598
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5022 0.112
h = 0.0001 0.004
y[1] (numeric) = 1.41532633367 0.0792183035251
y[1] (closed_form) = 1.41532626054 0.0792183339988
absolute error = 7.922e-08
relative error = 5.589e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.505
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.169
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5023 0.116
h = 0.003 0.006
y[1] (numeric) = 1.41536501483 0.0820488406649
y[1] (closed_form) = 1.41536479317 0.0820487526019
absolute error = 2.385e-07
relative error = 1.682e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.505
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.2
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5053 0.122
h = 0.0001 0.005
y[1] (numeric) = 1.41743727191 0.0863183637677
y[1] (closed_form) = 1.41743696337 0.0863191051226
absolute error = 8.030e-07
relative error = 5.655e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.508
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.87
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=77.2MB, alloc=52.3MB, time=1.00
x[1] = 0.5054 0.127
h = 0.0001 0.003
y[1] (numeric) = 1.417463967 0.0898580049847
y[1] (closed_form) = 1.41746380505 0.0898582257409
absolute error = 2.738e-07
relative error = 1.928e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.509
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.506
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5055 0.13
h = 0.001 0.001
y[1] (numeric) = 1.41750732363 0.0919819252721
y[1] (closed_form) = 1.41750737283 0.0919821307784
absolute error = 2.113e-07
relative error = 1.488e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.509
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.182
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5065 0.131
h = 0.001 0.003
y[1] (numeric) = 1.41820572762 0.0926988840947
y[1] (closed_form) = 1.41820587746 0.0926990468339
absolute error = 2.212e-07
relative error = 1.557e-05 %
Correct digits = 7
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 = 5.612
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5075 0.134
h = 0.0001 0.004
y[1] (numeric) = 1.41888569098 0.0948315081491
y[1] (closed_form) = 1.41888563232 0.0948317496795
absolute error = 2.486e-07
relative error = 1.748e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.511
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.177
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5076 0.138
h = 0.003 0.006
y[1] (numeric) = 1.41891826844 0.0976639242691
y[1] (closed_form) = 1.41891806077 0.0976640484538
absolute error = 2.420e-07
relative error = 1.701e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.511
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
memory used=122.5MB, alloc=52.3MB, time=1.55
x[1] = 0.5106 0.144
h = 0.0001 0.005
y[1] (numeric) = 1.42098260868 0.101940656411
y[1] (closed_form) = 1.42098231966 0.101941608965
absolute error = 9.954e-07
relative error = 6.987e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.875
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5107 0.149
h = 0.0001 0.003
y[1] (numeric) = 1.42100168187 0.105482630374
y[1] (closed_form) = 1.4210015358 0.105483062401
absolute error = 4.561e-07
relative error = 3.201e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.51
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5108 0.152
h = 0.001 0.001
y[1] (numeric) = 1.4210404833 0.107608018326
y[1] (closed_form) = 1.42104054785 0.107608433769
absolute error = 4.204e-07
relative error = 2.950e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.185
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5118 0.153
h = 0.001 0.003
y[1] (numeric) = 1.42173779364 0.108326948801
y[1] (closed_form) = 1.42173795837 0.108327320912
absolute error = 4.069e-07
relative error = 2.854e-05 %
Correct digits = 7
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 = 5.627
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5128 0.156
h = 0.0001 0.004
y[1] (numeric) = 1.42241359979 0.110462421185
y[1] (closed_form) = 1.42241355694 0.110462873277
absolute error = 4.541e-07
relative error = 3.183e-05 %
Correct digits = 6
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 = 3.186
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=167.9MB, alloc=52.3MB, time=2.09
x[1] = 0.5129 0.16
h = 0.003 0.006
y[1] (numeric) = 1.42244009762 0.113296752055
y[1] (closed_form) = 1.42243990529 0.113297087994
absolute error = 3.871e-07
relative error = 2.713e-05 %
Correct digits = 7
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] = 0.5159 0.166
h = 0.0001 0.005
y[1] (numeric) = 1.42449658314 0.117580730199
y[1] (closed_form) = 1.42449631495 0.117581893379
absolute error = 1.194e-06
relative error = 8.351e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.521
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] = 0.516 0.171
h = 0.0001 0.003
y[1] (numeric) = 1.42450806453 0.121125081383
y[1] (closed_form) = 1.42450793567 0.121125724162
absolute error = 6.556e-07
relative error = 4.586e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.514
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5161 0.174
h = 0.001 0.001
y[1] (numeric) = 1.42454232927 0.123251963412
y[1] (closed_form) = 1.42454241051 0.123252588288
absolute error = 6.301e-07
relative error = 4.407e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.188
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5171 0.175
h = 0.001 0.003
y[1] (numeric) = 1.42523856086 0.123972868644
y[1] (closed_form) = 1.42523874178 0.123973449633
absolute error = 6.085e-07
relative error = 4.253e-05 %
Correct digits = 6
memory used=213.2MB, alloc=52.3MB, time=2.64
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 = 5.642
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5181 0.178
h = 0.0001 0.004
y[1] (numeric) = 1.42591023641 0.126111210424
y[1] (closed_form) = 1.42591021068 0.126111872563
absolute error = 6.626e-07
relative error = 4.629e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.524
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.194
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5182 0.182
h = 0.003 0.006
y[1] (numeric) = 1.42593067909 0.128947491285
y[1] (closed_form) = 1.42593050345 0.128948038465
absolute error = 5.747e-07
relative error = 4.014e-05 %
Correct digits = 6
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 = 4.233
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5212 0.188
h = 0.0001 0.005
y[1] (numeric) = 1.42797937227 0.133238751288
y[1] (closed_form) = 1.42797912623 0.133240124507
absolute error = 1.395e-06
relative error = 9.727e-05 %
Correct digits = 6
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 = 1.885
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5213 0.193
h = 0.0001 0.003
y[1] (numeric) = 1.4279832925 0.136785523508
y[1] (closed_form) = 1.42798318216 0.136786376504
absolute error = 8.601e-07
relative error = 5.996e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.529
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.518
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=258.5MB, alloc=52.3MB, time=3.19
x[1] = 0.5214 0.196
h = 0.001 0.001
y[1] (numeric) = 1.42801303939 0.138913925624
y[1] (closed_form) = 1.4280131386 0.138914759412
absolute error = 8.397e-07
relative error = 5.852e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.529
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.192
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5224 0.197
h = 0.0001 0.004
y[1] (numeric) = 1.42870820706 0.139636808481
y[1] (closed_form) = 1.42870840547 0.139637597836
absolute error = 8.139e-07
relative error = 5.670e-05 %
Correct digits = 6
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 = 7.158
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5225 0.201
h = 0.003 0.006
y[1] (numeric) = 1.42872371316 0.142474700446
y[1] (closed_form) = 1.42872348193 0.142475399338
absolute error = 7.361e-07
relative error = 5.127e-05 %
Correct digits = 6
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 = 4.242
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5255 0.207
h = 0.0001 0.005
y[1] (numeric) = 1.43076566178 0.146772164496
y[1] (closed_form) = 1.43076536482 0.146773688394
absolute error = 1.553e-06
relative error = 0.0001079 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.534
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.889
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5256 0.212
h = 0.0001 0.003
y[1] (numeric) = 1.43076306898 0.150320965675
y[1] (closed_form) = 1.43076290463 0.150321969505
absolute error = 1.017e-06
relative error = 7.071e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.534
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.521
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=303.9MB, alloc=52.3MB, time=3.74
x[1] = 0.5257 0.215
h = 0.001 0.001
y[1] (numeric) = 1.43078892384 0.152450643243
y[1] (closed_form) = 1.43078896857 0.152451626746
absolute error = 9.845e-07
relative error = 6.842e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.535
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.194
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5267 0.216
h = 0.001 0.003
y[1] (numeric) = 1.43148316399 0.153175218057
y[1] (closed_form) = 1.43148330751 0.15317615666
absolute error = 9.495e-07
relative error = 6.595e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.536
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.67
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5277 0.219
h = 0.0001 0.004
y[1] (numeric) = 1.43214719021 0.155318905028
y[1] (closed_form) = 1.43214712883 0.155319926918
absolute error = 1.024e-06
relative error = 7.107e-05 %
Correct digits = 6
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 = 3.21
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5278 0.223
h = 0.003 0.006
y[1] (numeric) = 1.43215640805 0.158158834911
y[1] (closed_form) = 1.43215619598 0.158159744061
absolute error = 9.336e-07
relative error = 6.479e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.538
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.254
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5308 0.229
h = 0.0001 0.005
y[1] (numeric) = 1.43419068061 0.16246364536
y[1] (closed_form) = 1.43419040818 0.162465378173
absolute error = 1.754e-06
relative error = 0.0001215 %
Correct digits = 6
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 = 1.894
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=349.2MB, alloc=52.3MB, time=4.29
x[1] = 0.5309 0.234
h = 0.0001 0.003
y[1] (numeric) = 1.43418058446 0.166014947699
y[1] (closed_form) = 1.43418044107 0.16601616072
absolute error = 1.221e-06
relative error = 8.460e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.526
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.531 0.237
h = 0.001 0.001
y[1] (numeric) = 1.43420195698 0.168146192899
y[1] (closed_form) = 1.43420202209 0.168147384316
absolute error = 1.193e-06
relative error = 8.263e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.198
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.532 0.238
h = 0.001 0.003
y[1] (numeric) = 1.43489516074 0.168872750228
y[1] (closed_form) = 1.43489532414 0.168873896217
absolute error = 1.158e-06
relative error = 8.012e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.543
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.687
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.533 0.241
h = 0.0001 0.004
y[1] (numeric) = 1.43555513328 0.171019364432
y[1] (closed_form) = 1.43555509275 0.171020594822
absolute error = 1.231e-06
relative error = 8.515e-05 %
Correct digits = 6
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 = 3.219
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5331 0.245
h = 0.003 0.006
y[1] (numeric) = 1.43555836784 0.173861342464
y[1] (closed_form) = 1.43555817623 0.173862461309
absolute error = 1.135e-06
relative error = 7.850e-05 %
Correct digits = 6
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=394.7MB, alloc=52.3MB, time=4.84
x[1] = 0.5361 0.251
h = 0.0001 0.005
y[1] (numeric) = 1.43758502733 0.178173532026
y[1] (closed_form) = 1.43758478069 0.178175473119
absolute error = 1.957e-06
relative error = 0.0001351 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.548
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.9
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5362 0.256
h = 0.0001 0.003
y[1] (numeric) = 1.43756745985 0.181727377418
y[1] (closed_form) = 1.4375673387 0.181728799047
absolute error = 1.427e-06
relative error = 9.847e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.549
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.53
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5363 0.259
h = 0.001 0.001
y[1] (numeric) = 1.43758436968 0.18386021509
y[1] (closed_form) = 1.43758445642 0.183861613852
absolute error = 1.401e-06
relative error = 9.670e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.549
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.201
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5373 0.26
h = 0.001 0.003
y[1] (numeric) = 1.43827655181 0.184588757137
y[1] (closed_form) = 1.43827673634 0.184590109953
absolute error = 1.365e-06
relative error = 9.416e-05 %
Correct digits = 6
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 = 5.703
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5383 0.263
h = 0.0001 0.004
y[1] (numeric) = 1.43893249794 0.186738317717
y[1] (closed_form) = 1.43893247953 0.186739756028
absolute error = 1.438e-06
relative error = 9.913e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.552
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.229
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=440.0MB, alloc=52.3MB, time=5.38
x[1] = 0.5384 0.267
h = 0.003 0.006
y[1] (numeric) = 1.43892977521 0.189582377054
y[1] (closed_form) = 1.43892960535 0.189583705015
absolute error = 1.339e-06
relative error = 9.224e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.552
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.279
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5414 0.273
h = 0.0001 0.005
y[1] (numeric) = 1.44094888478 0.19390197735
y[1] (closed_form) = 1.44094866515 0.193904126073
absolute error = 2.160e-06
relative error = 0.0001486 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.556
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.906
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5415 0.278
h = 0.0001 0.003
y[1] (numeric) = 1.44092387844 0.197458407004
y[1] (closed_form) = 1.44092378078 0.197460036642
absolute error = 1.633e-06
relative error = 0.0001123 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.557
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.535
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5416 0.281
h = 0.001 0.001
y[1] (numeric) = 1.44093634548 0.199592861572
y[1] (closed_form) = 1.44093645511 0.199594467095
absolute error = 1.609e-06
relative error = 0.0001106 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.557
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.205
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5426 0.282
h = 0.001 0.003
y[1] (numeric) = 1.44162752068 0.200323390311
y[1] (closed_form) = 1.44162772759 0.200324949381
absolute error = 1.573e-06
relative error = 0.0001081 %
Correct digits = 6
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 = 5.72
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=485.5MB, alloc=52.3MB, time=5.94
x[1] = 0.5436 0.285
h = 0.0001 0.004
y[1] (numeric) = 1.44227946783 0.202475915913
y[1] (closed_form) = 1.44227947278 0.202477561553
absolute error = 1.646e-06
relative error = 0.000113 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.56
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.239
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5437 0.289
h = 0.003 0.006
y[1] (numeric) = 1.44227081413 0.205322089159
y[1] (closed_form) = 1.4422706673 0.205323625642
absolute error = 1.543e-06
relative error = 0.0001059 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.56
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.292
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5467 0.295
h = 0.0001 0.005
y[1] (numeric) = 1.44428243706 0.209649130725
y[1] (closed_form) = 1.44428224569 0.209651486416
absolute error = 2.363e-06
relative error = 0.0001619 %
Correct digits = 6
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 = 1.911
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5468 0.3
h = 0.0001 0.003
y[1] (numeric) = 1.44425002477 0.213208185159
y[1] (closed_form) = 1.44424995185 0.213210022191
absolute error = 1.838e-06
relative error = 0.0001259 %
Correct digits = 6
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 = 1.539
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5469 0.303
h = 0.001 0.001
y[1] (numeric) = 1.44425806918 0.215344280629
y[1] (closed_form) = 1.44425820293 0.215346092314
absolute error = 1.817e-06
relative error = 0.0001244 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.565
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.208
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=530.9MB, alloc=52.3MB, time=6.48
x[1] = 0.5479 0.304
h = 0.0001 0.004
y[1] (numeric) = 1.44494825211 0.216076797812
y[1] (closed_form) = 1.44494848263 0.216078562547
absolute error = 1.780e-06
relative error = 0.0001218 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.566
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.26
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.548 0.308
h = 0.003 0.006
y[1] (numeric) = 1.44493476447 0.218924714437
y[1] (closed_form) = 1.44493456733 0.218926402709
absolute error = 1.700e-06
relative error = 0.0001163 %
Correct digits = 6
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 = 4.303
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.551 0.314
h = 0.0001 0.005
y[1] (numeric) = 1.44693990477 0.223258096673
y[1] (closed_form) = 1.44693966757 0.223260602822
absolute error = 2.517e-06
relative error = 0.0001719 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.57
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.916
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5511 0.319
h = 0.0001 0.003
y[1] (numeric) = 1.44690111243 0.22681935467
y[1] (closed_form) = 1.44690099068 0.226821342525
absolute error = 1.992e-06
relative error = 0.000136 %
Correct digits = 6
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 = 1.543
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5512 0.322
h = 0.001 0.001
y[1] (numeric) = 1.44690534638 0.228956829123
y[1] (closed_form) = 1.44690543076 0.228958790576
absolute error = 1.963e-06
relative error = 0.000134 %
Correct digits = 6
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 = 1.212
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=576.4MB, alloc=52.3MB, time=7.03
x[1] = 0.5522 0.323
h = 0.001 0.003
y[1] (numeric) = 1.44759466319 0.229691047542
y[1] (closed_form) = 1.4475948439 0.229692961619
absolute error = 1.923e-06
relative error = 0.0001312 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.573
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.752
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5532 0.326
h = 0.0001 0.004
y[1] (numeric) = 1.44823920673 0.231849091424
y[1] (closed_form) = 1.44823918734 0.231851094028
absolute error = 2.003e-06
relative error = 0.0001365 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.574
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.257
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5533 0.33
h = 0.003 0.006
y[1] (numeric) = 1.44821956205 0.234699213138
y[1] (closed_form) = 1.44821939027 0.234701108798
absolute error = 1.903e-06
relative error = 0.0001297 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.575
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.316
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5563 0.336
h = 0.0001 0.005
y[1] (numeric) = 1.45021733338 0.239040091348
y[1] (closed_form) = 1.45021712666 0.239042803208
absolute error = 2.720e-06
relative error = 0.000185 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.578
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.922
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5564 0.341
h = 0.0001 0.003
y[1] (numeric) = 1.45017119691 0.242604048078
y[1] (closed_form) = 1.45017110219 0.24260624216
absolute error = 2.196e-06
relative error = 0.0001494 %
Correct digits = 6
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
memory used=621.9MB, alloc=52.3MB, time=7.58
x[1] = 0.5565 0.344
h = 0.001 0.001
y[1] (numeric) = 1.45017104609 0.244743207226
y[1] (closed_form) = 1.45017115685 0.244745373703
absolute error = 2.169e-06
relative error = 0.0001475 %
Correct digits = 6
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 = 1.215
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5575 0.345
h = 0.001 0.003
y[1] (numeric) = 1.45085939775 0.245479416935
y[1] (closed_form) = 1.45085960432 0.245481535557
absolute error = 2.129e-06
relative error = 0.0001447 %
Correct digits = 6
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 = 5.771
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5585 0.348
h = 0.0001 0.004
y[1] (numeric) = 1.45150002118 0.247640476771
y[1] (closed_form) = 1.45150002867 0.247642684936
absolute error = 2.208e-06
relative error = 0.00015 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.582
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.267
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5586 0.352
h = 0.003 0.006
y[1] (numeric) = 1.4514745223 0.250492802914
y[1] (closed_form) = 1.45147437711 0.250494905325
absolute error = 2.107e-06
relative error = 0.0001431 %
Correct digits = 6
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 = 4.33
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5616 0.358
h = 0.0001 0.005
y[1] (numeric) = 1.45346498818 0.254841204562
y[1] (closed_form) = 1.45346481313 0.254844121431
absolute error = 2.922e-06
relative error = 0.000198 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.586
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.928
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=667.3MB, alloc=52.3MB, time=8.13
x[1] = 0.5617 0.363
h = 0.0001 0.003
y[1] (numeric) = 1.4534115416 0.258407898557
y[1] (closed_form) = 1.45341147512 0.25841029821
absolute error = 2.401e-06
relative error = 0.0001626 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.587
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.553
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5618 0.366
h = 0.001 0.001
y[1] (numeric) = 1.45340702682 0.2605487652
y[1] (closed_form) = 1.45340716516 0.260551136061
absolute error = 2.375e-06
relative error = 0.0001608 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.588
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.219
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5628 0.367
h = 0.001 0.003
y[1] (numeric) = 1.45409442783 0.261286967325
y[1] (closed_form) = 1.45409466146 0.261289289863
absolute error = 2.334e-06
relative error = 0.000158 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.589
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.789
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5638 0.37
h = 0.0001 0.004
y[1] (numeric) = 1.45473115899 0.263451059852
y[1] (closed_form) = 1.45473119456 0.263453472929
absolute error = 2.413e-06
relative error = 0.0001632 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.278
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5639 0.374
h = 0.003 0.006
y[1] (numeric) = 1.45469983346 0.266305620873
y[1] (closed_form) = 1.45469971607 0.266307929381
absolute error = 2.311e-06
relative error = 0.0001563 %
Correct digits = 6
memory used=712.8MB, alloc=52.3MB, time=8.68
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 = 4.344
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5669 0.38
h = 0.0001 0.005
y[1] (numeric) = 1.45668305743 0.270661572363
y[1] (closed_form) = 1.4566829152 0.270664693525
absolute error = 3.124e-06
relative error = 0.0002109 %
Correct digits = 6
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 = 1.934
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.567 0.385
h = 0.0001 0.003
y[1] (numeric) = 1.45662233513 0.274231041454
y[1] (closed_form) = 1.45662229808 0.274233646009
absolute error = 2.605e-06
relative error = 0.0001757 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.596
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.558
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5671 0.388
h = 0.001 0.001
y[1] (numeric) = 1.45661347741 0.276373637966
y[1] (closed_form) = 1.45661364449 0.276376212558
absolute error = 2.580e-06
relative error = 0.000174 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.596
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.223
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5681 0.389
h = 0.001 0.003
y[1] (numeric) = 1.4572999422 0.277113833421
y[1] (closed_form) = 1.45730020404 0.277116359232
absolute error = 2.539e-06
relative error = 0.0001712 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.597
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.808
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=758.3MB, alloc=52.3MB, time=9.22
x[1] = 0.5691 0.392
h = 0.0001 0.004
y[1] (numeric) = 1.457932809 0.279280974886
y[1] (closed_form) = 1.45793287382 0.279283592212
absolute error = 2.618e-06
relative error = 0.0001764 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.599
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.288
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5692 0.396
h = 0.003 0.006
y[1] (numeric) = 1.45789568462 0.282137800669
y[1] (closed_form) = 1.45789559624 0.28214031461
absolute error = 2.515e-06
relative error = 0.0001694 %
Correct digits = 6
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] = 0.5722 0.402
h = 0.0001 0.005
y[1] (numeric) = 1.45987173026 0.286501327357
y[1] (closed_form) = 1.459871622 0.286504652086
absolute error = 3.326e-06
relative error = 0.0002236 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.603
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
x[1] = 0.5723 0.407
h = 0.0001 0.003
y[1] (numeric) = 1.45980376696 0.290073608673
y[1] (closed_form) = 1.4598037605 0.290076417447
absolute error = 2.809e-06
relative error = 0.0001887 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.604
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.563
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5724 0.41
h = 0.001 0.001
y[1] (numeric) = 1.4597905875 0.292217957003
y[1] (closed_form) = 1.45979078449 0.29222073466
absolute error = 2.785e-06
relative error = 0.000187 %
Correct digits = 6
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 = 1.227
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=803.7MB, alloc=52.3MB, time=9.77
x[1] = 0.5734 0.411
h = 0.0001 0.004
y[1] (numeric) = 1.46047613043 0.292960146493
y[1] (closed_form) = 1.46047642164 0.292962874921
absolute error = 2.744e-06
relative error = 0.0001842 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.606
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.373
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5735 0.415
h = 0.003 0.006
y[1] (numeric) = 1.46043428097 0.295818837208
y[1] (closed_form) = 1.46043414741 0.295821502644
absolute error = 2.669e-06
relative error = 0.0001791 %
Correct digits = 6
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 = 4.37
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5765 0.421
h = 0.0001 0.005
y[1] (numeric) = 1.46240410799 0.300188819402
y[1] (closed_form) = 1.46240395882 0.300192294033
absolute error = 3.478e-06
relative error = 0.000233 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.611
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.946
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5766 0.426
h = 0.0001 0.003
y[1] (numeric) = 1.46232990583 0.303763464897
y[1] (closed_form) = 1.46232985557 0.303766424128
absolute error = 2.960e-06
relative error = 0.0001982 %
Correct digits = 6
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 = 1.568
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5767 0.429
h = 0.001 0.001
y[1] (numeric) = 1.46231300228 0.305909287251
y[1] (closed_form) = 1.46231315487 0.305912214377
absolute error = 2.931e-06
relative error = 0.0001962 %
Correct digits = 6
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 = 1.231
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=849.1MB, alloc=52.3MB, time=10.32
x[1] = 0.5777 0.43
h = 0.001 0.003
y[1] (numeric) = 1.46299773938 0.3066531828
y[1] (closed_form) = 1.46299798575 0.306656060312
absolute error = 2.888e-06
relative error = 0.0001932 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.613
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.844
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5787 0.433
h = 0.0001 0.004
y[1] (numeric) = 1.46362345329 0.308825993958
y[1] (closed_form) = 1.46362350457 0.308828964761
absolute error = 2.971e-06
relative error = 0.0001986 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.615
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.309
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5788 0.437
h = 0.003 0.006
y[1] (numeric) = 1.46357558574 0.311687043259
y[1] (closed_form) = 1.46357548338 0.311689912866
absolute error = 2.871e-06
relative error = 0.0001919 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.616
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.385
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5818 0.443
h = 0.0001 0.005
y[1] (numeric) = 1.46553835237 0.316064645821
y[1] (closed_form) = 1.46553823926 0.316068322651
absolute error = 3.679e-06
relative error = 0.0002454 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.62
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
x[1] = 0.5819 0.448
h = 0.0001 0.003
y[1] (numeric) = 1.46545697421 0.319642171178
y[1] (closed_form) = 1.46545695669 0.319645333341
absolute error = 3.162e-06
relative error = 0.0002108 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.62
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
memory used=894.5MB, alloc=52.3MB, time=10.87
x[1] = 0.582 0.451
h = 0.001 0.001
y[1] (numeric) = 1.46543578862 0.321789785317
y[1] (closed_form) = 1.46543597324 0.32179291425
absolute error = 3.134e-06
relative error = 0.0002089 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.621
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.235
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.583 0.452
h = 0.001 0.003
y[1] (numeric) = 1.46611963038 0.32253567584
y[1] (closed_form) = 1.46611990824 0.32253875473
absolute error = 3.091e-06
relative error = 0.0002059 %
Correct digits = 6
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 = 5.864
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.584 0.455
h = 0.0001 0.004
y[1] (numeric) = 1.46674155996 0.324711580069
y[1] (closed_form) = 1.46674164379 0.324714753169
absolute error = 3.174e-06
relative error = 0.0002113 %
Correct digits = 6
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 = 3.32
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5841 0.459
h = 0.003 0.006
y[1] (numeric) = 1.46668797419 0.327574976848
y[1] (closed_form) = 1.46668790417 0.327578049924
absolute error = 3.074e-06
relative error = 0.0002045 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.625
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.4
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5871 0.465
h = 0.0001 0.005
y[1] (numeric) = 1.4686437439 0.331960222181
y[1] (closed_form) = 1.46864366795 0.331964100451
absolute error = 3.879e-06
relative error = 0.0002576 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.629
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.96
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=940.1MB, alloc=52.3MB, time=11.42
x[1] = 0.5872 0.47
h = 0.0001 0.003
y[1] (numeric) = 1.46855522533 0.335540662519
y[1] (closed_form) = 1.46855524167 0.335544026896
absolute error = 3.364e-06
relative error = 0.0002233 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.63
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.578
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5873 0.473
h = 0.001 0.001
y[1] (numeric) = 1.46852977941 0.337690089175
y[1] (closed_form) = 1.46852999717 0.337693419216
absolute error = 3.337e-06
relative error = 0.0002215 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.63
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.239
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5883 0.474
h = 0.001 0.003
y[1] (numeric) = 1.46921273997 0.3384379748
y[1] (closed_form) = 1.46921305042 0.338441254378
absolute error = 3.294e-06
relative error = 0.0002185 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.631
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.884
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5893 0.477
h = 0.0001 0.004
y[1] (numeric) = 1.46983091333 0.340616986485
y[1] (closed_form) = 1.46983103082 0.34062036117
absolute error = 3.377e-06
relative error = 0.0002238 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.633
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.331
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5894 0.481
h = 0.003 0.006
y[1] (numeric) = 1.46977163808 0.343482758447
y[1] (closed_form) = 1.46977160153 0.343486034277
absolute error = 3.276e-06
relative error = 0.000217 %
Correct digits = 6
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 = 4.415
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=985.4MB, alloc=52.3MB, time=11.97
x[1] = 0.5924 0.487
h = 0.0001 0.005
y[1] (numeric) = 1.47172047428 0.347875667942
y[1] (closed_form) = 1.47172043655 0.347879746884
absolute error = 4.079e-06
relative error = 0.0002697 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.638
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.966
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5925 0.492
h = 0.0001 0.003
y[1] (numeric) = 1.47162485114 0.351459057678
y[1] (closed_form) = 1.47162490244 0.35146262354
absolute error = 3.566e-06
relative error = 0.0002357 %
Correct digits = 6
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 = 1.584
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5926 0.495
h = 0.001 0.001
y[1] (numeric) = 1.47159516675 0.353610317157
y[1] (closed_form) = 1.47159541875 0.353613847594
absolute error = 3.539e-06
relative error = 0.0002339 %
Correct digits = 6
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 = 1.244
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5936 0.496
h = 0.001 0.003
y[1] (numeric) = 1.47227726015 0.354360197816
y[1] (closed_form) = 1.4722776043 0.354363677381
absolute error = 3.497e-06
relative error = 0.0002309 %
Correct digits = 6
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 = 5.905
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5946 0.499
h = 0.0001 0.004
y[1] (numeric) = 1.47289170545 0.356542330868
y[1] (closed_form) = 1.4728918577 0.356545906418
absolute error = 3.579e-06
relative error = 0.0002362 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.642
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.343
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1030.8MB, alloc=52.3MB, time=12.52
x[1] = 0.5947 0.503
h = 0.003 0.006
y[1] (numeric) = 1.47282676966 0.359410505155
y[1] (closed_form) = 1.47282676771 0.359413983014
absolute error = 3.478e-06
relative error = 0.0002294 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.643
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.431
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5977 0.509
h = 0.0001 0.005
y[1] (numeric) = 1.47476873564 0.363811099204
y[1] (closed_form) = 1.4747687372 0.363815378041
absolute error = 4.279e-06
relative error = 0.0002817 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.647
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] = 0.5978 0.514
h = 0.0001 0.003
y[1] (numeric) = 1.47466604403 0.36739747205
y[1] (closed_form) = 1.4746661314 0.367401238661
absolute error = 3.768e-06
relative error = 0.0002479 %
Correct digits = 6
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 = 1.589
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5979 0.517
h = 0.001 0.001
y[1] (numeric) = 1.47463214318 0.369550584237
y[1] (closed_form) = 1.47463243049 0.369554314349
absolute error = 3.741e-06
relative error = 0.0002461 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.649
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] = 0.5989 0.518
h = 0.0001 0.004
y[1] (numeric) = 1.47531338339 0.370302459673
y[1] (closed_form) = 1.47531376231 0.370306138512
absolute error = 3.698e-06
relative error = 0.0002431 %
Correct digits = 6
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 = 7.498
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1076.3MB, alloc=52.3MB, time=13.06
x[1] = 0.599 0.522
h = 0.003 0.006
y[1] (numeric) = 1.4752438362 0.373172609574
y[1] (closed_form) = 1.47524379405 0.373176238295
absolute error = 3.629e-06
relative error = 0.0002385 %
Correct digits = 6
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 = 4.444
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.602 0.528
h = 0.0001 0.005
y[1] (numeric) = 1.47717984727 0.377579752991
y[1] (closed_form) = 1.47717981265 0.377584180868
absolute error = 4.428e-06
relative error = 0.0002904 %
Correct digits = 6
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 = 1.979
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6021 0.533
h = 0.0001 0.003
y[1] (numeric) = 1.47707106437 0.381168636451
y[1] (closed_form) = 1.47707111279 0.381172552829
absolute error = 3.917e-06
relative error = 0.0002568 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.656
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.594
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6022 0.536
h = 0.001 0.001
y[1] (numeric) = 1.47703352947 0.383323309119
y[1] (closed_form) = 1.47703377719 0.383327188078
absolute error = 3.887e-06
relative error = 0.0002547 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.657
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6032 0.537
h = 0.001 0.003
y[1] (numeric) = 1.47771402264 0.384076891302
y[1] (closed_form) = 1.47771436152 0.384080718646
absolute error = 3.842e-06
relative error = 0.0002517 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.658
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.943
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1121.8MB, alloc=52.3MB, time=13.61
x[1] = 0.6042 0.54
h = 0.0001 0.004
y[1] (numeric) = 1.47832156827 0.386264824287
y[1] (closed_form) = 1.47832171725 0.38626874921
absolute error = 3.928e-06
relative error = 0.0002571 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.365
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6043 0.544
h = 0.003 0.006
y[1] (numeric) = 1.47824614787 0.389137472449
y[1] (closed_form) = 1.47824614235 0.389141301831
absolute error = 3.829e-06
relative error = 0.0002505 %
Correct digits = 6
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 = 4.46
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6073 0.55
h = 0.0001 0.005
y[1] (numeric) = 1.48017540596 0.393552336493
y[1] (closed_form) = 1.48017541255 0.393556962807
absolute error = 4.626e-06
relative error = 0.0003021 %
Correct digits = 6
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 = 1.987
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6074 0.555
h = 0.0001 0.003
y[1] (numeric) = 1.48005962197 0.397144264371
y[1] (closed_form) = 1.48005970844 0.397148380107
absolute error = 4.117e-06
relative error = 0.0002686 %
Correct digits = 6
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 = 1.6
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6075 0.558
h = 0.001 0.001
y[1] (numeric) = 1.48001791165 0.399300825884
y[1] (closed_form) = 1.48001819667 0.39930490316
absolute error = 4.087e-06
relative error = 0.0002666 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.667
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.256
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1167.4MB, alloc=52.3MB, time=14.16
x[1] = 0.6085 0.559
h = 0.001 0.003
y[1] (numeric) = 1.48069757739 0.400056402031
y[1] (closed_form) = 1.480697953 0.40006042731
absolute error = 4.043e-06
relative error = 0.0002636 %
Correct digits = 6
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 = 5.965
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6095 0.562
h = 0.0001 0.004
y[1] (numeric) = 1.48130147537 0.402247493931
y[1] (closed_form) = 1.48130166216 0.402251617611
absolute error = 4.128e-06
relative error = 0.0002689 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.669
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.378
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6096 0.566
h = 0.003 0.006
y[1] (numeric) = 1.48122047792 0.405122619314
y[1] (closed_form) = 1.4812205101 0.405126648602
absolute error = 4.029e-06
relative error = 0.0002624 %
Correct digits = 6
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] = 0.6126 0.572
h = 0.0001 0.005
y[1] (numeric) = 1.48314304594 0.409545221584
y[1] (closed_form) = 1.48314309477 0.40955004553
absolute error = 4.824e-06
relative error = 0.0003135 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.674
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.994
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6127 0.577
h = 0.0001 0.003
y[1] (numeric) = 1.48302029759 0.413140225596
y[1] (closed_form) = 1.48302042316 0.413144539925
absolute error = 4.316e-06
relative error = 0.0002804 %
Correct digits = 6
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 = 1.606
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1212.9MB, alloc=52.3MB, time=14.72
x[1] = 0.6128 0.58
h = 0.001 0.001
y[1] (numeric) = 1.48297443422 0.415298694634
y[1] (closed_form) = 1.48297475756 0.415302969477
absolute error = 4.287e-06
relative error = 0.0002784 %
Correct digits = 6
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 = 1.261
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6138 0.581
h = 0.001 0.003
y[1] (numeric) = 1.48365328621 0.416056263958
y[1] (closed_form) = 1.4836536996 0.416060486433
absolute error = 4.243e-06
relative error = 0.0002753 %
Correct digits = 6
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 = 5.987
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6148 0.584
h = 0.0001 0.004
y[1] (numeric) = 1.48425356469 0.418250526895
y[1] (closed_form) = 1.48425379034 0.418254848572
absolute error = 4.328e-06
relative error = 0.0002806 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.679
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.39
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6149 0.588
h = 0.003 0.006
y[1] (numeric) = 1.4841670198 0.42112815448
y[1] (closed_form) = 1.48416709074 0.421132382907
absolute error = 4.229e-06
relative error = 0.0002741 %
Correct digits = 6
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 = 4.493
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6179 0.594
h = 0.0001 0.005
y[1] (numeric) = 1.4860829605 0.42555851162
y[1] (closed_form) = 1.48608305255 0.425563532387
absolute error = 5.022e-06
relative error = 0.0003249 %
Correct digits = 5
memory used=1258.4MB, alloc=52.3MB, time=15.26
Radius of convergence (given) for eq 1 = 2.684
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.001
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.618 0.599
h = 0.0001 0.003
y[1] (numeric) = 1.48595328468 0.429156622791
y[1] (closed_form) = 1.48595345037 0.429161134937
absolute error = 4.515e-06
relative error = 0.0002919 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.686
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.612
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6181 0.602
h = 0.001 0.001
y[1] (numeric) = 1.48590329071 0.431317017614
y[1] (closed_form) = 1.48590365338 0.431321489265
absolute error = 4.486e-06
relative error = 0.00029 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.686
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] = 0.6191 0.603
h = 0.001 0.003
y[1] (numeric) = 1.48658134255 0.432076579153
y[1] (closed_form) = 1.48658179473 0.432080998075
absolute error = 4.442e-06
relative error = 0.0002869 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.688
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.01
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6201 0.606
h = 0.0001 0.004
y[1] (numeric) = 1.48717802965 0.434274024796
y[1] (closed_form) = 1.48717829519 0.4342785437
absolute error = 4.527e-06
relative error = 0.0002922 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.689
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.403
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1303.9MB, alloc=52.3MB, time=15.82
x[1] = 0.6202 0.61
h = 0.003 0.006
y[1] (numeric) = 1.48708596707 0.437154179007
y[1] (closed_form) = 1.4870860778 0.437158605799
absolute error = 4.428e-06
relative error = 0.0002857 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.69
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.51
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6232 0.616
h = 0.0001 0.005
y[1] (numeric) = 1.488995343 0.441592306725
y[1] (closed_form) = 1.48899547924 0.441597523496
absolute error = 5.219e-06
relative error = 0.000336 %
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 = 2.009
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6233 0.621
h = 0.0001 0.003
y[1] (numeric) = 1.48885877678 0.44519355539
y[1] (closed_form) = 1.48885898359 0.445198264568
absolute error = 4.714e-06
relative error = 0.0003033 %
Correct digits = 6
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 = 1.618
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6234 0.624
h = 0.001 0.001
y[1] (numeric) = 1.48880467475 0.447355893841
y[1] (closed_form) = 1.48880507777 0.447360561533
absolute error = 4.685e-06
relative error = 0.0003014 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.697
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] = 0.6244 0.625
h = 0.0001 0.004
y[1] (numeric) = 1.48948193994 0.448117446462
y[1] (closed_form) = 1.48948243191 0.448122061072
absolute error = 4.641e-06
relative error = 0.0002984 %
Correct digits = 6
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 = 7.633
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=16.37
x[1] = 0.6245 0.629
h = 0.003 0.006
y[1] (numeric) = 1.48938538313 0.450999676157
y[1] (closed_form) = 1.48938545842 0.451004252875
absolute error = 4.577e-06
relative error = 0.0002941 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.699
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] = 0.6275 0.635
h = 0.0001 0.005
y[1] (numeric) = 1.49128906546 0.455444427211
y[1] (closed_form) = 1.49128917003 0.455449791893
absolute error = 5.366e-06
relative error = 0.0003441 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.703
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.015
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6276 0.64
h = 0.0001 0.003
y[1] (numeric) = 1.49114656015 0.459048318819
y[1] (closed_form) = 1.49114673267 0.459053176784
absolute error = 4.861e-06
relative error = 0.0003116 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.704
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] = 0.6277 0.643
h = 0.001 0.001
y[1] (numeric) = 1.49108891673 0.461212295685
y[1] (closed_form) = 1.49108928478 0.461217111315
absolute error = 4.830e-06
relative error = 0.0003094 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.705
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.275
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6287 0.644
h = 0.001 0.003
y[1] (numeric) = 1.49176549182 0.461975551972
y[1] (closed_form) = 1.49176594836 0.461980314218
absolute error = 4.784e-06
relative error = 0.0003063 %
Correct digits = 6
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 = 6.052
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1394.6MB, alloc=52.3MB, time=16.92
x[1] = 0.6297 0.647
h = 0.0001 0.004
y[1] (numeric) = 1.49235553275 0.464178907426
y[1] (closed_form) = 1.49235580466 0.464183771072
absolute error = 4.871e-06
relative error = 0.0003117 %
Correct digits = 6
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 = 3.427
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6298 0.651
h = 0.003 0.006
y[1] (numeric) = 1.49225325183 0.467063761337
y[1] (closed_form) = 1.4922533688 0.467068534967
absolute error = 4.775e-06
relative error = 0.0003054 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.709
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.542
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6328 0.657
h = 0.0001 0.005
y[1] (numeric) = 1.49415048505 0.471516310485
y[1] (closed_form) = 1.4941506356 0.471521869641
absolute error = 5.561e-06
relative error = 0.0003549 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.714
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.023
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6329 0.662
h = 0.0001 0.003
y[1] (numeric) = 1.49400115835 0.475123394654
y[1] (closed_form) = 1.49400137384 0.475128448183
absolute error = 5.058e-06
relative error = 0.0003226 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.629
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.633 0.665
h = 0.001 0.001
y[1] (numeric) = 1.49393944884 0.477289347524
y[1] (closed_form) = 1.49393985906 0.477294357759
absolute error = 5.027e-06
relative error = 0.0003205 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.716
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.279
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=17.46
x[1] = 0.634 0.666
h = 0.001 0.003
y[1] (numeric) = 1.49461526214 0.478054592495
y[1] (closed_form) = 1.49461576028 0.47805954901
absolute error = 4.981e-06
relative error = 0.0003175 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.717
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.075
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.635 0.669
h = 0.0001 0.004
y[1] (numeric) = 1.49520179182 0.48026116192
y[1] (closed_form) = 1.49520210645 0.480266220562
absolute error = 5.068e-06
relative error = 0.0003227 %
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 = 3.44
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6351 0.673
h = 0.003 0.006
y[1] (numeric) = 1.49509407866 0.483148609655
y[1] (closed_form) = 1.49509423829 0.483153579399
absolute error = 4.972e-06
relative error = 0.0003165 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.72
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.56
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6381 0.679
h = 0.0001 0.005
y[1] (numeric) = 1.49698492469 0.487608969994
y[1] (closed_form) = 1.49698512214 0.487614722787
absolute error = 5.756e-06
relative error = 0.0003656 %
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 = 2.031
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6382 0.684
h = 0.0001 0.003
y[1] (numeric) = 1.49682881406 0.491219275109
y[1] (closed_form) = 1.49682907348 0.491224523396
absolute error = 5.255e-06
relative error = 0.0003336 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.725
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.636
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1485.6MB, alloc=52.3MB, time=18.01
x[1] = 0.6383 0.687
h = 0.001 0.001
y[1] (numeric) = 1.49676306123 0.493387220653
y[1] (closed_form) = 1.49676351457 0.493392424701
absolute error = 5.224e-06
relative error = 0.0003315 %
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 = 1.284
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6393 0.688
h = 0.001 0.003
y[1] (numeric) = 1.49743812591 0.494154452699
y[1] (closed_form) = 1.49743866663 0.494159602704
absolute error = 5.178e-06
relative error = 0.0003284 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.727
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.099
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6403 0.691
h = 0.0001 0.004
y[1] (numeric) = 1.49802117232 0.496364246069
y[1] (closed_form) = 1.49802153061 0.496369498908
absolute error = 5.265e-06
relative error = 0.0003336 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.729
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.453
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6404 0.695
h = 0.003 0.006
y[1] (numeric) = 1.49790805707 0.499254309942
y[1] (closed_form) = 1.49790826033 0.499259474994
absolute error = 5.169e-06
relative error = 0.0003274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.73
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.577
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6434 0.701
h = 0.0001 0.005
y[1] (numeric) = 1.49979257757 0.503722493686
y[1] (closed_form) = 1.49979282283 0.503728439272
absolute error = 5.951e-06
relative error = 0.0003761 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.735
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.039
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1531.1MB, alloc=52.3MB, time=18.56
x[1] = 0.6435 0.706
h = 0.0001 0.003
y[1] (numeric) = 1.49962972059 0.507336047458
y[1] (closed_form) = 1.49963002488 0.50734148969
absolute error = 5.451e-06
relative error = 0.0003443 %
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] = 0.6436 0.709
h = 0.001 0.001
y[1] (numeric) = 1.49955994725 0.509506001938
y[1] (closed_form) = 1.49956044465 0.509511399005
absolute error = 5.420e-06
relative error = 0.0003422 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.737
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] = 0.6446 0.71
h = 0.001 0.003
y[1] (numeric) = 1.5002342764 0.510275219296
y[1] (closed_form) = 1.50023486061 0.510280562004
absolute error = 5.375e-06
relative error = 0.0003392 %
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 = 6.123
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6456 0.713
h = 0.0001 0.004
y[1] (numeric) = 1.50081386742 0.512488246158
y[1] (closed_form) = 1.50081427032 0.512493692388
absolute error = 5.461e-06
relative error = 0.0003444 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.74
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.467
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6457 0.717
h = 0.003 0.006
y[1] (numeric) = 1.50069538031 0.515380947946
y[1] (closed_form) = 1.50069562816 0.515386307493
absolute error = 5.365e-06
relative error = 0.0003381 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.741
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.596
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1576.5MB, alloc=52.3MB, time=19.12
x[1] = 0.6487 0.723
h = 0.0001 0.005
y[1] (numeric) = 1.50257363669 0.519856966438
y[1] (closed_form) = 1.50257393064 0.51986310397
absolute error = 6.145e-06
relative error = 0.0003865 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.746
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.047
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6488 0.728
h = 0.0001 0.003
y[1] (numeric) = 1.50240407101 0.52347379591
y[1] (closed_form) = 1.50240442109 0.523479431267
absolute error = 5.646e-06
relative error = 0.0003549 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.747
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] = 0.6489 0.731
h = 0.001 0.001
y[1] (numeric) = 1.50233030003 0.525645775188
y[1] (closed_form) = 1.5023308424 0.525651364472
absolute error = 5.616e-06
relative error = 0.0003528 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.748
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.295
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6499 0.732
h = 0.0001 0.004
y[1] (numeric) = 1.5030039066 0.526416975941
y[1] (closed_form) = 1.50300453524 0.526422510557
absolute error = 5.570e-06
relative error = 0.0003498 %
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 = 7.778
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.65 0.736
h = 0.003 0.006
y[1] (numeric) = 1.50288104469 0.529311842498
y[1] (closed_form) = 1.50288126165 0.529317350766
absolute error = 5.513e-06
relative error = 0.000346 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.75
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.611
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1622.0MB, alloc=52.3MB, time=19.67
x[1] = 0.653 0.742
h = 0.0001 0.005
y[1] (numeric) = 1.50475386456 0.533794539684
y[1] (closed_form) = 1.50475413115 0.533800823763
absolute error = 6.290e-06
relative error = 0.0003939 %
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 = 2.054
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6531 0.747
h = 0.0001 0.003
y[1] (numeric) = 1.50457851502 0.537414130616
y[1] (closed_form) = 1.50457883526 0.537419913526
absolute error = 5.792e-06
relative error = 0.0003625 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.756
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.654
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6532 0.75
h = 0.001 0.001
y[1] (numeric) = 1.50450129699 0.539587817922
y[1] (closed_form) = 1.5045018088 0.539593553978
absolute error = 5.759e-06
relative error = 0.0003603 %
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 = 1.299
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6542 0.751
h = 0.001 0.003
y[1] (numeric) = 1.5051742683 0.540360715864
y[1] (closed_form) = 1.50517486591 0.54036639699
absolute error = 5.712e-06
relative error = 0.0003572 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.758
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.168
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6552 0.754
h = 0.0001 0.004
y[1] (numeric) = 1.50574746489 0.542579743102
y[1] (closed_form) = 1.50574788322 0.542585528996
absolute error = 5.801e-06
relative error = 0.0003624 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.76
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.492
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1667.4MB, alloc=52.3MB, time=20.24
x[1] = 0.6553 0.758
h = 0.0001 0.004
y[1] (numeric) = 1.50561903068 0.54547734643
y[1] (closed_form) = 1.50561929396 0.545483047674
absolute error = 5.707e-06
relative error = 0.0003564 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.761
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.761
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6554 0.762
h = 0.003 0.006
y[1] (numeric) = 1.50548942561 0.548375133749
y[1] (closed_form) = 1.50548968889 0.548380834993
absolute error = 5.707e-06
relative error = 0.0003562 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.763
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.632
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6584 0.768
h = 0.0001 0.005
y[1] (numeric) = 1.50735474583 0.552866817332
y[1] (closed_form) = 1.50735506352 0.552873291467
absolute error = 6.482e-06
relative error = 0.0004037 %
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 = 2.063
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6585 0.773
h = 0.0001 0.003
y[1] (numeric) = 1.50717148968 0.556490064931
y[1] (closed_form) = 1.50717185764 0.55649603924
absolute error = 5.986e-06
relative error = 0.0003726 %
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 = 1.662
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6586 0.776
h = 0.001 0.001
y[1] (numeric) = 1.50708955846 0.558666016099
y[1] (closed_form) = 1.50709011706 0.558671942494
absolute error = 5.953e-06
relative error = 0.0003704 %
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 = 1.305
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1712.8MB, alloc=52.3MB, time=20.79
x[1] = 0.6596 0.777
h = 0.001 0.003
y[1] (numeric) = 1.50776163814 0.559441210012
y[1] (closed_form) = 1.5077622819 0.559447081118
absolute error = 5.906e-06
relative error = 0.0003673 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.771
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.196
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6606 0.78
h = 0.0001 0.004
y[1] (numeric) = 1.50833075663 0.561663935716
y[1] (closed_form) = 1.50833122238 0.561669912375
absolute error = 5.995e-06
relative error = 0.0003725 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.773
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] = 0.6607 0.784
h = 0.003 0.006
y[1] (numeric) = 1.50819602589 0.564564509718
y[1] (closed_form) = 1.50819633657 0.564570402996
absolute error = 5.901e-06
relative error = 0.0003665 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.774
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.65
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6637 0.79
h = 0.0001 0.005
y[1] (numeric) = 1.51005526601 0.569064060259
y[1] (closed_form) = 1.51005563504 0.569070723777
absolute error = 6.674e-06
relative error = 0.0004136 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.778
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.071
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6638 0.795
h = 0.0001 0.003
y[1] (numeric) = 1.50986541461 0.572690663422
y[1] (closed_form) = 1.50986583112 0.572696828379
absolute error = 6.179e-06
relative error = 0.0003826 %
Correct digits = 5
memory used=1758.3MB, alloc=52.3MB, time=21.35
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 = 1.669
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6639 0.798
h = 0.001 0.001
y[1] (numeric) = 1.50977955462 0.57486868621
y[1] (closed_form) = 1.50978016093 0.574874802394
absolute error = 6.146e-06
relative error = 0.0003804 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.781
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
x[1] = 0.6649 0.799
h = 0.001 0.003
y[1] (numeric) = 1.51045095047 0.575645857417
y[1] (closed_form) = 1.51045164139 0.575651918031
absolute error = 6.100e-06
relative error = 0.0003774 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.782
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.221
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6659 0.802
h = 0.0001 0.004
y[1] (numeric) = 1.51101672491 0.57787185228
y[1] (closed_form) = 1.51101723892 0.577878019061
absolute error = 6.188e-06
relative error = 0.0003825 %
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 = 3.523
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.666 0.806
h = 0.003 0.006
y[1] (numeric) = 1.51087674385 0.580775148158
y[1] (closed_form) = 1.51087710283 0.580781232632
absolute error = 6.095e-06
relative error = 0.0003765 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.785
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.669
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1803.8MB, alloc=52.3MB, time=21.90
x[1] = 0.669 0.812
h = 0.0001 0.005
y[1] (numeric) = 1.51272996409 0.585282573631
y[1] (closed_form) = 1.51273038528 0.585289425665
absolute error = 6.865e-06
relative error = 0.0004232 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.08
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6691 0.817
h = 0.0001 0.003
y[1] (numeric) = 1.51253355535 0.588912556767
y[1] (closed_form) = 1.51253402126 0.588918911529
absolute error = 6.372e-06
relative error = 0.0003926 %
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 = 1.675
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6692 0.82
h = 0.001 0.001
y[1] (numeric) = 1.51244378959 0.591092665453
y[1] (closed_form) = 1.51244444446 0.591098970599
absolute error = 6.339e-06
relative error = 0.0003904 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.792
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] = 0.6702 0.821
h = 0.001 0.003
y[1] (numeric) = 1.51311451412 0.591871811449
y[1] (closed_form) = 1.51311525304 0.591878060755
absolute error = 6.293e-06
relative error = 0.0003873 %
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 = 6.247
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6712 0.824
h = 0.0001 0.004
y[1] (numeric) = 1.51367697197 0.594101082965
y[1] (closed_form) = 1.51367753509 0.594107439035
absolute error = 6.381e-06
relative error = 0.0003924 %
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 = 3.537
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1849.2MB, alloc=52.3MB, time=22.45
x[1] = 0.6713 0.828
h = 0.003 0.006
y[1] (numeric) = 1.51353177108 0.59700711986
y[1] (closed_form) = 1.51353217922 0.597013394687
absolute error = 6.288e-06
relative error = 0.0003865 %
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 = 4.689
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6743 0.834
h = 0.0001 0.005
y[1] (numeric) = 1.51537903129 0.601522427446
y[1] (closed_form) = 1.51537950545 0.601529467127
absolute error = 7.056e-06
relative error = 0.0004328 %
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 = 2.088
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6744 0.839
h = 0.0001 0.003
y[1] (numeric) = 1.51517610316 0.605155814325
y[1] (closed_form) = 1.51517661932 0.605162358047
absolute error = 6.564e-06
relative error = 0.0004023 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.803
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] = 0.6745 0.842
h = 0.001 0.001
y[1] (numeric) = 1.51508245463 0.607338022803
y[1] (closed_form) = 1.5150831589 0.607344516082
absolute error = 6.531e-06
relative error = 0.0004001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.804
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] = 0.6755 0.843
h = 0.001 0.003
y[1] (numeric) = 1.51575252021 0.608119140953
y[1] (closed_form) = 1.51575330798 0.608125578129
absolute error = 6.485e-06
relative error = 0.0003971 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.805
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.273
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1894.6MB, alloc=52.3MB, time=22.99
x[1] = 0.6765 0.846
h = 0.0001 0.004
y[1] (numeric) = 1.51631168885 0.610351696227
y[1] (closed_form) = 1.51631230192 0.610358240747
absolute error = 6.573e-06
relative error = 0.0004021 %
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 = 3.552
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6766 0.85
h = 0.003 0.006
y[1] (numeric) = 1.5161612986 0.61326049277
y[1] (closed_form) = 1.51616175675 0.613266957103
absolute error = 6.481e-06
relative error = 0.0003962 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.808
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.708
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6796 0.856
h = 0.0001 0.005
y[1] (numeric) = 1.51800265831 0.617783688874
y[1] (closed_form) = 1.51800318622 0.617790915327
absolute error = 7.246e-06
relative error = 0.0004421 %
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 = 2.097
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6797 0.861
h = 0.0001 0.003
y[1] (numeric) = 1.51779324875 0.621420502633
y[1] (closed_form) = 1.51779381598 0.621427234465
absolute error = 6.756e-06
relative error = 0.0004119 %
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 = 1.689
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6798 0.864
h = 0.001 0.001
y[1] (numeric) = 1.51769574045 0.623604824419
y[1] (closed_form) = 1.51769649494 0.623611504997
absolute error = 6.723e-06
relative error = 0.0004097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.816
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
memory used=1940.1MB, alloc=52.3MB, time=23.53
x[1] = 0.6808 0.865
h = 0.0001 0.004
y[1] (numeric) = 1.51836515933 0.624387911955
y[1] (closed_form) = 1.51836599677 0.624394536177
absolute error = 6.677e-06
relative error = 0.0004067 %
Correct digits = 5
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 = 7.97
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6809 0.869
h = 0.003 0.006
y[1] (numeric) = 1.51821054349 0.627298970794
y[1] (closed_form) = 1.51821097608 0.627305582064
absolute error = 6.625e-06
relative error = 0.0004033 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.818
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.725
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6839 0.875
h = 0.0001 0.005
y[1] (numeric) = 1.52004677757 0.631828892287
y[1] (closed_form) = 1.52004728313 0.631836263348
absolute error = 7.388e-06
relative error = 0.0004488 %
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 = 2.105
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.684 0.88
h = 0.0001 0.003
y[1] (numeric) = 1.51983177821 0.635468597252
y[1] (closed_form) = 1.51983232079 0.635475474828
absolute error = 6.899e-06
relative error = 0.0004188 %
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 = 1.695
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6841 0.883
h = 0.001 0.001
y[1] (numeric) = 1.51973094058 0.637654703034
y[1] (closed_form) = 1.51973166969 0.637661528662
absolute error = 6.864e-06
relative error = 0.0004165 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.826
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
memory used=1985.5MB, alloc=52.3MB, time=24.08
x[1] = 0.6851 0.884
h = 0.001 0.003
y[1] (numeric) = 1.52039978912 0.638439475934
y[1] (closed_form) = 1.52040060071 0.638446244987
absolute error = 6.818e-06
relative error = 0.0004134 %
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 = 6.321
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6861 0.887
h = 0.0001 0.004
y[1] (numeric) = 1.52095287045 0.64067812071
y[1] (closed_form) = 1.52095350938 0.64068499815
absolute error = 6.907e-06
relative error = 0.0004185 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.829
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.579
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6862 0.891
h = 0.003 0.006
y[1] (numeric) = 1.52079287178 0.643592039226
y[1] (closed_form) = 1.52079335593 0.643598838423
absolute error = 6.816e-06
relative error = 0.0004128 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.745
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6892 0.897
h = 0.0001 0.005
y[1] (numeric) = 1.52262331509 0.648129859833
y[1] (closed_form) = 1.52262387585 0.648137416043
absolute error = 7.577e-06
relative error = 0.0004579 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.835
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.113
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6893 0.902
h = 0.0001 0.003
y[1] (numeric) = 1.52240190465 0.65177303353
y[1] (closed_form) = 1.5224024998 0.651780097633
absolute error = 7.089e-06
relative error = 0.0004281 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.837
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2030.9MB, alloc=52.3MB, time=24.62
x[1] = 0.6894 0.905
h = 0.001 0.001
y[1] (numeric) = 1.52229724988 0.653961277049
y[1] (closed_form) = 1.52229803071 0.653968288422
absolute error = 7.055e-06
relative error = 0.0004258 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.838
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
x[1] = 0.6904 0.906
h = 0.001 0.003
y[1] (numeric) = 1.52296547424 0.654748013996
y[1] (closed_form) = 1.52296633699 0.654754968558
absolute error = 7.008e-06
relative error = 0.0004227 %
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 = 6.348
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6914 0.909
h = 0.0001 0.004
y[1] (numeric) = 1.52351534393 0.656989961094
y[1] (closed_form) = 1.52351603512 0.656997024572
absolute error = 7.097e-06
relative error = 0.0004278 %
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 = 3.594
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6915 0.913
h = 0.003 0.006
y[1] (numeric) = 1.52335024289 0.659906690163
y[1] (closed_form) = 1.52335077941 0.65991367643
absolute error = 7.007e-06
relative error = 0.0004221 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.842
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.765
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6945 0.919
h = 0.0001 0.005
y[1] (numeric) = 1.5251749539 0.664452414144
y[1] (closed_form) = 1.5251755706 0.664460154622
absolute error = 7.765e-06
relative error = 0.0004668 %
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 = 2.122
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2076.3MB, alloc=52.3MB, time=25.16
x[1] = 0.6946 0.924
h = 0.0001 0.003
y[1] (numeric) = 1.52494717031 0.668099077945
y[1] (closed_form) = 1.52494781881 0.668106327714
absolute error = 7.279e-06
relative error = 0.0004372 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.849
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.71
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6947 0.927
h = 0.001 0.001
y[1] (numeric) = 1.52483872136 0.670289471656
y[1] (closed_form) = 1.52483955469 0.670296667931
absolute error = 7.244e-06
relative error = 0.0004349 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.85
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] = 0.6957 0.928
h = 0.001 0.003
y[1] (numeric) = 1.52550633344 0.671078169532
y[1] (closed_form) = 1.52550724814 0.671085308765
absolute error = 7.198e-06
relative error = 0.0004319 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.851
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.375
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6967 0.931
h = 0.0001 0.004
y[1] (numeric) = 1.52605301839 0.673323424618
y[1] (closed_form) = 1.52605376262 0.673330673281
absolute error = 7.287e-06
relative error = 0.0004369 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.853
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.61
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6968 0.935
h = 0.003 0.006
y[1] (numeric) = 1.52588284543 0.676242980962
y[1] (closed_form) = 1.52588343509 0.676250153437
absolute error = 7.197e-06
relative error = 0.0004312 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.854
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.785
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2121.7MB, alloc=52.3MB, time=25.70
x[1] = 0.6998 0.941
h = 0.0001 0.005
y[1] (numeric) = 1.52770188223 0.680796611859
y[1] (closed_form) = 1.52770255559 0.680804535722
absolute error = 7.952e-06
relative error = 0.0004755 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.859
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
x[1] = 0.6999 0.946
h = 0.0001 0.003
y[1] (numeric) = 1.52746776338 0.684446786532
y[1] (closed_form) = 1.52746846599 0.684454221105
absolute error = 7.468e-06
relative error = 0.0004461 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.861
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] = 0.7 0.949
h = 0.001 0.001
y[1] (numeric) = 1.5273555432 0.686639342529
y[1] (closed_form) = 1.52735642977 0.686646722858
absolute error = 7.433e-06
relative error = 0.0004439 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.862
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.348
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.701 0.95
h = 0.001 0.003
y[1] (numeric) = 1.52802255477 0.687429998099
y[1] (closed_form) = 1.52802352218 0.687437321164
absolute error = 7.387e-06
relative error = 0.0004409 %
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 = 6.402
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.702 0.953
h = 0.0001 0.004
y[1] (numeric) = 1.52856608174 0.689678566484
y[1] (closed_form) = 1.52856687978 0.689685999476
absolute error = 7.476e-06
relative error = 0.0004458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.865
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.625
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2167.1MB, alloc=52.3MB, time=26.24
x[1] = 0.7021 0.957
h = 0.003 0.006
y[1] (numeric) = 1.52839086727 0.692600966343
y[1] (closed_form) = 1.52839151086 0.692608324161
absolute error = 7.386e-06
relative error = 0.0004402 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.867
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.806
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7051 0.963
h = 0.0001 0.005
y[1] (numeric) = 1.53020428755 0.697162506995
y[1] (closed_form) = 1.5302050183 0.69717061336
absolute error = 8.139e-06
relative error = 0.000484 %
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 = 2.141
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7052 0.968
h = 0.0001 0.003
y[1] (numeric) = 1.52996387129 0.700816212714
y[1] (closed_form) = 1.52996462877 0.700823831224
absolute error = 7.656e-06
relative error = 0.000455 %
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 = 1.725
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7053 0.971
h = 0.001 0.001
y[1] (numeric) = 1.52984790279 0.703010942733
y[1] (closed_form) = 1.52984884337 0.703018506267
absolute error = 7.622e-06
relative error = 0.0004527 %
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 = 1.354
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7063 0.972
h = 0.0001 0.004
y[1] (numeric) = 1.53051432551 0.70380355265
y[1] (closed_form) = 1.53051534638 0.703811058707
absolute error = 7.575e-06
relative error = 0.0004497 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.876
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.136
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2212.6MB, alloc=52.3MB, time=26.79
x[1] = 0.7064 0.976
h = 0.003 0.006
y[1] (numeric) = 1.53033500615 0.706728281868
y[1] (closed_form) = 1.53033562819 0.706735784944
absolute error = 7.529e-06
relative error = 0.0004466 %
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 = 4.823
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7094 0.982
h = 0.0001 0.005
y[1] (numeric) = 1.53214354355 0.711296566746
y[1] (closed_form) = 1.53214425571 0.711304815948
absolute error = 8.280e-06
relative error = 0.0004902 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.882
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.148
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7095 0.987
h = 0.0001 0.003
y[1] (numeric) = 1.53189769458 0.714953253174
y[1] (closed_form) = 1.53189843133 0.714961015743
absolute error = 7.797e-06
relative error = 0.0004612 %
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 = 1.731
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7096 0.99
h = 0.001 0.001
y[1] (numeric) = 1.53177849188 0.71714981937
y[1] (closed_form) = 1.53177941098 0.717157526334
absolute error = 7.762e-06
relative error = 0.0004589 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.885
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.359
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7106 0.991
h = 0.001 0.003
y[1] (numeric) = 1.53244439374 0.717944101933
y[1] (closed_form) = 1.53244539268 0.717951751236
absolute error = 7.714e-06
relative error = 0.0004558 %
Correct digits = 5
memory used=2258.1MB, alloc=52.3MB, time=27.33
Radius of convergence (given) for eq 1 = 2.886
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.453
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7116 0.994
h = 0.0001 0.004
y[1] (numeric) = 1.5329820756 0.720198811664
y[1] (closed_form) = 1.53298290718 0.720206571785
absolute error = 7.805e-06
relative error = 0.0004608 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.888
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.654
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7117 0.998
h = 0.003 0.006
y[1] (numeric) = 1.53279752655 0.72312648505
y[1] (closed_form) = 1.53279820392 0.723134171861
absolute error = 7.717e-06
relative error = 0.0004553 %
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 = 4.844
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7147 1.004
h = 0.0001 0.005
y[1] (numeric) = 1.53460055369 0.727702683824
y[1] (closed_form) = 1.53460132453 0.727711113888
absolute error = 8.465e-06
relative error = 0.0004984 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.894
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.158
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7148 1.009
h = 0.0001 0.003
y[1] (numeric) = 1.53434847736 0.731362937726
y[1] (closed_form) = 1.53434927034 0.731370882627
absolute error = 7.984e-06
relative error = 0.0004697 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.896
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.738
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2303.6MB, alloc=52.3MB, time=27.88
x[1] = 0.7149 1.012
h = 0.001 0.001
y[1] (numeric) = 1.53422556873 0.733561699124
y[1] (closed_form) = 1.53422654319 0.733569587715
absolute error = 7.949e-06
relative error = 0.0004674 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.897
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.365
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7159 1.013
h = 0.001 0.003
y[1] (numeric) = 1.53489090313 0.734357929656
y[1] (closed_form) = 1.53489195688 0.734365760386
absolute error = 7.901e-06
relative error = 0.0004644 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.899
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.482
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7169 1.016
h = 0.0001 0.004
y[1] (numeric) = 1.53542550274 0.736615966282
y[1] (closed_form) = 1.53542639022 0.736623908281
absolute error = 7.991e-06
relative error = 0.0004693 %
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 = 3.67
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.717 1.02
h = 0.003 0.006
y[1] (numeric) = 1.53523599874 0.739546527412
y[1] (closed_form) = 1.53523673216 0.739554397089
absolute error = 7.904e-06
relative error = 0.0004638 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.902
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] = 0.72 1.026
h = 0.0001 0.005
y[1] (numeric) = 1.53703357214 0.744130640994
y[1] (closed_form) = 1.53703440233 0.744139251032
absolute error = 8.650e-06
relative error = 0.0005065 %
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 = 2.167
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2349.0MB, alloc=52.3MB, time=28.42
x[1] = 0.7201 1.031
h = 0.0001 0.003
y[1] (numeric) = 1.53677530614 0.747794480883
y[1] (closed_form) = 1.53677615604 0.747802607244
absolute error = 8.171e-06
relative error = 0.0004781 %
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 = 1.746
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7202 1.034
h = 0.001 0.001
y[1] (numeric) = 1.53664871436 0.749995448225
y[1] (closed_form) = 1.53664974488 0.750003517586
absolute error = 8.135e-06
relative error = 0.0004757 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.371
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7212 1.035
h = 0.001 0.003
y[1] (numeric) = 1.53731349258 0.750793623078
y[1] (closed_form) = 1.53731460185 0.750801634386
absolute error = 8.088e-06
relative error = 0.0004727 %
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 = 6.51
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7222 1.038
h = 0.0001 0.004
y[1] (numeric) = 1.53784503614 0.753054990594
y[1] (closed_form) = 1.53784598022 0.753063113607
absolute error = 8.178e-06
relative error = 0.0004776 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.913
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.686
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7223 1.042
h = 0.003 0.006
y[1] (numeric) = 1.53765060742 0.755988453915
y[1] (closed_form) = 1.5376513976 0.755996505584
absolute error = 8.090e-06
relative error = 0.0004722 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.915
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.887
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2394.4MB, alloc=52.3MB, time=28.96
x[1] = 0.7253 1.048
h = 0.0001 0.005
y[1] (numeric) = 1.53944278319 0.760580482571
y[1] (closed_form) = 1.53944367337 0.760589271696
absolute error = 8.834e-06
relative error = 0.0005145 %
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 = 2.177
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7254 1.053
h = 0.0001 0.003
y[1] (numeric) = 1.5391783651 0.764247926395
y[1] (closed_form) = 1.53917927262 0.764256233344
absolute error = 8.356e-06
relative error = 0.0004863 %
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 = 1.754
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7255 1.056
h = 0.001 0.001
y[1] (numeric) = 1.5390481129 0.766451110087
y[1] (closed_form) = 1.53904920017 0.766459359362
absolute error = 8.321e-06
relative error = 0.0004839 %
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 = 1.377
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7265 1.057
h = 0.001 0.003
y[1] (numeric) = 1.5397123461 0.767251225513
y[1] (closed_form) = 1.53971351158 0.767259416551
absolute error = 8.274e-06
relative error = 0.0004809 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.924
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.539
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7275 1.06
h = 0.0001 0.004
y[1] (numeric) = 1.54024085966 0.769515927592
y[1] (closed_form) = 1.54024186103 0.769524230753
absolute error = 8.363e-06
relative error = 0.0004857 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.926
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.703
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2439.8MB, alloc=52.3MB, time=29.50
x[1] = 0.7276 1.064
h = 0.003 0.006
y[1] (numeric) = 1.54004153635 0.772452307102
y[1] (closed_form) = 1.54004238399 0.772460539889
absolute error = 8.276e-06
relative error = 0.0004804 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.928
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.909
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7306 1.07
h = 0.0001 0.005
y[1] (numeric) = 1.54182837016 0.777052250472
y[1] (closed_form) = 1.54182932097 0.777061217796
absolute error = 9.018e-06
relative error = 0.0005223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.933
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] = 0.7307 1.075
h = 0.0001 0.003
y[1] (numeric) = 1.5415578375 0.780723315621
y[1] (closed_form) = 1.54155880331 0.780731802286
absolute error = 8.541e-06
relative error = 0.0004943 %
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 = 1.761
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7308 1.078
h = 0.001 0.001
y[1] (numeric) = 1.54142394755 0.782928725735
y[1] (closed_form) = 1.54142509224 0.782937154065
absolute error = 8.506e-06
relative error = 0.000492 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.936
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] = 0.7318 1.079
h = 0.0001 0.004
y[1] (numeric) = 1.54208764676 0.783730777893
y[1] (closed_form) = 1.54208886913 0.78373914781
absolute error = 8.459e-06
relative error = 0.000489 %
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 = 8.31
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2485.2MB, alloc=52.3MB, time=30.04
x[1] = 0.7319 1.083
h = 0.003 0.006
y[1] (numeric) = 1.54188433838 0.78666954478
y[1] (closed_form) = 1.54188516825 0.786677920988
absolute error = 8.417e-06
relative error = 0.0004863 %
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 = 4.927
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7349 1.089
h = 0.0001 0.005
y[1] (numeric) = 1.543666524 0.791276237375
y[1] (closed_form) = 1.54366745977 0.791285345636
absolute error = 9.156e-06
relative error = 0.0005278 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.944
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.195
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.735 1.094
h = 0.0001 0.003
y[1] (numeric) = 1.54339071466 0.794950360919
y[1] (closed_form) = 1.54339166341 0.794958989809
absolute error = 8.681e-06
relative error = 0.0005 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.946
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] = 0.7351 1.097
h = 0.001 0.001
y[1] (numeric) = 1.54325368488 0.797157652311
y[1] (closed_form) = 1.54325481178 0.7971662223
absolute error = 8.644e-06
relative error = 0.0004976 %
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 = 1.388
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7361 1.098
h = 0.001 0.003
y[1] (numeric) = 1.54391691019 0.797961362212
y[1] (closed_form) = 1.5439181143 0.797969873635
absolute error = 8.596e-06
relative error = 0.0004946 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.948
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.592
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2530.6MB, alloc=52.3MB, time=30.58
x[1] = 0.7371 1.101
h = 0.0001 0.004
y[1] (numeric) = 1.54443981457 0.800232242456
y[1] (closed_form) = 1.54444085657 0.800240866754
absolute error = 8.687e-06
relative error = 0.0004994 %
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 = 3.733
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7372 1.105
h = 0.003 0.006
y[1] (numeric) = 1.54423142843 0.803174026602
y[1] (closed_form) = 1.54423231702 0.803182582307
absolute error = 8.602e-06
relative error = 0.0004942 %
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 = 4.949
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7402 1.111
h = 0.0001 0.005
y[1] (numeric) = 1.54600837454 0.807788632271
y[1] (closed_form) = 1.5460093721 0.807797917087
absolute error = 9.338e-06
relative error = 0.0005353 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.957
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.204
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7403 1.116
h = 0.0001 0.003
y[1] (numeric) = 1.54572651994 0.811466408496
y[1] (closed_form) = 1.54572752821 0.811475215483
absolute error = 8.865e-06
relative error = 0.0005078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.959
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.776
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7404 1.119
h = 0.001 0.001
y[1] (numeric) = 1.54558589432 0.81367594445
y[1] (closed_form) = 1.54558707986 0.813684691904
absolute error = 8.827e-06
relative error = 0.0005054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.96
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.395
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=31.12
x[1] = 0.7414 1.12
h = 0.001 0.003
y[1] (numeric) = 1.54624860587 0.814481583822
y[1] (closed_form) = 1.5462498681 0.814490272546
absolute error = 8.780e-06
relative error = 0.0005024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.961
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] = 0.7424 1.123
h = 0.0001 0.004
y[1] (numeric) = 1.54676855384 0.816755807707
y[1] (closed_form) = 1.54676965501 0.816764609682
absolute error = 8.871e-06
relative error = 0.0005071 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.963
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.75
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7425 1.127
h = 0.003 0.006
y[1] (numeric) = 1.54655535873 0.819700546025
y[1] (closed_form) = 1.5465563067 0.81970928035
absolute error = 8.786e-06
relative error = 0.0005019 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.965
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.971
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7455 1.133
h = 0.0001 0.005
y[1] (numeric) = 1.54832711976 0.82432306269
y[1] (closed_form) = 1.54832817971 0.824332523174
absolute error = 9.520e-06
relative error = 0.0005427 %
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 = 2.214
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7456 1.138
h = 0.0001 0.003
y[1] (numeric) = 1.54803925711 0.828004507439
y[1] (closed_form) = 1.54804032553 0.828013491649
absolute error = 9.048e-06
relative error = 0.0005154 %
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 = 1.784
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=31.66
x[1] = 0.7457 1.141
h = 0.001 0.001
y[1] (numeric) = 1.54789505811 0.830216297105
y[1] (closed_form) = 1.54789630293 0.830225221163
absolute error = 9.010e-06
relative error = 0.000513 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.973
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.401
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7467 1.142
h = 0.001 0.003
y[1] (numeric) = 1.54855726659 0.83102386185
y[1] (closed_form) = 1.54855858755 0.831032727023
absolute error = 8.963e-06
relative error = 0.00051 %
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 = 6.652
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7477 1.145
h = 0.0001 0.004
y[1] (numeric) = 1.54907428353 0.833301431858
y[1] (closed_form) = 1.54907544452 0.833310410643
absolute error = 9.054e-06
relative error = 0.0005147 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.977
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.766
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7478 1.149
h = 0.003 0.006
y[1] (numeric) = 1.54885630928 0.836249136677
y[1] (closed_form) = 1.54885731726 0.836258048745
absolute error = 8.969e-06
relative error = 0.0005095 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.978
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.993
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7508 1.155
h = 0.0001 0.005
y[1] (numeric) = 1.5506229392 0.840879561687
y[1] (closed_form) = 1.55062406212 0.840889196954
absolute error = 9.700e-06
relative error = 0.0005499 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.983
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.224
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2666.7MB, alloc=52.3MB, time=32.20
x[1] = 0.7509 1.16
h = 0.0001 0.003
y[1] (numeric) = 1.55032910558 0.844564690284
y[1] (closed_form) = 1.55033023476 0.844573850842
absolute error = 9.230e-06
relative error = 0.0005228 %
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 = 1.792
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.751 1.163
h = 0.001 0.001
y[1] (numeric) = 1.55018135561 0.846778742494
y[1] (closed_form) = 1.55018266031 0.846787842297
absolute error = 9.193e-06
relative error = 0.0005204 %
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 = 1.407
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.752 1.164
h = 0.001 0.003
y[1] (numeric) = 1.55084307154 0.847588228436
y[1] (closed_form) = 1.55084445187 0.847597269204
absolute error = 9.146e-06
relative error = 0.0005175 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.988
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.681
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.753 1.167
h = 0.0001 0.004
y[1] (numeric) = 1.55135718271 0.849869146755
y[1] (closed_form) = 1.55135840412 0.849878301484
absolute error = 9.236e-06
relative error = 0.0005221 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.99
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.783
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7531 1.171
h = 0.003 0.006
y[1] (numeric) = 1.55113445901 0.852819829988
y[1] (closed_form) = 1.55113552763 0.852828918922
absolute error = 9.152e-06
relative error = 0.000517 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.992
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.016
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=32.74
x[1] = 0.7561 1.177
h = 0.0001 0.005
y[1] (numeric) = 1.55289601133 0.857458160139
y[1] (closed_form) = 1.5528971978 0.857467969304
absolute error = 9.881e-06
relative error = 0.000557 %
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 = 2.234
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7562 1.182
h = 0.0001 0.003
y[1] (numeric) = 1.55259624371 0.861146987388
y[1] (closed_form) = 1.55259743425 0.861156323422
absolute error = 9.412e-06
relative error = 0.0005301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.999
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7563 1.185
h = 0.001 0.001
y[1] (numeric) = 1.55244496507 0.863363310671
y[1] (closed_form) = 1.55244633027 0.863372585358
absolute error = 9.375e-06
relative error = 0.0005277 %
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 = 1.414
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7573 1.186
h = 0.0001 0.004
y[1] (numeric) = 1.55310619887 0.864174713551
y[1] (closed_form) = 1.55310763917 0.864183929061
absolute error = 9.327e-06
relative error = 0.0005248 %
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 = 8.492
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7574 1.19
h = 0.003 0.006
y[1] (numeric) = 1.55287960836 0.867127833748
y[1] (closed_form) = 1.55288066274 0.867137064138
absolute error = 9.290e-06
relative error = 0.0005223 %
Correct digits = 5
memory used=2757.5MB, alloc=52.3MB, time=33.29
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 = 5.035
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7604 1.196
h = 0.0001 0.005
y[1] (numeric) = 1.55463673846 0.871772905776
y[1] (closed_form) = 1.55463791318 0.87178285387
absolute error = 1.002e-05
relative error = 0.000562 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.008
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.243
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7605 1.201
h = 0.0001 0.003
y[1] (numeric) = 1.55433184824 0.875464858081
y[1] (closed_form) = 1.55433302517 0.875474334384
absolute error = 9.549e-06
relative error = 0.0005353 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.01
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.807
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7606 1.204
h = 0.001 0.001
y[1] (numeric) = 1.55417752286 0.877683101151
y[1] (closed_form) = 1.55417887371 0.8776925156
absolute error = 9.511e-06
relative error = 0.0005329 %
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 = 1.419
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7616 1.205
h = 0.001 0.003
y[1] (numeric) = 1.55483832713 0.878496145024
y[1] (closed_form) = 1.55483975264 0.878505500172
absolute error = 9.463e-06
relative error = 0.0005299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.013
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.737
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2803.0MB, alloc=52.3MB, time=33.83
x[1] = 0.7626 1.208
h = 0.0001 0.004
y[1] (numeric) = 1.55534705796 0.880783264715
y[1] (closed_form) = 1.5553483265 0.880792734446
absolute error = 9.554e-06
relative error = 0.0005345 %
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 = 3.815
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7627 1.212
h = 0.003 0.006
y[1] (numeric) = 1.55511553955 0.883739464643
y[1] (closed_form) = 1.5551166557 0.883748870276
absolute error = 9.472e-06
relative error = 0.0005295 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.017
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.058
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7657 1.218
h = 0.0001 0.005
y[1] (numeric) = 1.55686769049 0.888392435045
y[1] (closed_form) = 1.55686892978 0.888402555399
absolute error = 1.020e-05
relative error = 0.0005688 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.022
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
x[1] = 0.7658 1.223
h = 0.0001 0.003
y[1] (numeric) = 1.55655693449 0.892088112646
y[1] (closed_form) = 1.55655817387 0.892097762807
absolute error = 9.729e-06
relative error = 0.0005423 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.024
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] = 0.7659 1.226
h = 0.001 0.001
y[1] (numeric) = 1.55639912164 0.894308642116
y[1] (closed_form) = 1.55640053408 0.894318229858
absolute error = 9.691e-06
relative error = 0.0005399 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.025
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
memory used=2848.3MB, alloc=52.3MB, time=34.37
x[1] = 0.7669 1.227
h = 0.001 0.003
y[1] (numeric) = 1.55705946287 0.895123594927
y[1] (closed_form) = 1.55706094944 0.895133123238
absolute error = 9.644e-06
relative error = 0.0005369 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.027
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.768
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7679 1.23
h = 0.0001 0.004
y[1] (numeric) = 1.55756535912 0.897414067935
y[1] (closed_form) = 1.55756668978 0.897423711137
absolute error = 9.735e-06
relative error = 0.0005415 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.029
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.832
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.768 1.234
h = 0.003 0.006
y[1] (numeric) = 1.55732917551 0.900373278469
y[1] (closed_form) = 1.55733035402 0.900382858469
absolute error = 9.652e-06
relative error = 0.0005366 %
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 = 5.081
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.771 1.24
h = 0.0001 0.005
y[1] (numeric) = 1.55907639948 0.905034142523
y[1] (closed_form) = 1.55907770388 0.905044434257
absolute error = 1.037e-05
relative error = 0.0005755 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.036
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.263
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7711 1.245
h = 0.0001 0.003
y[1] (numeric) = 1.55875981426 0.908733558799
y[1] (closed_form) = 1.55876111667 0.908743381944
absolute error = 9.909e-06
relative error = 0.0005492 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.038
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
memory used=2893.8MB, alloc=52.3MB, time=34.91
x[1] = 0.7712 1.248
h = 0.001 0.001
y[1] (numeric) = 1.55859853601 0.910956382343
y[1] (closed_form) = 1.5586000106 0.910966142519
absolute error = 9.871e-06
relative error = 0.0005468 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.039
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.432
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7722 1.249
h = 0.001 0.003
y[1] (numeric) = 1.55925842424 0.911773239624
y[1] (closed_form) = 1.55925997246 0.911782940244
absolute error = 9.823e-06
relative error = 0.0005438 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.041
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.799
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7732 1.252
h = 0.0001 0.004
y[1] (numeric) = 1.55976151047 0.91406706707
y[1] (closed_form) = 1.5597629038 0.914076882877
absolute error = 9.914e-06
relative error = 0.0005484 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.043
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.85
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7733 1.256
h = 0.003 0.006
y[1] (numeric) = 1.55952069092 0.91702929858
y[1] (closed_form) = 1.55952193235 0.917039052071
absolute error = 9.832e-06
relative error = 0.0005435 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.044
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.104
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7763 1.262
h = 0.0001 0.005
y[1] (numeric) = 1.56126303968 0.921698051065
y[1] (closed_form) = 1.56126440969 0.921708513299
absolute error = 1.055e-05
relative error = 0.000582 %
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 = 2.274
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2939.2MB, alloc=52.3MB, time=35.46
x[1] = 0.7764 1.267
h = 0.0001 0.003
y[1] (numeric) = 1.56094066163 0.925401218908
y[1] (closed_form) = 1.56094202761 0.925411214168
absolute error = 1.009e-05
relative error = 0.0005559 %
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 = 1.832
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7765 1.27
h = 0.001 0.001
y[1] (numeric) = 1.56077593993 0.927626343913
y[1] (closed_form) = 1.56077747722 0.927636275665
absolute error = 1.005e-05
relative error = 0.0005535 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.053
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.438
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7775 1.271
h = 0.001 0.003
y[1] (numeric) = 1.56143538509 0.928445101129
y[1] (closed_form) = 1.5614369955 0.928454973207
absolute error = 1.000e-05
relative error = 0.0005506 %
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 = 6.83
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7785 1.274
h = 0.0001 0.004
y[1] (numeric) = 1.56193568566 0.930742283875
y[1] (closed_form) = 1.56193714221 0.930752271422
absolute error = 1.009e-05
relative error = 0.0005551 %
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 = 3.868
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7786 1.278
h = 0.003 0.006
y[1] (numeric) = 1.56169025931 0.933707546347
y[1] (closed_form) = 1.56169156421 0.933717472456
absolute error = 1.001e-05
relative error = 0.0005502 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.058
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.128
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2984.7MB, alloc=52.3MB, time=36.00
x[1] = 0.7816 1.284
h = 0.0001 0.005
y[1] (numeric) = 1.56342778412 0.938384181555
y[1] (closed_form) = 1.56342922025 0.938394813412
absolute error = 1.073e-05
relative error = 0.0005884 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.064
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.284
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7817 1.289
h = 0.0001 0.003
y[1] (numeric) = 1.5630996495 0.942091113387
y[1] (closed_form) = 1.56310107959 0.942101279891
absolute error = 1.027e-05
relative error = 0.0005625 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.066
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] = 0.7818 1.292
h = 0.001 0.001
y[1] (numeric) = 1.5629315062 0.944318546956
y[1] (closed_form) = 1.56293310674 0.944328649428
absolute error = 1.023e-05
relative error = 0.0005601 %
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] = 0.7828 1.293
h = 0.0001 0.004
y[1] (numeric) = 1.5635905181 0.945139199508
y[1] (closed_form) = 1.56359219123 0.945149242194
absolute error = 1.018e-05
relative error = 0.0005572 %
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 = 8.682
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7829 1.297
h = 0.003 0.006
y[1] (numeric) = 1.56334134108 0.948106940735
y[1] (closed_form) = 1.56334263503 0.948117006234
absolute error = 1.015e-05
relative error = 0.000555 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.147
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3030.2MB, alloc=52.3MB, time=36.55
x[1] = 0.7859 1.303
h = 0.0001 0.005
y[1] (numeric) = 1.5650746605 0.952790299555
y[1] (closed_form) = 1.56507608796 0.952801068253
absolute error = 1.086e-05
relative error = 0.0005929 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.076
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.786 1.308
h = 0.0001 0.003
y[1] (numeric) = 1.56474155467 0.956500412905
y[1] (closed_form) = 1.56474297436 0.956510717629
absolute error = 1.040e-05
relative error = 0.0005672 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.078
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.847
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7861 1.311
h = 0.001 0.001
y[1] (numeric) = 1.564570456 0.95872979868
y[1] (closed_form) = 1.5645720454 0.95874003892
absolute error = 1.036e-05
relative error = 0.0005647 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.079
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.451
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7871 1.312
h = 0.001 0.003
y[1] (numeric) = 1.5652290802 0.959552073938
y[1] (closed_form) = 1.56523074177 0.959562254295
absolute error = 1.032e-05
relative error = 0.0005618 %
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 = 6.888
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7881 1.315
h = 0.0001 0.004
y[1] (numeric) = 1.56572422152 0.961855469032
y[1] (closed_form) = 1.56572573115 0.961865765361
absolute error = 1.041e-05
relative error = 0.0005663 %
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 = 3.9
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3075.6MB, alloc=52.3MB, time=37.09
x[1] = 0.7882 1.319
h = 0.003 0.006
y[1] (numeric) = 1.56547026372 0.964826342656
y[1] (closed_form) = 1.56547162216 0.964836579156
absolute error = 1.033e-05
relative error = 0.0005615 %
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 = 5.171
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7912 1.325
h = 0.0001 0.005
y[1] (numeric) = 1.56719885344 0.969517572924
y[1] (closed_form) = 1.56720034794 0.969528509624
absolute error = 1.104e-05
relative error = 0.000599 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.09
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.303
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7913 1.33
h = 0.0001 0.003
y[1] (numeric) = 1.56686005789 0.97323147257
y[1] (closed_form) = 1.56686154266 0.97324194693
absolute error = 1.058e-05
relative error = 0.0005735 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.092
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.856
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7914 1.333
h = 0.001 0.001
y[1] (numeric) = 1.56668557795 0.97546317965
y[1] (closed_form) = 1.56668723157 0.975473589026
absolute error = 1.054e-05
relative error = 0.0005711 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.093
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.457
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7924 1.334
h = 0.001 0.003
y[1] (numeric) = 1.56734378684 0.976287341636
y[1] (closed_form) = 1.56734551212 0.976297691028
absolute error = 1.049e-05
relative error = 0.0005682 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.095
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.92
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3121.1MB, alloc=52.3MB, time=37.63
x[1] = 0.7934 1.337
h = 0.0001 0.004
y[1] (numeric) = 1.56783621115 0.978594093391
y[1] (closed_form) = 1.56783778551 0.978604559003
absolute error = 1.058e-05
relative error = 0.0005726 %
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 = 3.918
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7935 1.341
h = 0.003 0.006
y[1] (numeric) = 1.56757772906 0.98156802484
y[1] (closed_form) = 1.5675791525 0.981578431472
absolute error = 1.050e-05
relative error = 0.0005679 %
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 = 5.195
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7965 1.347
h = 0.0001 0.005
y[1] (numeric) = 1.56930163902 0.986267119524
y[1] (closed_form) = 1.56930320102 0.986278223356
absolute error = 1.121e-05
relative error = 0.000605 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.314
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7966 1.352
h = 0.0001 0.003
y[1] (numeric) = 1.5689571895 0.989984816574
y[1] (closed_form) = 1.56895873985 0.989995459707
absolute error = 1.076e-05
relative error = 0.0005798 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.106
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.864
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7967 1.355
h = 0.001 0.001
y[1] (numeric) = 1.56877934985 0.992218851282
y[1] (closed_form) = 1.56878106819 0.992229428942
absolute error = 1.072e-05
relative error = 0.0005773 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.108
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.464
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3166.5MB, alloc=52.3MB, time=38.17
x[1] = 0.7977 1.356
h = 0.001 0.003
y[1] (numeric) = 1.56943715286 0.993044895225
y[1] (closed_form) = 1.56943894236 0.993055412807
absolute error = 1.067e-05
relative error = 0.0005744 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.109
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.952
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7987 1.359
h = 0.0001 0.004
y[1] (numeric) = 1.56992688381 0.995355003552
y[1] (closed_form) = 1.5699285234 0.995365637588
absolute error = 1.076e-05
relative error = 0.0005788 %
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 = 3.937
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7988 1.363
h = 0.003 0.006
y[1] (numeric) = 1.56966390603 0.998332001399
y[1] (closed_form) = 1.56966539498 0.998342577296
absolute error = 1.068e-05
relative error = 0.0005741 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.219
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8018 1.369
h = 0.0001 0.005
y[1] (numeric) = 1.57138318569 1.00303895303
y[1] (closed_form) = 1.57138481564 1.00305022313
absolute error = 1.139e-05
relative error = 0.0006108 %
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 = 2.325
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8019 1.374
h = 0.0001 0.003
y[1] (numeric) = 1.57103311778 1.00676045815
y[1] (closed_form) = 1.57103473419 1.0067712692
absolute error = 1.093e-05
relative error = 0.0005858 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.121
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.873
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3212.0MB, alloc=52.3MB, time=38.72
x[1] = 0.802 1.377
h = 0.001 0.001
y[1] (numeric) = 1.57085193987 1.00899682655
y[1] (closed_form) = 1.57085372342 1.00900757164
absolute error = 1.089e-05
relative error = 0.0005834 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.122
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.471
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.803 1.378
h = 0.001 0.003
y[1] (numeric) = 1.57150934632 1.00982474763
y[1] (closed_form) = 1.57151120053 1.00983543255
absolute error = 1.084e-05
relative error = 0.0005805 %
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 = 6.984
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.804 1.381
h = 0.0001 0.004
y[1] (numeric) = 1.57199640736 1.0121382122
y[1] (closed_form) = 1.57199811266 1.01214901381
absolute error = 1.094e-05
relative error = 0.0005849 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.955
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8041 1.385
h = 0.003 0.006
y[1] (numeric) = 1.57172896235 1.01511828467
y[1] (closed_form) = 1.57173051729 1.01512902897
absolute error = 1.086e-05
relative error = 0.0005802 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.127
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.243
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8071 1.391
h = 0.0001 0.005
y[1] (numeric) = 1.57344366069 1.01983308536
y[1] (closed_form) = 1.57344535905 1.01984452085
absolute error = 1.156e-05
relative error = 0.0006166 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.133
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.336
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3257.4MB, alloc=52.3MB, time=39.26
x[1] = 0.8072 1.396
h = 0.0001 0.003
y[1] (numeric) = 1.57308800979 1.02355840879
y[1] (closed_form) = 1.57308969275 1.02356938688
absolute error = 1.111e-05
relative error = 0.0005918 %
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 = 1.882
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8073 1.399
h = 0.001 0.001
y[1] (numeric) = 1.57290351494 1.02579711667
y[1] (closed_form) = 1.57290536418 1.02580802835
absolute error = 1.107e-05
relative error = 0.0005894 %
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 = 1.478
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8083 1.4
h = 0.003 0.006
y[1] (numeric) = 1.57356053404 1.02662691001
y[1] (closed_form) = 1.57356245344 1.02663776144
absolute error = 1.102e-05
relative error = 0.0005865 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.138
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.88
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8113 1.406
h = 0.0001 0.005
y[1] (numeric) = 1.5752728503 1.03134690829
y[1] (closed_form) = 1.57527437097 1.03135875963
absolute error = 1.195e-05
relative error = 0.0006346 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.143
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.343
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8114 1.411
h = 0.0001 0.003
y[1] (numeric) = 1.57491347585 1.0350750036
y[1] (closed_form) = 1.5749149799 1.03508639871
absolute error = 1.149e-05
relative error = 0.0006099 %
Correct digits = 5
memory used=3302.9MB, alloc=52.3MB, time=39.80
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 = 1.888
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8115 1.414
h = 0.001 0.001
y[1] (numeric) = 1.57472677074 1.03731540694
y[1] (closed_form) = 1.57472844047 1.03732673535
absolute error = 1.145e-05
relative error = 0.0006072 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.483
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8125 1.415
h = 0.001 0.003
y[1] (numeric) = 1.57538357567 1.03814649481
y[1] (closed_form) = 1.57538531523 1.03815776293
absolute error = 1.140e-05
relative error = 0.0006043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.148
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.04
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8135 1.418
h = 0.0001 0.004
y[1] (numeric) = 1.57586626733 1.04046568899
y[1] (closed_form) = 1.57586785968 1.04047707411
absolute error = 1.150e-05
relative error = 0.0006088 %
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 = 3.987
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8136 1.422
h = 0.003 0.006
y[1] (numeric) = 1.57559142415 1.04345107975
y[1] (closed_form) = 1.57559286664 1.04346240893
absolute error = 1.142e-05
relative error = 0.0006043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.153
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.285
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3348.5MB, alloc=52.3MB, time=40.34
x[1] = 0.8166 1.428
h = 0.0001 0.005
y[1] (numeric) = 1.57729869679 1.04817922247
y[1] (closed_form) = 1.57730028656 1.04819123773
absolute error = 1.212e-05
relative error = 0.00064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.158
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.354
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8167 1.433
h = 0.0001 0.003
y[1] (numeric) = 1.5769337989 1.05191115151
y[1] (closed_form) = 1.57693537024 1.05192271222
absolute error = 1.167e-05
relative error = 0.0006155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.897
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8168 1.436
h = 0.001 0.001
y[1] (numeric) = 1.57674381273 1.05415390304
y[1] (closed_form) = 1.5767455489 1.0541653966
absolute error = 1.162e-05
relative error = 0.0006129 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.162
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.49
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8178 1.437
h = 0.001 0.003
y[1] (numeric) = 1.57740024542 1.0549868546
y[1] (closed_form) = 1.57740205093 1.05499828779
absolute error = 1.157e-05
relative error = 0.0006099 %
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 = 7.073
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8188 1.44
h = 0.0001 0.004
y[1] (numeric) = 1.57788032919 1.05730940249
y[1] (closed_form) = 1.57788198848 1.05732095288
absolute error = 1.167e-05
relative error = 0.0006144 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.165
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.005
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3393.9MB, alloc=52.3MB, time=40.88
x[1] = 0.8189 1.444
h = 0.003 0.006
y[1] (numeric) = 1.5776010947 1.06029788759
y[1] (closed_form) = 1.57760260443 1.06030938285
absolute error = 1.159e-05
relative error = 0.0006099 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.167
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.31
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8219 1.45
h = 0.0001 0.005
y[1] (numeric) = 1.57930391513 1.06503385496
y[1] (closed_form) = 1.57930557441 1.0650460333
absolute error = 1.229e-05
relative error = 0.0006452 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.173
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] = 0.822 1.455
h = 0.0001 0.003
y[1] (numeric) = 1.57893352866 1.06876962687
y[1] (closed_form) = 1.57893516774 1.06878135231
absolute error = 1.184e-05
relative error = 0.000621 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.175
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.906
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8221 1.458
h = 0.001 0.001
y[1] (numeric) = 1.57874028242 1.07101473171
y[1] (closed_form) = 1.57874208548 1.07102638958
absolute error = 1.180e-05
relative error = 0.0006183 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.176
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.497
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8231 1.459
h = 0.001 0.003
y[1] (numeric) = 1.57939635175 1.07184954197
y[1] (closed_form) = 1.57939822366 1.0718611394
absolute error = 1.175e-05
relative error = 0.0006155 %
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 = 7.106
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3439.2MB, alloc=52.3MB, time=41.42
x[1] = 0.8241 1.462
h = 0.0001 0.004
y[1] (numeric) = 1.57987385036 1.07417544246
y[1] (closed_form) = 1.57987557703 1.07418715726
absolute error = 1.184e-05
relative error = 0.0006198 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.18
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.024
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8242 1.466
h = 0.003 0.006
y[1] (numeric) = 1.57959025244 1.0771670289
y[1] (closed_form) = 1.57959182985 1.07717868937
absolute error = 1.177e-05
relative error = 0.0006154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.182
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.335
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8272 1.472
h = 0.0001 0.005
y[1] (numeric) = 1.58128866787 1.08191081158
y[1] (closed_form) = 1.58129039707 1.08192315215
absolute error = 1.246e-05
relative error = 0.0006504 %
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 = 2.376
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8273 1.477
h = 0.0001 0.003
y[1] (numeric) = 1.5809128275 1.08565043507
y[1] (closed_form) = 1.58091453474 1.0856623244
absolute error = 1.201e-05
relative error = 0.0006263 %
Correct digits = 5
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 = 1.915
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8274 1.48
h = 0.001 0.001
y[1] (numeric) = 1.58071634208 1.08789789813
y[1] (closed_form) = 1.58071821246 1.08790971946
absolute error = 1.197e-05
relative error = 0.0006237 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.191
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.504
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3484.6MB, alloc=52.3MB, time=41.96
x[1] = 0.8284 1.481
h = 0.0001 0.004
y[1] (numeric) = 1.5813720568 1.08873456204
y[1] (closed_form) = 1.58137399554 1.08874632287
absolute error = 1.192e-05
relative error = 0.0006208 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.193
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.033
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8285 1.485
h = 0.003 0.006
y[1] (numeric) = 1.58108490617 1.09172868298
y[1] (closed_form) = 1.58108647786 1.09174047902
absolute error = 1.190e-05
relative error = 0.0006194 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.195
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.356
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8315 1.491
h = 0.0001 0.005
y[1] (numeric) = 1.58277947445 1.09647913336
y[1] (closed_form) = 1.58278119985 1.09649160695
absolute error = 1.259e-05
relative error = 0.000654 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.2
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.386
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8316 1.496
h = 0.0001 0.003
y[1] (numeric) = 1.58239892114 1.10022201443
y[1] (closed_form) = 1.58240062308 1.1002340382
absolute error = 1.214e-05
relative error = 0.0006301 %
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 = 1.922
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8317 1.499
h = 0.001 0.001
y[1] (numeric) = 1.582199636 1.10247147285
y[1] (closed_form) = 1.58220150035 1.10248342826
absolute error = 1.210e-05
relative error = 0.0006274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.204
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.51
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3530.1MB, alloc=52.3MB, time=42.51
x[1] = 0.8327 1.5
h = 0.001 0.003
y[1] (numeric) = 1.58285503039 1.10330972418
y[1] (closed_form) = 1.5828569627 1.10332161902
absolute error = 1.205e-05
relative error = 0.0006246 %
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 = 7.167
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8337 1.503
h = 0.0001 0.004
y[1] (numeric) = 1.58332773853 1.10564182923
y[1] (closed_form) = 1.58332952742 1.10565384177
absolute error = 1.215e-05
relative error = 0.0006289 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.208
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.059
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8338 1.507
h = 0.003 0.006
y[1] (numeric) = 1.58303605781 1.10863915287
y[1] (closed_form) = 1.58303769799 1.10865111254
absolute error = 1.207e-05
relative error = 0.0006246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.21
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.381
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8368 1.513
h = 0.0001 0.005
y[1] (numeric) = 1.58472630785 1.11339740079
y[1] (closed_form) = 1.58472810387 1.11341003502
absolute error = 1.276e-05
relative error = 0.0006589 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.215
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.397
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8369 1.518
h = 0.0001 0.003
y[1] (numeric) = 1.58434036451 1.11714414901
y[1] (closed_form) = 1.58434213539 1.1171563351
absolute error = 1.231e-05
relative error = 0.0006352 %
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 = 1.931
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3575.6MB, alloc=52.3MB, time=43.05
x[1] = 0.837 1.521
h = 0.001 0.001
y[1] (numeric) = 1.58413787865 1.11939597439
y[1] (closed_form) = 1.58413981111 1.11940809172
absolute error = 1.227e-05
relative error = 0.0006326 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.219
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.517
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.838 1.522
h = 0.001 0.003
y[1] (numeric) = 1.58479293446 1.12023606999
y[1] (closed_form) = 1.58479493439 1.12024812669
absolute error = 1.222e-05
relative error = 0.0006297 %
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 = 7.201
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.839 1.525
h = 0.0001 0.004
y[1] (numeric) = 1.58526312138 1.12257152359
y[1] (closed_form) = 1.58526497886 1.12258369815
absolute error = 1.232e-05
relative error = 0.000634 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.223
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.078
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8391 1.529
h = 0.003 0.006
y[1] (numeric) = 1.58496715601 1.12557196718
y[1] (closed_form) = 1.5849688651 1.12558408963
absolute error = 1.224e-05
relative error = 0.0006298 %
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 = 5.406
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8421 1.535
h = 0.0001 0.005
y[1] (numeric) = 1.58665313369 1.13033800228
y[1] (closed_form) = 1.58665500072 1.13035079632
absolute error = 1.293e-05
relative error = 0.0006637 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.23
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.408
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3621.0MB, alloc=52.3MB, time=43.60
x[1] = 0.8422 1.54
h = 0.0001 0.003
y[1] (numeric) = 1.58626183442 1.13408862527
y[1] (closed_form) = 1.58626367464 1.13410097283
absolute error = 1.248e-05
relative error = 0.0006402 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.233
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.94
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8423 1.543
h = 0.001 0.001
y[1] (numeric) = 1.58605616837 1.13634282184
y[1] (closed_form) = 1.58605816933 1.13635510025
absolute error = 1.244e-05
relative error = 0.0006376 %
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 = 1.524
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8433 1.544
h = 0.001 0.003
y[1] (numeric) = 1.58671089401 1.13718475655
y[1] (closed_form) = 1.58671296197 1.1371969743
absolute error = 1.239e-05
relative error = 0.0006348 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.235
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.235
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8443 1.547
h = 0.0001 0.004
y[1] (numeric) = 1.58717858167 1.13952355683
y[1] (closed_form) = 1.58718050814 1.13953589256
absolute error = 1.249e-05
relative error = 0.000639 %
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 = 4.097
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8444 1.551
h = 0.003 0.006
y[1] (numeric) = 1.5868783589 1.14252712616
y[1] (closed_form) = 1.5868801373 1.14253941055
absolute error = 1.241e-05
relative error = 0.0006348 %
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 = 5.432
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3666.4MB, alloc=52.3MB, time=44.13
x[1] = 0.8474 1.557
h = 0.0001 0.005
y[1] (numeric) = 1.58856010963 1.14730093776
y[1] (closed_form) = 1.58856204802 1.14731389076
absolute error = 1.310e-05
relative error = 0.0006684 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.245
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.419
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8475 1.562
h = 0.0001 0.003
y[1] (numeric) = 1.58816348831 1.15105544275
y[1] (closed_form) = 1.58816539826 1.15106795095
absolute error = 1.265e-05
relative error = 0.0006451 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.248
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.949
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8476 1.565
h = 0.001 0.001
y[1] (numeric) = 1.58795466245 1.15331201453
y[1] (closed_form) = 1.58795673231 1.1533244532
absolute error = 1.261e-05
relative error = 0.0006425 %
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 = 1.531
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8486 1.566
h = 0.001 0.003
y[1] (numeric) = 1.58860906622 1.15415578318
y[1] (closed_form) = 1.58861120261 1.15416816113
absolute error = 1.256e-05
relative error = 0.0006397 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.251
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
x[1] = 0.8496 1.569
h = 0.0001 0.004
y[1] (numeric) = 1.58907427641 1.15649792807
y[1] (closed_form) = 1.58907627226 1.15651042414
absolute error = 1.265e-05
relative error = 0.0006439 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.253
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.116
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3711.9MB, alloc=52.3MB, time=44.68
x[1] = 0.8497 1.573
h = 0.003 0.006
y[1] (numeric) = 1.5887698233 1.15950462865
y[1] (closed_form) = 1.58877167141 1.15951707413
absolute error = 1.258e-05
relative error = 0.0006397 %
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 = 5.457
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8527 1.579
h = 0.0001 0.005
y[1] (numeric) = 1.59044739202 1.16428620574
y[1] (closed_form) = 1.59044940212 1.16429931687
absolute error = 1.326e-05
relative error = 0.0006729 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.261
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.431
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8528 1.584
h = 0.0001 0.003
y[1] (numeric) = 1.59004548232 1.1680445996
y[1] (closed_form) = 1.59004746237 1.1680572676
absolute error = 1.282e-05
relative error = 0.0006499 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.263
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.959
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8529 1.587
h = 0.001 0.001
y[1] (numeric) = 1.58983351692 1.17030355039
y[1] (closed_form) = 1.58983565605 1.17031614849
absolute error = 1.278e-05
relative error = 0.0006473 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.265
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.538
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8539 1.588
h = 0.0001 0.004
y[1] (numeric) = 1.590487607 1.17114914775
y[1] (closed_form) = 1.5904898122 1.1711616851
absolute error = 1.273e-05
relative error = 0.0006445 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.266
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.24
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3757.4MB, alloc=52.3MB, time=45.22
x[1] = 0.854 1.592
h = 0.003 0.006
y[1] (numeric) = 1.59017970939 1.17415840642
y[1] (closed_form) = 1.59018155446 1.17417098524
absolute error = 1.271e-05
relative error = 0.0006432 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.268
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.479
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.857 1.598
h = 0.0001 0.005
y[1] (numeric) = 1.59185362169 1.17894660964
y[1] (closed_form) = 1.59185563049 1.17895985159
absolute error = 1.339e-05
relative error = 0.0006761 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.274
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.44
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8571 1.603
h = 0.0001 0.003
y[1] (numeric) = 1.59144714029 1.18270829368
y[1] (closed_form) = 1.59144911766 1.18272109392
absolute error = 1.295e-05
relative error = 0.0006532 %
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 = 1.966
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8572 1.606
h = 0.001 0.001
y[1] (numeric) = 1.5912324602 1.18496925806
y[1] (closed_form) = 1.59123459594 1.18498198808
absolute error = 1.291e-05
relative error = 0.0006506 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.278
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8582 1.607
h = 0.001 0.003
y[1] (numeric) = 1.59188626504 1.18581642171
y[1] (closed_form) = 1.59188846645 1.18582909094
absolute error = 1.286e-05
relative error = 0.0006478 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.279
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.332
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3802.8MB, alloc=52.3MB, time=45.76
x[1] = 0.8592 1.61
h = 0.0001 0.004
y[1] (numeric) = 1.5923468827 1.18816475514
y[1] (closed_form) = 1.59234894532 1.18817754272
absolute error = 1.295e-05
relative error = 0.0006519 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.281
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.152
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8593 1.614
h = 0.003 0.006
y[1] (numeric) = 1.59203459196 1.19117724628
y[1] (closed_form) = 1.59203650744 1.19118998465
absolute error = 1.288e-05
relative error = 0.0006479 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.283
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.505
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8623 1.62
h = 0.0001 0.005
y[1] (numeric) = 1.59370440478 1.19597319422
y[1] (closed_form) = 1.59370648591 1.19598659275
absolute error = 1.356e-05
relative error = 0.0006805 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.289
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.452
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8624 1.625
h = 0.0001 0.003
y[1] (numeric) = 1.59329269699 1.19973877936
y[1] (closed_form) = 1.59329474515 1.19975173786
absolute error = 1.312e-05
relative error = 0.0006578 %
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 = 1.976
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8625 1.628
h = 0.001 0.001
y[1] (numeric) = 1.59307491466 1.2020021295
y[1] (closed_form) = 1.59307712037 1.20201501744
absolute error = 1.308e-05
relative error = 0.0006552 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.293
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3848.4MB, alloc=52.3MB, time=46.30
x[1] = 0.8635 1.629
h = 0.001 0.003
y[1] (numeric) = 1.59372842081 1.20285111217
y[1] (closed_form) = 1.59373069172 1.20286393929
absolute error = 1.303e-05
relative error = 0.0006524 %
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 = 7.367
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8645 1.632
h = 0.0001 0.004
y[1] (numeric) = 1.59418662221 1.2052027836
y[1] (closed_form) = 1.59418875527 1.20521572916
absolute error = 1.312e-05
relative error = 0.0006565 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.297
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.171
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8646 1.636
h = 0.003 0.006
y[1] (numeric) = 1.59387017757 1.2082184205
y[1] (closed_form) = 1.59387216382 1.20823131757
absolute error = 1.305e-05
relative error = 0.0006524 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.299
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.531
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8676 1.642
h = 0.0001 0.005
y[1] (numeric) = 1.59553593452 1.21302210127
y[1] (closed_form) = 1.59553808832 1.21303565556
absolute error = 1.372e-05
relative error = 0.0006847 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.304
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.463
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3893.7MB, alloc=52.3MB, time=46.84
x[1] = 0.8677 1.647
h = 0.0001 0.003
y[1] (numeric) = 1.5951190334 1.21679159338
y[1] (closed_form) = 1.59512115269 1.21680470931
absolute error = 1.329e-05
relative error = 0.0006622 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.307
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.985
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8678 1.65
h = 0.001 0.001
y[1] (numeric) = 1.59489816871 1.2190573325
y[1] (closed_form) = 1.59490044473 1.21907037752
absolute error = 1.324e-05
relative error = 0.0006596 %
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 = 1.559
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8688 1.651
h = 0.001 0.003
y[1] (numeric) = 1.59555138403 1.21990812889
y[1] (closed_form) = 1.59555372479 1.21992111307
absolute error = 1.319e-05
relative error = 0.0006569 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.401
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8698 1.654
h = 0.0001 0.004
y[1] (numeric) = 1.59600719018 1.22226313559
y[1] (closed_form) = 1.59600939402 1.22227623832
absolute error = 1.329e-05
relative error = 0.0006609 %
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 = 4.191
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8699 1.658
h = 0.003 0.006
y[1] (numeric) = 1.59568661804 1.22528192267
y[1] (closed_form) = 1.59568867541 1.22529497763
absolute error = 1.322e-05
relative error = 0.0006569 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.314
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.557
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3939.3MB, alloc=52.3MB, time=47.39
x[1] = 0.8729 1.664
h = 0.0001 0.005
y[1] (numeric) = 1.59734836227 1.23009332411
y[1] (closed_form) = 1.59735058904 1.23010703334
absolute error = 1.389e-05
relative error = 0.0006889 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.32
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.475
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.873 1.669
h = 0.0001 0.003
y[1] (numeric) = 1.59692630065 1.23386672873
y[1] (closed_form) = 1.59692849141 1.23388000128
absolute error = 1.345e-05
relative error = 0.0006666 %
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 = 1.994
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8731 1.672
h = 0.001 0.001
y[1] (numeric) = 1.59670237334 1.23613485983
y[1] (closed_form) = 1.59670472001 1.23614806114
absolute error = 1.341e-05
relative error = 0.000664 %
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 = 1.566
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8741 1.673
h = 0.001 0.003
y[1] (numeric) = 1.59735530558 1.23698746462
y[1] (closed_form) = 1.59735771654 1.23700060506
absolute error = 1.336e-05
relative error = 0.0006613 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.326
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.436
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8751 1.676
h = 0.0001 0.004
y[1] (numeric) = 1.59780873729 1.2393458037
y[1] (closed_form) = 1.59781101226 1.23935906278
absolute error = 1.345e-05
relative error = 0.0006653 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.328
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.211
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3984.8MB, alloc=52.3MB, time=47.93
x[1] = 0.8752 1.68
h = 0.003 0.006
y[1] (numeric) = 1.59748406387 1.24236774513
y[1] (closed_form) = 1.59748619271 1.24238095714
absolute error = 1.338e-05
relative error = 0.0006613 %
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 = 5.583
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8782 1.686
h = 0.0001 0.005
y[1] (numeric) = 1.59914183808 1.24718685482
y[1] (closed_form) = 1.59914413812 1.24720071818
absolute error = 1.405e-05
relative error = 0.0006929 %
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] = 0.8783 1.691
h = 0.0001 0.003
y[1] (numeric) = 1.59871464856 1.25096417715
y[1] (closed_form) = 1.59871691111 1.25097760549
absolute error = 1.362e-05
relative error = 0.0006708 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.338
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
x[1] = 0.8784 1.694
h = 0.001 0.001
y[1] (numeric) = 1.59848767824 1.25323470304
y[1] (closed_form) = 1.5984900959 1.25324805983
absolute error = 1.357e-05
relative error = 0.0006683 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.574
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8794 1.695
h = 0.0001 0.004
y[1] (numeric) = 1.59914033504 1.25408911089
y[1] (closed_form) = 1.59914281654 1.25410240679
absolute error = 1.353e-05
relative error = 0.0006655 %
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 = 9.453
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4030.2MB, alloc=52.3MB, time=48.47
x[1] = 0.8795 1.699
h = 0.003 0.006
y[1] (numeric) = 1.59881232198 1.25711362851
y[1] (closed_form) = 1.59881445026 1.25712697162
absolute error = 1.351e-05
relative error = 0.0006643 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.343
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.605
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8825 1.705
h = 0.0001 0.005
y[1] (numeric) = 1.60046662115 1.26193931645
y[1] (closed_form) = 1.60046892218 1.2619533084
absolute error = 1.418e-05
relative error = 0.0006957 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.349
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.497
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8826 1.71
h = 0.0001 0.003
y[1] (numeric) = 1.6000349969 1.26571995437
y[1] (closed_form) = 1.60003725918 1.26573351273
absolute error = 1.375e-05
relative error = 0.0006738 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.352
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.012
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8827 1.713
h = 0.001 0.001
y[1] (numeric) = 1.59980539428 1.2679925078
y[1] (closed_form) = 1.59980781097 1.26800599433
absolute error = 1.370e-05
relative error = 0.0006712 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.353
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.58
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8837 1.714
h = 0.001 0.003
y[1] (numeric) = 1.60045779863 1.2688484602
y[1] (closed_form) = 1.60046027879 1.26886188582
absolute error = 1.365e-05
relative error = 0.0006685 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.355
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.501
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4075.6MB, alloc=52.3MB, time=49.01
x[1] = 0.8847 1.717
h = 0.0001 0.004
y[1] (numeric) = 1.6009068272 1.27121296416
y[1] (closed_form) = 1.60090917305 1.27122650857
absolute error = 1.375e-05
relative error = 0.0006724 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.357
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.248
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8848 1.721
h = 0.003 0.006
y[1] (numeric) = 1.60057455375 1.27424073716
y[1] (closed_form) = 1.6005767541 1.27425423581
absolute error = 1.368e-05
relative error = 0.0006685 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.359
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.632
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8878 1.727
h = 0.0001 0.005
y[1] (numeric) = 1.60222496126 1.27907411002
y[1] (closed_form) = 1.60222733611 1.27908825459
absolute error = 1.434e-05
relative error = 0.0006996 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.365
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.508
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8879 1.732
h = 0.0001 0.003
y[1] (numeric) = 1.60178826914 1.28285867488
y[1] (closed_form) = 1.60179060381 1.28287238753
absolute error = 1.391e-05
relative error = 0.0006778 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.367
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.021
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.888 1.735
h = 0.001 0.001
y[1] (numeric) = 1.6015556596 1.28513362806
y[1] (closed_form) = 1.60155814788 1.28514726858
absolute error = 1.387e-05
relative error = 0.0006752 %
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 = 1.587
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4121.1MB, alloc=52.3MB, time=49.56
x[1] = 0.889 1.736
h = 0.001 0.003
y[1] (numeric) = 1.60220780251 1.28599137361
y[1] (closed_form) = 1.60221035381 1.2860049532
absolute error = 1.382e-05
relative error = 0.0006725 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.537
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.89 1.739
h = 0.0001 0.004
y[1] (numeric) = 1.60265451515 1.28835920111
y[1] (closed_form) = 1.60265693304 1.28837289955
absolute error = 1.391e-05
relative error = 0.0006765 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.373
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.268
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8901 1.743
h = 0.003 0.006
y[1] (numeric) = 1.60231821439 1.29139013926
y[1] (closed_form) = 1.60232048714 1.29140379262
absolute error = 1.384e-05
relative error = 0.0006726 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.658
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8931 1.749
h = 0.0001 0.005
y[1] (numeric) = 1.60396477165 1.29623118388
y[1] (closed_form) = 1.60396722058 1.29624548026
absolute error = 1.450e-05
relative error = 0.0007033 %
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 = 2.52
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8932 1.754
h = 0.0001 0.003
y[1] (numeric) = 1.60352304361 1.30001967997
y[1] (closed_form) = 1.60352545097 1.30003354611
absolute error = 1.407e-05
relative error = 0.0006818 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.383
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.031
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4166.5MB, alloc=52.3MB, time=50.10
x[1] = 0.8933 1.757
h = 0.001 0.001
y[1] (numeric) = 1.60328744636 1.3022970352
y[1] (closed_form) = 1.60329000652 1.30231082891
absolute error = 1.403e-05
relative error = 0.0006792 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.385
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.595
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8943 1.758
h = 0.001 0.003
y[1] (numeric) = 1.60393933517 1.30315656848
y[1] (closed_form) = 1.60394195791 1.30317030126
absolute error = 1.398e-05
relative error = 0.0006765 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.386
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.572
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8953 1.761
h = 0.0001 0.004
y[1] (numeric) = 1.60438375194 1.30552771606
y[1] (closed_form) = 1.60438624217 1.30554156774
absolute error = 1.407e-05
relative error = 0.0006804 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.389
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.288
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8954 1.765
h = 0.003 0.006
y[1] (numeric) = 1.60404344939 1.30856182256
y[1] (closed_form) = 1.60404579483 1.30857562983
absolute error = 1.401e-05
relative error = 0.0006765 %
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 = 5.685
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8984 1.771
h = 0.0001 0.005
y[1] (numeric) = 1.60568619733 1.31341052555
y[1] (closed_form) = 1.60568872061 1.31342497294
absolute error = 1.467e-05
relative error = 0.000707 %
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 = 2.532
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4212.0MB, alloc=52.3MB, time=50.64
x[1] = 0.8985 1.776
h = 0.0001 0.003
y[1] (numeric) = 1.60523946512 1.31720295688
y[1] (closed_form) = 1.60524194545 1.31721697569
absolute error = 1.424e-05
relative error = 0.0006856 %
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 = 2.04
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8986 1.779
h = 0.001 0.001
y[1] (numeric) = 1.60500089923 1.31948271625
y[1] (closed_form) = 1.60500353157 1.31949666236
absolute error = 1.419e-05
relative error = 0.0006831 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.401
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.602
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8996 1.78
h = 0.001 0.003
y[1] (numeric) = 1.60565254117 1.32034403185
y[1] (closed_form) = 1.60565523566 1.32035791702
absolute error = 1.414e-05
relative error = 0.0006804 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.608
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9006 1.783
h = 0.0001 0.004
y[1] (numeric) = 1.60609468194 1.32271849591
y[1] (closed_form) = 1.6060972448 1.32273250003
absolute error = 1.424e-05
relative error = 0.0006842 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.405
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.308
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9007 1.787
h = 0.003 0.006
y[1] (numeric) = 1.60575040294 1.32575577371
y[1] (closed_form) = 1.60575282137 1.32576973409
absolute error = 1.417e-05
relative error = 0.0006804 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.407
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.712
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4257.6MB, alloc=52.3MB, time=51.18
x[1] = 0.9037 1.793
h = 0.0001 0.005
y[1] (numeric) = 1.60738938205 1.33061212145
y[1] (closed_form) = 1.60739197993 1.33062671907
absolute error = 1.483e-05
relative error = 0.0007106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.413
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.544
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9038 1.798
h = 0.0001 0.003
y[1] (numeric) = 1.60693767718 1.33440849173
y[1] (closed_form) = 1.60694023076 1.33442266243
absolute error = 1.440e-05
relative error = 0.0006894 %
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 = 2.05
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9039 1.801
h = 0.001 0.001
y[1] (numeric) = 1.60669616158 1.33669065717
y[1] (closed_form) = 1.60669886639 1.3367047549
absolute error = 1.435e-05
relative error = 0.0006868 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.417
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.61
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9049 1.802
h = 0.0001 0.004
y[1] (numeric) = 1.60734756377 1.33755374966
y[1] (closed_form) = 1.60735033029 1.33756778645
absolute error = 1.431e-05
relative error = 0.0006842 %
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 = 9.672
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.905 1.806
h = 0.003 0.006
y[1] (numeric) = 1.60700004654 1.34059361685
y[1] (closed_form) = 1.60700246669 1.34060770606
absolute error = 1.430e-05
relative error = 0.0006831 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.735
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4303.0MB, alloc=52.3MB, time=51.73
x[1] = 0.908 1.812
h = 0.0001 0.005
y[1] (numeric) = 1.6086357228 1.34545648961
y[1] (closed_form) = 1.60863832382 1.3454712136
absolute error = 1.495e-05
relative error = 0.000713 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.426
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.554
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9081 1.817
h = 0.0001 0.003
y[1] (numeric) = 1.60817971571 1.34925619443
y[1] (closed_form) = 1.60818227127 1.34927049292
absolute error = 1.453e-05
relative error = 0.0006919 %
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 = 2.058
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9082 1.82
h = 0.001 0.001
y[1] (numeric) = 1.60793564747 1.35154039753
y[1] (closed_form) = 1.60793835358 1.3515546228
absolute error = 1.448e-05
relative error = 0.0006894 %
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 = 1.616
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9092 1.821
h = 0.001 0.003
y[1] (numeric) = 1.60858682785 1.3524050124
y[1] (closed_form) = 1.6085895953 1.35241917673
absolute error = 1.443e-05
relative error = 0.0006867 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.674
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9102 1.824
h = 0.0001 0.004
y[1] (numeric) = 1.60902474634 1.35478561107
y[1] (closed_form) = 1.60902738379 1.35479989443
absolute error = 1.452e-05
relative error = 0.0006905 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.435
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.346
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4348.6MB, alloc=52.3MB, time=52.27
x[1] = 0.9103 1.828
h = 0.003 0.006
y[1] (numeric) = 1.60867309705 1.35782875035
y[1] (closed_form) = 1.60867559072 1.35784299119
absolute error = 1.446e-05
relative error = 0.0006868 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.437
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.762
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9133 1.834
h = 0.0001 0.005
y[1] (numeric) = 1.61030507882 1.3626992424
y[1] (closed_form) = 1.6103077549 1.36271411515
absolute error = 1.511e-05
relative error = 0.0007164 %
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 = 2.566
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9134 1.839
h = 0.0001 0.003
y[1] (numeric) = 1.60984415705 1.3665028927
y[1] (closed_form) = 1.60984678637 1.3665173416
absolute error = 1.469e-05
relative error = 0.0006955 %
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 = 2.068
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9135 1.842
h = 0.001 0.001
y[1] (numeric) = 1.60959717394 1.36878950523
y[1] (closed_form) = 1.60959995303 1.36880388066
absolute error = 1.464e-05
relative error = 0.000693 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.447
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.624
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9145 1.843
h = 0.001 0.003
y[1] (numeric) = 1.61024812763 1.36965588693
y[1] (closed_form) = 1.61025096763 1.36967020142
absolute error = 1.459e-05
relative error = 0.0006903 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.448
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.711
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4394.0MB, alloc=52.3MB, time=52.81
x[1] = 0.9155 1.846
h = 0.0001 0.004
y[1] (numeric) = 1.61068382594 1.3720397913
y[1] (closed_form) = 1.61068653682 1.37205422484
absolute error = 1.469e-05
relative error = 0.0006941 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.451
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.366
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9156 1.85
h = 0.003 0.006
y[1] (numeric) = 1.61032827164 1.37508610938
y[1] (closed_form) = 1.6103308391 1.37510050105
absolute error = 1.462e-05
relative error = 0.0006904 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.453
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.789
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9186 1.856
h = 0.0001 0.005
y[1] (numeric) = 1.61195659814 1.37996420649
y[1] (closed_form) = 1.61195934952 1.37997922722
absolute error = 1.527e-05
relative error = 0.0007196 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.459
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.579
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9187 1.861
h = 0.0001 0.003
y[1] (numeric) = 1.61149079254 1.38377180516
y[1] (closed_form) = 1.61149349589 1.38378640369
absolute error = 1.485e-05
relative error = 0.000699 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.462
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.078
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9188 1.864
h = 0.001 0.001
y[1] (numeric) = 1.6112409131 1.38606082859
y[1] (closed_form) = 1.61124376544 1.38607535339
absolute error = 1.480e-05
relative error = 0.0006964 %
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
memory used=4439.4MB, alloc=52.3MB, time=53.35
x[1] = 0.9198 1.865
h = 0.001 0.003
y[1] (numeric) = 1.61189164693 1.38692897165
y[1] (closed_form) = 1.61189455975 1.38694343552
absolute error = 1.475e-05
relative error = 0.0006938 %
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] = 0.9208 1.868
h = 0.0001 0.004
y[1] (numeric) = 1.61232514419 1.38931617763
y[1] (closed_form) = 1.61232792875 1.38933076058
absolute error = 1.485e-05
relative error = 0.0006976 %
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] = 0.9209 1.872
h = 0.003 0.006
y[1] (numeric) = 1.6119657095 1.3923656766
y[1] (closed_form) = 1.611968351 1.39238021831
absolute error = 1.478e-05
relative error = 0.0006939 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.469
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.816
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9239 1.878
h = 0.0001 0.005
y[1] (numeric) = 1.61359041953 1.39725136436
y[1] (closed_form) = 1.61359324644 1.39726653228
absolute error = 1.543e-05
relative error = 0.0007228 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.475
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.591
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4484.8MB, alloc=52.3MB, time=53.89
x[1] = 0.924 1.883
h = 0.0001 0.003
y[1] (numeric) = 1.61311976073 1.40106291404
y[1] (closed_form) = 1.61312253835 1.40107766142
absolute error = 1.501e-05
relative error = 0.0007024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.478
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.087
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9241 1.886
h = 0.001 0.001
y[1] (numeric) = 1.61286700335 1.40335434965
y[1] (closed_form) = 1.61286992918 1.40336902306
absolute error = 1.496e-05
relative error = 0.0006998 %
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 = 1.639
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9251 1.887
h = 0.001 0.003
y[1] (numeric) = 1.61351752405 1.40422424859
y[1] (closed_form) = 1.61352050995 1.40423886109
absolute error = 1.491e-05
relative error = 0.0006973 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.784
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9261 1.89
h = 0.0001 0.004
y[1] (numeric) = 1.61394883921 1.40661475199
y[1] (closed_form) = 1.61395169769 1.40662948356
absolute error = 1.501e-05
relative error = 0.0007009 %
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 = 4.408
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9262 1.894
h = 0.003 0.006
y[1] (numeric) = 1.61358554856 1.40966743373
y[1] (closed_form) = 1.61358826436 1.40968212469
absolute error = 1.494e-05
relative error = 0.0006973 %
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 = 5.844
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4530.3MB, alloc=52.3MB, time=54.43
x[1] = 0.9292 1.9
h = 0.0001 0.005
y[1] (numeric) = 1.61520668047 1.41456069751
y[1] (closed_form) = 1.61520958312 1.41457601186
absolute error = 1.559e-05
relative error = 0.000726 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.491
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.603
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9293 1.905
h = 0.0001 0.003
y[1] (numeric) = 1.61473119887 1.41837620058
y[1] (closed_form) = 1.61473405099 1.41839109603
absolute error = 1.517e-05
relative error = 0.0007056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.494
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.097
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9294 1.908
h = 0.001 0.001
y[1] (numeric) = 1.61447558179 1.42067004952
y[1] (closed_form) = 1.61447858136 1.42068487077
absolute error = 1.512e-05
relative error = 0.0007032 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.496
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] = 0.9304 1.909
h = 0.0001 0.004
y[1] (numeric) = 1.61512589601 1.42154169886
y[1] (closed_form) = 1.61512895524 1.42155645921
absolute error = 1.507e-05
relative error = 0.0007006 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.497
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.895
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9305 1.913
h = 0.003 0.006
y[1] (numeric) = 1.61475946499 1.42459697877
y[1] (closed_form) = 1.61476218463 1.4246117963
absolute error = 1.507e-05
relative error = 0.0006996 %
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 = 5.867
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4575.9MB, alloc=52.3MB, time=54.98
x[1] = 0.9335 1.919
h = 0.0001 0.005
y[1] (numeric) = 1.61637745736 1.4294967099
y[1] (closed_form) = 1.6163803651 1.42951214841
absolute error = 1.571e-05
relative error = 0.000728 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.505
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.613
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9336 1.924
h = 0.0001 0.003
y[1] (numeric) = 1.61589780148 1.43331556066
y[1] (closed_form) = 1.61590065763 1.43333058167
absolute error = 1.529e-05
relative error = 0.0007079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.508
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.106
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9337 1.927
h = 0.001 0.001
y[1] (numeric) = 1.61563970862 1.43561145394
y[1] (closed_form) = 1.61564271156 1.43562640055
absolute error = 1.525e-05
relative error = 0.0007054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.654
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9347 1.928
h = 0.001 0.003
y[1] (numeric) = 1.61628982958 1.43648460322
y[1] (closed_form) = 1.61629289183 1.43649948893
absolute error = 1.520e-05
relative error = 0.0007028 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.511
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.852
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9357 1.931
h = 0.0001 0.004
y[1] (numeric) = 1.61671709494 1.43888120526
y[1] (closed_form) = 1.61672003134 1.43889621007
absolute error = 1.529e-05
relative error = 0.0007064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.446
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4621.3MB, alloc=52.3MB, time=55.52
x[1] = 0.9358 1.935
h = 0.003 0.006
y[1] (numeric) = 1.61634665571 1.44193976844
y[1] (closed_form) = 1.61634945011 1.44195473379
absolute error = 1.522e-05
relative error = 0.0007028 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.516
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.895
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9388 1.941
h = 0.0001 0.005
y[1] (numeric) = 1.61796114039 1.4468470484
y[1] (closed_form) = 1.61796412426 1.44686263191
absolute error = 1.587e-05
relative error = 0.000731 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.626
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9389 1.946
h = 0.0001 0.003
y[1] (numeric) = 1.61747671762 1.45066985665
y[1] (closed_form) = 1.61747964871 1.4506850243
absolute error = 1.545e-05
relative error = 0.000711 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.525
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] = 0.939 1.949
h = 0.001 0.001
y[1] (numeric) = 1.61721579864 1.45296816519
y[1] (closed_form) = 1.61721887576 1.45298325822
absolute error = 1.540e-05
relative error = 0.0007085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.527
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
x[1] = 0.94 1.95
h = 0.001 0.003
y[1] (numeric) = 1.61786572528 1.45384305472
y[1] (closed_form) = 1.61786886129 1.45385808688
absolute error = 1.536e-05
relative error = 0.000706 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.528
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.889
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4666.8MB, alloc=52.3MB, time=56.06
x[1] = 0.941 1.953
h = 0.0001 0.004
y[1] (numeric) = 1.61829086172 1.45624294175
y[1] (closed_form) = 1.61829387273 1.45625809299
absolute error = 1.545e-05
relative error = 0.0007096 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.53
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.467
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9411 1.957
h = 0.003 0.006
y[1] (numeric) = 1.61791663541 1.45930469223
y[1] (closed_form) = 1.61791950478 1.45931980462
absolute error = 1.538e-05
relative error = 0.000706 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.533
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.923
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9441 1.963
h = 0.0001 0.005
y[1] (numeric) = 1.61952764952 1.46421950591
y[1] (closed_form) = 1.61953070972 1.46423523367
absolute error = 1.602e-05
relative error = 0.0007339 %
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 = 2.638
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9442 1.968
h = 0.0001 0.003
y[1] (numeric) = 1.61903848959 1.4680462733
y[1] (closed_form) = 1.61904149585 1.46806158684
absolute error = 1.561e-05
relative error = 0.0007141 %
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 = 2.126
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9443 1.971
h = 0.001 0.001
y[1] (numeric) = 1.61877476234 1.47034699782
y[1] (closed_form) = 1.61877791386 1.47036223652
absolute error = 1.556e-05
relative error = 0.0007116 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.543
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.669
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4712.3MB, alloc=52.3MB, time=56.60
x[1] = 0.9453 1.972
h = 0.001 0.003
y[1] (numeric) = 1.61942450102 1.47122362211
y[1] (closed_form) = 1.61942771103 1.47123879996
absolute error = 1.551e-05
relative error = 0.000709 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.545
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.926
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9463 1.975
h = 0.0001 0.004
y[1] (numeric) = 1.61984752676 1.47362678949
y[1] (closed_form) = 1.61985061259 1.47364208641
absolute error = 1.561e-05
relative error = 0.0007126 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.547
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.488
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9464 1.979
h = 0.003 0.006
y[1] (numeric) = 1.61946953708 1.47669172839
y[1] (closed_form) = 1.61947248165 1.47670698705
absolute error = 1.554e-05
relative error = 0.0007091 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.549
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.951
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9494 1.985
h = 0.0001 0.005
y[1] (numeric) = 1.62107711735 1.48161406053
y[1] (closed_form) = 1.62108025407 1.48162993177
absolute error = 1.618e-05
relative error = 0.0007367 %
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 = 2.65
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9495 1.99
h = 0.0001 0.003
y[1] (numeric) = 1.62058324977 1.48544478848
y[1] (closed_form) = 1.62058633139 1.48546024713
absolute error = 1.576e-05
relative error = 0.000717 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.558
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.136
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4757.8MB, alloc=52.3MB, time=57.14
x[1] = 0.9496 1.993
h = 0.001 0.001
y[1] (numeric) = 1.62031673195 1.48774792956
y[1] (closed_form) = 1.62031995809 1.48776331317
absolute error = 1.572e-05
relative error = 0.0007145 %
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 = 1.677
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9506 1.994
h = 0.001 0.003
y[1] (numeric) = 1.62096628894 1.4886262831
y[1] (closed_form) = 1.62096957317 1.48864160589
absolute error = 1.567e-05
relative error = 0.000712 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.561
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.963
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9516 1.997
h = 0.0001 0.004
y[1] (numeric) = 1.62138722202 1.4910327261
y[1] (closed_form) = 1.62139038288 1.49104816795
absolute error = 1.576e-05
relative error = 0.0007156 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.564
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.509
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9517 2.001
h = 0.003 0.006
y[1] (numeric) = 1.6210054925 1.49410085435
y[1] (closed_form) = 1.62100851248 1.49411625852
absolute error = 1.570e-05
relative error = 0.000712 %
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 = 5.979
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9547 2.007
h = 0.0001 0.005
y[1] (numeric) = 1.62260967524 1.49903068952
y[1] (closed_form) = 1.62261288866 1.4990467035
absolute error = 1.633e-05
relative error = 0.0007394 %
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 = 2.663
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4803.3MB, alloc=52.3MB, time=57.70
x[1] = 0.9548 2.012
h = 0.0001 0.003
y[1] (numeric) = 1.62211112927 1.50286537922
y[1] (closed_form) = 1.62211428647 1.50288098224
absolute error = 1.592e-05
relative error = 0.0007199 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.575
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.146
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9549 2.015
h = 0.001 0.001
y[1] (numeric) = 1.62184183845 1.5051709373
y[1] (closed_form) = 1.62184513942 1.50518646508
absolute error = 1.587e-05
relative error = 0.0007174 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.577
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.685
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9559 2.016
h = 0.0001 0.004
y[1] (numeric) = 1.62249121992 1.50605101459
y[1] (closed_form) = 1.62249457858 1.50606648158
absolute error = 1.583e-05
relative error = 0.000715 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.578
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.12
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.956 2.02
h = 0.003 0.006
y[1] (numeric) = 1.62210644431 1.50912174585
y[1] (closed_form) = 1.62210947007 1.50913727435
absolute error = 1.582e-05
relative error = 0.0007141 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.002
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.959 2.026
h = 0.0001 0.005
y[1] (numeric) = 1.6237076422 1.51405798705
y[1] (closed_form) = 1.62371086251 1.514074123
absolute error = 1.645e-05
relative error = 0.0007411 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.586
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
memory used=4848.8MB, alloc=52.3MB, time=58.24
x[1] = 0.9591 2.031
h = 0.0001 0.003
y[1] (numeric) = 1.62320504528 1.51789603241
y[1] (closed_form) = 1.6232082084 1.51791175879
absolute error = 1.604e-05
relative error = 0.0007218 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.589
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] = 0.9592 2.034
h = 0.001 0.001
y[1] (numeric) = 1.62293335272 1.52020363846
y[1] (closed_form) = 1.62293665897 1.52021928942
absolute error = 1.600e-05
relative error = 0.0007193 %
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] = 0.9602 2.035
h = 0.001 0.003
y[1] (numeric) = 1.62358256754 1.5210851931
y[1] (closed_form) = 1.62358593115 1.52110078329
absolute error = 1.595e-05
relative error = 0.0007169 %
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] = 0.9612 2.038
h = 0.0001 0.004
y[1] (numeric) = 1.62399961515 1.52349769394
y[1] (closed_form) = 1.62400285689 1.52351340315
absolute error = 1.604e-05
relative error = 0.0007203 %
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
x[1] = 0.9613 2.042
h = 0.003 0.006
y[1] (numeric) = 1.62361095066 1.52657171473
y[1] (closed_form) = 1.62361405221 1.52658738733
absolute error = 1.598e-05
relative error = 0.0007169 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.597
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
memory used=4894.0MB, alloc=52.3MB, time=58.77
x[1] = 0.9643 2.048
h = 0.0001 0.005
y[1] (numeric) = 1.62520881767 1.53151543033
y[1] (closed_form) = 1.625212115 1.53153170764
absolute error = 1.661e-05
relative error = 0.0007437 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.603
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.686
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9644 2.053
h = 0.0001 0.003
y[1] (numeric) = 1.6247015962 1.5353574394
y[1] (closed_form) = 1.62470483526 1.53537330875
absolute error = 1.620e-05
relative error = 0.0007245 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.606
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.164
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9645 2.056
h = 0.001 0.001
y[1] (numeric) = 1.62442716295 1.5376674631
y[1] (closed_form) = 1.6244305444 1.53768325686
absolute error = 1.615e-05
relative error = 0.0007221 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.608
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.7
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9655 2.057
h = 0.001 0.003
y[1] (numeric) = 1.62507621357 1.53855073132
y[1] (closed_form) = 1.62507965198 1.53856646434
absolute error = 1.610e-05
relative error = 0.0007196 %
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 = 8.07
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9665 2.06
h = 0.0001 0.004
y[1] (numeric) = 1.62549121915 1.54096649396
y[1] (closed_form) = 1.6254945365 1.54098234596
absolute error = 1.620e-05
relative error = 0.0007231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.612
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.57
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4939.6MB, alloc=52.3MB, time=59.32
x[1] = 0.9666 2.064
h = 0.003 0.006
y[1] (numeric) = 1.62509888112 1.544043706
y[1] (closed_form) = 1.62510205866 1.54405952196
absolute error = 1.613e-05
relative error = 0.0007196 %
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 = 6.059
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9696 2.07
h = 0.0001 0.005
y[1] (numeric) = 1.62669345237 1.54899488019
y[1] (closed_form) = 1.62669682689 1.54901129813
absolute error = 1.676e-05
relative error = 0.0007462 %
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] = 0.9697 2.075
h = 0.0001 0.003
y[1] (numeric) = 1.62618163498 1.55284085351
y[1] (closed_form) = 1.62618495015 1.55285686509
absolute error = 1.635e-05
relative error = 0.0007272 %
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 = 2.174
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9698 2.078
h = 0.001 0.001
y[1] (numeric) = 1.62590447819 1.55515329494
y[1] (closed_form) = 1.62590793503 1.55516923076
absolute error = 1.631e-05
relative error = 0.0007248 %
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] = 0.9708 2.079
h = 0.001 0.003
y[1] (numeric) = 1.62655337054 1.55603827123
y[1] (closed_form) = 1.62655688394 1.55605414635
absolute error = 1.626e-05
relative error = 0.0007223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.626
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.108
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4985.0MB, alloc=52.3MB, time=59.86
x[1] = 0.9718 2.082
h = 0.0001 0.004
y[1] (numeric) = 1.62696635141 1.55845729059
y[1] (closed_form) = 1.62696974456 1.55847328464
absolute error = 1.635e-05
relative error = 0.0007257 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.629
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.591
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9719 2.086
h = 0.003 0.006
y[1] (numeric) = 1.62657036267 1.56153769411
y[1] (closed_form) = 1.62657361637 1.56155365269
absolute error = 1.629e-05
relative error = 0.0007223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.631
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.087
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9749 2.092
h = 0.0001 0.005
y[1] (numeric) = 1.6281616729 1.56649631096
y[1] (closed_form) = 1.62816512475 1.56651286879
absolute error = 1.691e-05
relative error = 0.0007486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.637
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.711
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.975 2.097
h = 0.0001 0.003
y[1] (numeric) = 1.62764528795 1.57034624886
y[1] (closed_form) = 1.62764867942 1.57036240195
absolute error = 1.651e-05
relative error = 0.0007298 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.64
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] = 0.9751 2.1
h = 0.001 0.001
y[1] (numeric) = 1.62736542466 1.57266110796
y[1] (closed_form) = 1.62736895706 1.57267718511
absolute error = 1.646e-05
relative error = 0.0007273 %
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 = 1.716
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5030.5MB, alloc=52.3MB, time=60.40
x[1] = 0.9761 2.101
h = 0.001 0.003
y[1] (numeric) = 1.62801416456 1.57354778683
y[1] (closed_form) = 1.62801775314 1.57356380331
absolute error = 1.641e-05
relative error = 0.0007249 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.643
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.146
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9771 2.104
h = 0.0001 0.004
y[1] (numeric) = 1.62842513789 1.57597005774
y[1] (closed_form) = 1.628428607 1.57598619311
absolute error = 1.650e-05
relative error = 0.0007283 %
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 = 4.613
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9772 2.108
h = 0.003 0.006
y[1] (numeric) = 1.62802552106 1.57905365282
y[1] (closed_form) = 1.62802885111 1.57906975326
absolute error = 1.644e-05
relative error = 0.0007249 %
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 = 6.116
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9802 2.114
h = 0.0001 0.005
y[1] (numeric) = 1.62961360461 1.58401969626
y[1] (closed_form) = 1.62961713395 1.58403639326
absolute error = 1.707e-05
relative error = 0.0007509 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.654
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.724
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5076.0MB, alloc=52.3MB, time=60.95
x[1] = 0.9803 2.119
h = 0.0001 0.003
y[1] (numeric) = 1.62909268026 1.58787359888
y[1] (closed_form) = 1.62909614819 1.58788989274
absolute error = 1.666e-05
relative error = 0.0007323 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.657
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.195
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9804 2.122
h = 0.001 0.001
y[1] (numeric) = 1.62881012735 1.59019087547
y[1] (closed_form) = 1.62881373549 1.59020709323
absolute error = 1.661e-05
relative error = 0.0007299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.659
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.724
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9814 2.123
h = 0.0001 0.004
y[1] (numeric) = 1.62945872054 1.59107925141
y[1] (closed_form) = 1.62946238448 1.59109540854
absolute error = 1.657e-05
relative error = 0.0007275 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.36
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9815 2.127
h = 0.003 0.006
y[1] (numeric) = 1.62905614832 1.59416545088
y[1] (closed_form) = 1.62905948593 1.59418167343
absolute error = 1.656e-05
relative error = 0.0007266 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.662
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.14
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9845 2.133
h = 0.0001 0.005
y[1] (numeric) = 1.63064139344 1.59913783606
y[1] (closed_form) = 1.63064493133 1.59915465286
absolute error = 1.718e-05
relative error = 0.0007524 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.668
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.735
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5121.6MB, alloc=52.3MB, time=61.50
x[1] = 0.9846 2.138
h = 0.0001 0.003
y[1] (numeric) = 1.63011653687 1.60299509771
y[1] (closed_form) = 1.63012001247 1.60301151273
absolute error = 1.678e-05
relative error = 0.0007339 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.671
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.204
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9847 2.141
h = 0.001 0.001
y[1] (numeric) = 1.62983165345 1.60531442319
y[1] (closed_form) = 1.62983526864 1.60533076196
absolute error = 1.673e-05
relative error = 0.0007315 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.673
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.731
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9857 2.142
h = 0.001 0.003
y[1] (numeric) = 1.63048010477 1.60620425386
y[1] (closed_form) = 1.63048377543 1.60622053204
absolute error = 1.669e-05
relative error = 0.0007291 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.675
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.217
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9867 2.145
h = 0.0001 0.004
y[1] (numeric) = 1.630887349 1.6086325377
y[1] (closed_form) = 1.63089090164 1.60864893467
absolute error = 1.678e-05
relative error = 0.0007324 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.677
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.653
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9868 2.149
h = 0.003 0.006
y[1] (numeric) = 1.63048100273 1.61172202856
y[1] (closed_form) = 1.63048441701 1.61173839162
absolute error = 1.672e-05
relative error = 0.0007291 %
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 = 6.169
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5166.9MB, alloc=52.3MB, time=62.04
x[1] = 0.9898 2.155
h = 0.0001 0.005
y[1] (numeric) = 1.6320630842 1.61670181056
y[1] (closed_form) = 1.63206669985 1.61671876519
absolute error = 1.734e-05
relative error = 0.0007546 %
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 = 2.748
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9899 2.16
h = 0.0001 0.003
y[1] (numeric) = 1.63153374002 1.62056303698
y[1] (closed_form) = 1.63153729238 1.62057959142
absolute error = 1.693e-05
relative error = 0.0007363 %
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 = 2.214
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.99 2.163
h = 0.001 0.001
y[1] (numeric) = 1.63124619803 1.62288477949
y[1] (closed_form) = 1.63124988926 1.62290125753
absolute error = 1.689e-05
relative error = 0.0007339 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.69
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.739
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.991 2.164
h = 0.001 0.003
y[1] (numeric) = 1.63189451316 1.62377629708
y[1] (closed_form) = 1.6318982595 1.62379271458
absolute error = 1.684e-05
relative error = 0.0007315 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.692
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.255
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.992 2.167
h = 0.0001 0.004
y[1] (numeric) = 1.63229979803 1.62620781746
y[1] (closed_form) = 1.6323034271 1.6262243537
absolute error = 1.693e-05
relative error = 0.0007348 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.694
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.674
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5212.4MB, alloc=52.3MB, time=62.58
x[1] = 0.9921 2.171
h = 0.003 0.006
y[1] (numeric) = 1.6318898874 1.62930049946
y[1] (closed_form) = 1.6318933785 1.62931700232
absolute error = 1.687e-05
relative error = 0.0007315 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.697
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.198
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9951 2.177
h = 0.0001 0.005
y[1] (numeric) = 1.63346883844 1.63428766192
y[1] (closed_form) = 1.63347253197 1.63430475368
absolute error = 1.749e-05
relative error = 0.0007568 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.703
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.76
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9952 2.182
h = 0.0001 0.003
y[1] (numeric) = 1.63293503414 1.63815285267
y[1] (closed_form) = 1.63293866342 1.63816954582
absolute error = 1.708e-05
relative error = 0.0007386 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.706
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.224
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9953 2.185
h = 0.001 0.001
y[1] (numeric) = 1.63264485008 1.6404770117
y[1] (closed_form) = 1.63264861751 1.6404936283
absolute error = 1.704e-05
relative error = 0.0007362 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.708
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.747
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9963 2.186
h = 0.001 0.003
y[1] (numeric) = 1.63329303453 1.64137021073
y[1] (closed_form) = 1.63329685669 1.64138676683
absolute error = 1.699e-05
relative error = 0.0007338 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.709
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.293
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5257.8MB, alloc=52.3MB, time=63.12
x[1] = 0.9973 2.189
h = 0.0001 0.004
y[1] (numeric) = 1.63369637649 1.6438049622
y[1] (closed_form) = 1.63370008216 1.64382163698
absolute error = 1.708e-05
relative error = 0.000737 %
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 = 4.696
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9974 2.193
h = 0.003 0.006
y[1] (numeric) = 1.63328292344 1.6469008348
y[1] (closed_form) = 1.63328649152 1.64691747672
absolute error = 1.702e-05
relative error = 0.0007338 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.714
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.227
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0004 2.199
h = 0.0001 0.005
y[1] (numeric) = 1.63485877688 1.65189536125
y[1] (closed_form) = 1.63486254842 1.65191258942
absolute error = 1.764e-05
relative error = 0.0007588 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.72
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.773
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0005 2.204
h = 0.0001 0.003
y[1] (numeric) = 1.63432053974 1.65576451572
y[1] (closed_form) = 1.63432424608 1.65578134686
absolute error = 1.723e-05
relative error = 0.0007408 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.723
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] = 1.0006 2.207
h = 0.001 0.001
y[1] (numeric) = 1.63402772995 1.65809109064
y[1] (closed_form) = 1.63403157374 1.6581078451
absolute error = 1.719e-05
relative error = 0.0007384 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.725
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.755
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5303.3MB, alloc=52.3MB, time=63.66
x[1] = 1.0016 2.208
h = 0.001 0.003
y[1] (numeric) = 1.63467578914 1.65898596563
y[1] (closed_form) = 1.63467968729 1.65900265964
absolute error = 1.714e-05
relative error = 0.0007361 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.726
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.332
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0026 2.211
h = 0.0001 0.004
y[1] (numeric) = 1.63507720452 1.66142394267
y[1] (closed_form) = 1.63508098693 1.66144075527
absolute error = 1.723e-05
relative error = 0.0007393 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.729
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.718
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0027 2.215
h = 0.003 0.006
y[1] (numeric) = 1.63466023079 1.66452300519
y[1] (closed_form) = 1.63466387599 1.66453978546
absolute error = 1.717e-05
relative error = 0.000736 %
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 = 6.256
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0057 2.221
h = 0.0001 0.005
y[1] (numeric) = 1.63623301908 1.66952487907
y[1] (closed_form) = 1.63623686874 1.66954224295
absolute error = 1.779e-05
relative error = 0.0007608 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.737
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.786
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0058 2.226
h = 0.0001 0.003
y[1] (numeric) = 1.63569037615 1.67339799645
y[1] (closed_form) = 1.63569415968 1.67341496488
absolute error = 1.739e-05
relative error = 0.0007429 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.74
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
memory used=5348.8MB, alloc=52.3MB, time=64.21
x[1] = 1.0059 2.229
h = 0.001 0.001
y[1] (numeric) = 1.63539495685 1.67572698655
y[1] (closed_form) = 1.63539887713 1.67574387816
absolute error = 1.734e-05
relative error = 0.0007406 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.763
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0069 2.23
h = 0.0001 0.004
y[1] (numeric) = 1.63604289611 1.67662353202
y[1] (closed_form) = 1.63604687039 1.67664036324
absolute error = 1.729e-05
relative error = 0.0007382 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.744
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.59
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.007 2.234
h = 0.003 0.006
y[1] (numeric) = 1.63562305419 1.67972519722
y[1] (closed_form) = 1.63562670858 1.6797420974
absolute error = 1.729e-05
relative error = 0.0007375 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.746
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.28
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01 2.24
h = 0.0001 0.005
y[1] (numeric) = 1.63719314255 1.68473334621
y[1] (closed_form) = 1.63719700229 1.68475082775
absolute error = 1.790e-05
relative error = 0.0007621 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.752
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.797
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0101 2.245
h = 0.0001 0.003
y[1] (numeric) = 1.63664668156 1.68860982191
y[1] (closed_form) = 1.63665047436 1.68862690934
absolute error = 1.750e-05
relative error = 0.0007443 %
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 = 2.254
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5394.4MB, alloc=52.3MB, time=64.75
x[1] = 1.0102 2.248
h = 0.001 0.001
y[1] (numeric) = 1.63634900021 1.69094085942
y[1] (closed_form) = 1.63635292916 1.69095786991
absolute error = 1.746e-05
relative error = 0.0007419 %
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 = 1.77
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0112 2.249
h = 0.001 0.003
y[1] (numeric) = 1.63699682064 1.69183883707
y[1] (closed_form) = 1.63700080328 1.69185578721
absolute error = 1.741e-05
relative error = 0.0007396 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.758
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.404
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0122 2.252
h = 0.0001 0.004
y[1] (numeric) = 1.63739465565 1.69428277869
y[1] (closed_form) = 1.63739852393 1.69429984729
absolute error = 1.750e-05
relative error = 0.0007428 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.761
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.759
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0123 2.256
h = 0.003 0.006
y[1] (numeric) = 1.63697115003 1.69738773328
y[1] (closed_form) = 1.63697488181 1.69740477049
absolute error = 1.744e-05
relative error = 0.0007396 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.763
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.31
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0153 2.262
h = 0.0001 0.005
y[1] (numeric) = 1.63853823283 1.70240319904
y[1] (closed_form) = 1.63854217091 1.70242081501
absolute error = 1.805e-05
relative error = 0.0007639 %
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=5439.9MB, alloc=52.3MB, time=65.29
x[1] = 1.0154 2.267
h = 0.0001 0.003
y[1] (numeric) = 1.63798741581 1.70628363602
y[1] (closed_form) = 1.63799128605 1.70630085944
absolute error = 1.765e-05
relative error = 0.0007463 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.773
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] = 1.0155 2.27
h = 0.001 0.001
y[1] (numeric) = 1.63768715477 1.70861708725
y[1] (closed_form) = 1.63769116047 1.70863423361
absolute error = 1.761e-05
relative error = 0.000744 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.774
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] = 1.0165 2.271
h = 0.001 0.003
y[1] (numeric) = 1.63833486506 1.70951672531
y[1] (closed_form) = 1.63833892409 1.70953381136
absolute error = 1.756e-05
relative error = 0.0007417 %
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] = 1.0175 2.274
h = 0.0001 0.004
y[1] (numeric) = 1.63873081926 1.7119638765
y[1] (closed_form) = 1.63873476467 1.71198108093
absolute error = 1.765e-05
relative error = 0.0007448 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.778
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] = 1.0176 2.278
h = 0.003 0.006
y[1] (numeric) = 1.63830385419 1.71507201854
y[1] (closed_form) = 1.63830766347 1.71508919208
absolute error = 1.759e-05
relative error = 0.0007417 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.781
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.339
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5485.3MB, alloc=52.3MB, time=65.83
x[1] = 1.0206 2.284
h = 0.0001 0.005
y[1] (numeric) = 1.63986796281 1.72009478428
y[1] (closed_form) = 1.63987197934 1.72011253398
absolute error = 1.820e-05
relative error = 0.0007658 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.787
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] = 1.0207 2.289
h = 0.0001 0.003
y[1] (numeric) = 1.63931281616 1.72397918125
y[1] (closed_form) = 1.63931676397 1.72399653995
absolute error = 1.780e-05
relative error = 0.0007483 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.275
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0208 2.292
h = 0.001 0.001
y[1] (numeric) = 1.63900999126 1.72631504518
y[1] (closed_form) = 1.63901407383 1.7263323267
absolute error = 1.776e-05
relative error = 0.000746 %
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 = 1.787
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0218 2.293
h = 0.001 0.003
y[1] (numeric) = 1.63965759652 1.72721633818
y[1] (closed_form) = 1.63966173207 1.72723355946
absolute error = 1.771e-05
relative error = 0.0007437 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.793
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.482
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0228 2.296
h = 0.0001 0.004
y[1] (numeric) = 1.64005168558 1.72966669318
y[1] (closed_form) = 1.64005570823 1.72968403275
absolute error = 1.780e-05
relative error = 0.0007468 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.796
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.803
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5530.8MB, alloc=52.3MB, time=66.38
x[1] = 1.0229 2.3
h = 0.003 0.006
y[1] (numeric) = 1.63962128209 1.73277802146
y[1] (closed_form) = 1.63962516901 1.73279533064
absolute error = 1.774e-05
relative error = 0.0007436 %
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 = 6.368
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0259 2.306
h = 0.0001 0.005
y[1] (numeric) = 1.64118244757 1.73780807031
y[1] (closed_form) = 1.64118654264 1.73782595307
absolute error = 1.835e-05
relative error = 0.0007675 %
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] = 1.026 2.311
h = 0.0001 0.003
y[1] (numeric) = 1.64062299748 1.7416964258
y[1] (closed_form) = 1.64062702297 1.7417139191
absolute error = 1.795e-05
relative error = 0.0007502 %
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 = 2.285
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0261 2.314
h = 0.001 0.001
y[1] (numeric) = 1.6403176244 1.74403470133
y[1] (closed_form) = 1.64032178398 1.74405211734
absolute error = 1.791e-05
relative error = 0.0007479 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.809
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] = 1.0271 2.315
h = 0.001 0.003
y[1] (numeric) = 1.64096512966 1.74493764384
y[1] (closed_form) = 1.64096934186 1.74495499967
absolute error = 1.786e-05
relative error = 0.0007456 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.811
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.521
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5576.4MB, alloc=52.3MB, time=66.92
x[1] = 1.0281 2.318
h = 0.0001 0.004
y[1] (numeric) = 1.64135736908 1.74739119681
y[1] (closed_form) = 1.6413614691 1.74740867084
absolute error = 1.795e-05
relative error = 0.0007487 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.813
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.825
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0282 2.322
h = 0.003 0.006
y[1] (numeric) = 1.64092354806 1.75050570999
y[1] (closed_form) = 1.64092751273 1.75052315411
absolute error = 1.789e-05
relative error = 0.0007456 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.816
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.398
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0312 2.328
h = 0.0001 0.005
y[1] (numeric) = 1.64248180105 1.75554302502
y[1] (closed_form) = 1.64248597475 1.75556104015
absolute error = 1.849e-05
relative error = 0.0007692 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.849
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0313 2.333
h = 0.0001 0.003
y[1] (numeric) = 1.64191807349 1.75943533742
y[1] (closed_form) = 1.64192217677 1.75945296463
absolute error = 1.810e-05
relative error = 0.000752 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.825
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] = 1.0314 2.336
h = 0.001 0.001
y[1] (numeric) = 1.6416101678 1.76177602332
y[1] (closed_form) = 1.64161440449 1.76179357314
absolute error = 1.805e-05
relative error = 0.0007497 %
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 = 1.803
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5621.9MB, alloc=52.3MB, time=67.46
x[1] = 1.0324 2.337
h = 0.0001 0.004
y[1] (numeric) = 1.64225757802 1.76268060992
y[1] (closed_form) = 1.64226186697 1.76269809962
absolute error = 1.801e-05
relative error = 0.0007475 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.83
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0325 2.341
h = 0.003 0.006
y[1] (numeric) = 1.64182097252 1.76579772135
y[1] (closed_form) = 1.64182494789 1.76581528321
absolute error = 1.801e-05
relative error = 0.0007468 %
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 = 6.423
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0355 2.347
h = 0.0001 0.005
y[1] (numeric) = 1.64337665654 1.77084124305
y[1] (closed_form) = 1.64338084171 1.77085937374
absolute error = 1.861e-05
relative error = 0.0007702 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.861
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0356 2.352
h = 0.0001 0.003
y[1] (numeric) = 1.6428092206 1.77473690947
y[1] (closed_form) = 1.64281333462 1.77475465355
absolute error = 1.821e-05
relative error = 0.0007532 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.305
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0357 2.355
h = 0.001 0.001
y[1] (numeric) = 1.64249911859 1.77707963919
y[1] (closed_form) = 1.64250336543 1.77709730578
absolute error = 1.817e-05
relative error = 0.0007509 %
Correct digits = 5
memory used=5667.3MB, alloc=52.3MB, time=68.00
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.81
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0367 2.356
h = 0.001 0.003
y[1] (numeric) = 1.64314643141 1.77798563558
y[1] (closed_form) = 1.64315073022 1.77800324211
absolute error = 1.812e-05
relative error = 0.0007486 %
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 = 8.594
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0377 2.359
h = 0.0001 0.004
y[1] (numeric) = 1.64353523182 1.78044510194
y[1] (closed_form) = 1.64353941979 1.78046282649
absolute error = 1.821e-05
relative error = 0.0007516 %
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 = 4.866
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0378 2.363
h = 0.003 0.006
y[1] (numeric) = 1.64309506862 1.78356549734
y[1] (closed_form) = 1.64309912194 1.78358319287
absolute error = 1.815e-05
relative error = 0.0007486 %
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 = 6.452
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0408 2.369
h = 0.0001 0.005
y[1] (numeric) = 1.64464789646 1.7886162539
y[1] (closed_form) = 1.64465216043 1.78863451573
absolute error = 1.875e-05
relative error = 0.0007718 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.874
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5712.9MB, alloc=52.3MB, time=68.54
x[1] = 1.0409 2.374
h = 0.0001 0.003
y[1] (numeric) = 1.64407623081 1.79251587411
y[1] (closed_form) = 1.64408042282 1.79253375085
absolute error = 1.836e-05
relative error = 0.0007549 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.858
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.316
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.041 2.377
h = 0.001 0.001
y[1] (numeric) = 1.6437636248 1.7948610119
y[1] (closed_form) = 1.64376794896 1.79487881105
absolute error = 1.832e-05
relative error = 0.0007526 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.86
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] = 1.042 2.378
h = 0.001 0.003
y[1] (numeric) = 1.64441085167 1.79576864237
y[1] (closed_form) = 1.64441522746 1.79578638152
absolute error = 1.827e-05
relative error = 0.0007504 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.634
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.043 2.381
h = 0.0001 0.004
y[1] (numeric) = 1.64479784594 1.79823128993
y[1] (closed_form) = 1.64480211159 1.798249147
absolute error = 1.836e-05
relative error = 0.0007534 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.889
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0431 2.385
h = 0.003 0.006
y[1] (numeric) = 1.64435432396 1.80135486595
y[1] (closed_form) = 1.64435845535 1.80137269446
absolute error = 1.830e-05
relative error = 0.0007503 %
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 = 6.482
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5758.5MB, alloc=52.3MB, time=69.09
x[1] = 1.0461 2.391
h = 0.0001 0.005
y[1] (numeric) = 1.64590432527 1.80641284026
y[1] (closed_form) = 1.64590866812 1.80643123255
absolute error = 1.890e-05
relative error = 0.0007733 %
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 = 2.887
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0462 2.396
h = 0.0001 0.003
y[1] (numeric) = 1.64532845527 1.8103164122
y[1] (closed_form) = 1.64533272535 1.81033442092
absolute error = 1.851e-05
relative error = 0.0007566 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.876
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.326
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0463 2.399
h = 0.001 0.001
y[1] (numeric) = 1.64501336044 1.8126639566
y[1] (closed_form) = 1.64501776201 1.81268188764
absolute error = 1.846e-05
relative error = 0.0007543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.827
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0473 2.4
h = 0.001 0.003
y[1] (numeric) = 1.64566050609 1.81357321576
y[1] (closed_form) = 1.64566495896 1.81359108687
absolute error = 1.842e-05
relative error = 0.0007521 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.674
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0483 2.403
h = 0.0001 0.004
y[1] (numeric) = 1.6460457091 1.81603903848
y[1] (closed_form) = 1.64605005252 1.8160570274
absolute error = 1.851e-05
relative error = 0.000755 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.882
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.911
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5804.0MB, alloc=52.3MB, time=69.63
x[1] = 1.0484 2.407
h = 0.003 0.006
y[1] (numeric) = 1.64559884853 1.81916579331
y[1] (closed_form) = 1.64560305808 1.81918375414
absolute error = 1.845e-05
relative error = 0.000752 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.884
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.512
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0514 2.413
h = 0.0001 0.005
y[1] (numeric) = 1.64714605263 1.82423096823
y[1] (closed_form) = 1.64715047443 1.82424949032
absolute error = 1.904e-05
relative error = 0.0007748 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.9
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0515 2.418
h = 0.0001 0.003
y[1] (numeric) = 1.64656600339 1.8281384897
y[1] (closed_form) = 1.64657035164 1.82815662974
absolute error = 1.865e-05
relative error = 0.0007582 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.893
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.337
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0516 2.421
h = 0.001 0.001
y[1] (numeric) = 1.64624843479 1.83048843915
y[1] (closed_form) = 1.64625291388 1.83050650143
absolute error = 1.861e-05
relative error = 0.0007559 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.895
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.835
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0526 2.422
h = 0.001 0.003
y[1] (numeric) = 1.64689550391 1.83139932164
y[1] (closed_form) = 1.64690003395 1.83141732404
absolute error = 1.856e-05
relative error = 0.0007537 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.713
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5849.4MB, alloc=52.3MB, time=70.18
x[1] = 1.0536 2.425
h = 0.0001 0.004
y[1] (numeric) = 1.64727893037 1.83386831345
y[1] (closed_form) = 1.64728335165 1.83388643356
absolute error = 1.865e-05
relative error = 0.0007566 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.934
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0537 2.429
h = 0.003 0.006
y[1] (numeric) = 1.64682875125 1.83699824518
y[1] (closed_form) = 1.64683303904 1.83701633765
absolute error = 1.859e-05
relative error = 0.0007537 %
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 = 6.542
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0567 2.435
h = 0.0001 0.005
y[1] (numeric) = 1.64837318708 1.84207060349
y[1] (closed_form) = 1.6483776879 1.84208925473
absolute error = 1.919e-05
relative error = 0.0007762 %
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 = 2.913
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0568 2.44
h = 0.0001 0.003
y[1] (numeric) = 1.64778898353 1.84598207215
y[1] (closed_form) = 1.64779341003 1.84600034284
absolute error = 1.880e-05
relative error = 0.0007597 %
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 = 2.348
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0569 2.443
h = 0.001 0.001
y[1] (numeric) = 1.64746895608 1.84833442503
y[1] (closed_form) = 1.64747351276 1.84835261788
absolute error = 1.875e-05
relative error = 0.0007575 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.913
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.844
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5895.0MB, alloc=52.3MB, time=70.72
x[1] = 1.0579 2.444
h = 0.0001 0.004
y[1] (numeric) = 1.64811595326 1.84924692547
y[1] (closed_form) = 1.64812056056 1.84926505852
absolute error = 1.871e-05
relative error = 0.0007553 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.915
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.08
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.058 2.448
h = 0.003 0.006
y[1] (numeric) = 1.64766307 1.85237944862
y[1] (closed_form) = 1.64766736987 1.85239765673
absolute error = 1.871e-05
relative error = 0.0007547 %
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 = 6.567
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.061 2.454
h = 0.0001 0.005
y[1] (numeric) = 1.64920506065 1.85745794385
y[1] (closed_form) = 1.64920957422 1.85747670859
absolute error = 1.930e-05
relative error = 0.000777 %
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 = 2.925
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0611 2.459
h = 0.0001 0.003
y[1] (numeric) = 1.64861725401 1.86137275906
y[1] (closed_form) = 1.6486216926 1.86139114454
absolute error = 1.891e-05
relative error = 0.0007607 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.926
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.357
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0612 2.462
h = 0.001 0.001
y[1] (numeric) = 1.64829509331 1.86372715031
y[1] (closed_form) = 1.64829966152 1.86374545787
absolute error = 1.887e-05
relative error = 0.0007584 %
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 = 1.851
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5940.4MB, alloc=52.3MB, time=71.26
x[1] = 1.0622 2.463
h = 0.001 0.003
y[1] (numeric) = 1.64894201302 1.86464103837
y[1] (closed_form) = 1.64894663157 1.86465928618
absolute error = 1.882e-05
relative error = 0.0007562 %
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 = 8.787
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0632 2.466
h = 0.0001 0.004
y[1] (numeric) = 1.6493221348 1.86711589006
y[1] (closed_form) = 1.64932664586 1.86713425538
absolute error = 1.891e-05
relative error = 0.0007591 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.932
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.976
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0633 2.47
h = 0.003 0.006
y[1] (numeric) = 1.64886579553 1.87025168878
y[1] (closed_form) = 1.64887017382 1.87027002729
absolute error = 1.885e-05
relative error = 0.0007562 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.935
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.597
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0663 2.476
h = 0.0001 0.005
y[1] (numeric) = 1.65040507112 1.87533733561
y[1] (closed_form) = 1.65040966385 1.87535622831
absolute error = 1.944e-05
relative error = 0.0007783 %
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 = 2.938
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0664 2.481
h = 0.0001 0.003
y[1] (numeric) = 1.64981315599 1.8792560936
y[1] (closed_form) = 1.64981767299 1.87927460852
absolute error = 1.906e-05
relative error = 0.0007621 %
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 = 2.367
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=5985.9MB, alloc=52.3MB, time=71.80
x[1] = 1.0665 2.484
h = 0.001 0.001
y[1] (numeric) = 1.64948856388 1.88161288522
y[1] (closed_form) = 1.64949320986 1.88163132214
absolute error = 1.901e-05
relative error = 0.0007598 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.946
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] = 1.0675 2.485
h = 0.001 0.003
y[1] (numeric) = 1.65013542011 1.88252838134
y[1] (closed_form) = 1.65014011608 1.88254675859
absolute error = 1.897e-05
relative error = 0.0007577 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.948
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.827
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0685 2.488
h = 0.0001 0.004
y[1] (numeric) = 1.65051380666 1.8850063847
y[1] (closed_form) = 1.65051839583 1.88502487933
absolute error = 1.906e-05
relative error = 0.0007605 %
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 = 4.998
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0686 2.492
h = 0.003 0.006
y[1] (numeric) = 1.6500542052 1.88814535445
y[1] (closed_form) = 1.65005866197 1.88816382272
absolute error = 1.900e-05
relative error = 0.0007576 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.953
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.627
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0716 2.498
h = 0.0001 0.005
y[1] (numeric) = 1.65159079373 1.89323813557
y[1] (closed_form) = 1.65159546565 1.89325715557
absolute error = 1.959e-05
relative error = 0.0007795 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.959
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
memory used=6031.4MB, alloc=52.3MB, time=72.34
x[1] = 1.0717 2.503
h = 0.0001 0.003
y[1] (numeric) = 1.65099479442 1.89716083362
y[1] (closed_form) = 1.6509993899 1.89717947733
absolute error = 1.920e-05
relative error = 0.0007635 %
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 = 2.378
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0718 2.506
h = 0.001 0.001
y[1] (numeric) = 1.65066778545 1.89952002374
y[1] (closed_form) = 1.65067250926 1.89953858939
absolute error = 1.916e-05
relative error = 0.0007613 %
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 = 1.868
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0728 2.507
h = 0.001 0.003
y[1] (numeric) = 1.65131458258 1.90043712261
y[1] (closed_form) = 1.65131935607 1.90045562866
absolute error = 1.911e-05
relative error = 0.0007591 %
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 = 8.868
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0738 2.51
h = 0.0001 0.004
y[1] (numeric) = 1.65169124804 1.9029182714
y[1] (closed_form) = 1.65169591539 1.9029368947
absolute error = 1.920e-05
relative error = 0.0007619 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.968
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.021
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0739 2.514
h = 0.003 0.006
y[1] (numeric) = 1.65122840375 1.90606040986
y[1] (closed_form) = 1.65123293909 1.90607900723
absolute error = 1.914e-05
relative error = 0.0007591 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.971
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.658
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6076.9MB, alloc=52.3MB, time=72.88
x[1] = 1.0769 2.52
h = 0.0001 0.005
y[1] (numeric) = 1.6527623329 1.91116030793
y[1] (closed_form) = 1.65276708408 1.9111794546
absolute error = 1.973e-05
relative error = 0.0007808 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.977
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.965
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.077 2.525
h = 0.0001 0.003
y[1] (numeric) = 1.6521622735 1.91508694319
y[1] (closed_form) = 1.65216694753 1.91510571505
absolute error = 1.935e-05
relative error = 0.0007648 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.98
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] = 1.0771 2.528
h = 0.001 0.001
y[1] (numeric) = 1.65183286211 1.91744852989
y[1] (closed_form) = 1.65183766382 1.91746722362
absolute error = 1.930e-05
relative error = 0.0007626 %
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] = 1.0781 2.529
h = 0.001 0.003
y[1] (numeric) = 1.65247960449 1.91836722619
y[1] (closed_form) = 1.65248445556 1.9183858604
absolute error = 1.926e-05
relative error = 0.0007605 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.984
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.908
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0791 2.532
h = 0.0001 0.004
y[1] (numeric) = 1.65285456282 1.92085151416
y[1] (closed_form) = 1.65285930842 1.92087026549
absolute error = 1.934e-05
relative error = 0.0007633 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.986
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.044
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6122.4MB, alloc=52.3MB, time=73.43
x[1] = 1.0792 2.536
h = 0.003 0.006
y[1] (numeric) = 1.6523884949 1.9239968189
y[1] (closed_form) = 1.65239310887 1.92401554473
absolute error = 1.929e-05
relative error = 0.0007604 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.989
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.688
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0822 2.542
h = 0.0001 0.005
y[1] (numeric) = 1.65391979202 1.92910381653
y[1] (closed_form) = 1.6539246225 1.92912308924
absolute error = 1.987e-05
relative error = 0.0007819 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.995
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.978
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0823 2.547
h = 0.0001 0.003
y[1] (numeric) = 1.65331569644 1.93303438605
y[1] (closed_form) = 1.65332044907 1.93305328541
absolute error = 1.949e-05
relative error = 0.0007661 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.998
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.4
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0824 2.55
h = 0.001 0.001
y[1] (numeric) = 1.65298389691 1.93539836733
y[1] (closed_form) = 1.6529887766 1.93541718851
absolute error = 1.944e-05
relative error = 0.0007639 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.885
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0834 2.551
h = 0.0001 0.004
y[1] (numeric) = 1.65363058882 1.93631865578
y[1] (closed_form) = 1.65363551754 1.93633741752
absolute error = 1.940e-05
relative error = 0.0007618 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.002
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.32
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6167.9MB, alloc=52.3MB, time=73.97
x[1] = 1.0835 2.555
h = 0.003 0.006
y[1] (numeric) = 1.6531618938 1.93946654306
y[1] (closed_form) = 1.6531665211 1.93948538244
absolute error = 1.940e-05
relative error = 0.0007612 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.004
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.714
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0865 2.561
h = 0.0001 0.005
y[1] (numeric) = 1.65469086272 1.94457960691
y[1] (closed_form) = 1.65469570713 1.94459899111
absolute error = 1.998e-05
relative error = 0.0007825 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.011
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.99
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0866 2.566
h = 0.0001 0.003
y[1] (numeric) = 1.65408326508 1.94851351274
y[1] (closed_form) = 1.65408803104 1.94853252484
absolute error = 1.960e-05
relative error = 0.0007669 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.014
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] = 1.0867 2.569
h = 0.001 0.001
y[1] (numeric) = 1.6537493928 1.95087952533
y[1] (closed_form) = 1.65375428527 1.95089845919
absolute error = 1.956e-05
relative error = 0.0007646 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.016
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.892
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0877 2.57
h = 0.001 0.003
y[1] (numeric) = 1.65439602574 1.95180117949
y[1] (closed_form) = 1.65440096698 1.95182005397
absolute error = 1.951e-05
relative error = 0.0007625 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.017
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.983
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6213.5MB, alloc=52.3MB, time=74.52
x[1] = 1.0887 2.573
h = 0.0001 0.004
y[1] (numeric) = 1.65476780699 1.95429127198
y[1] (closed_form) = 1.65477264397 1.95431026336
absolute error = 1.960e-05
relative error = 0.0007653 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.087
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0888 2.577
h = 0.003 0.006
y[1] (numeric) = 1.65429575353 1.95744242378
y[1] (closed_form) = 1.65430045959 1.95746139043
absolute error = 1.954e-05
relative error = 0.0007625 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.023
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.744
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0918 2.583
h = 0.0001 0.005
y[1] (numeric) = 1.65582214068 1.96256255512
y[1] (closed_form) = 1.65582706448 1.9625820642
absolute error = 2.012e-05
relative error = 0.0007836 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.029
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.003
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0919 2.588
h = 0.0001 0.003
y[1] (numeric) = 1.6552105508 1.96650038964
y[1] (closed_form) = 1.65521539548 1.96651952808
absolute error = 1.974e-05
relative error = 0.0007681 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.032
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.42
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.092 2.591
h = 0.001 0.001
y[1] (numeric) = 1.65487431669 1.96886879308
y[1] (closed_form) = 1.65487928726 1.96888785323
absolute error = 1.970e-05
relative error = 0.0007658 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.034
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
memory used=6259.0MB, alloc=52.3MB, time=75.06
x[1] = 1.093 2.592
h = 0.001 0.003
y[1] (numeric) = 1.65552090699 1.96979202965
y[1] (closed_form) = 1.65552592601 1.96981103049
absolute error = 1.965e-05
relative error = 0.0007638 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.035
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.024
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.094 2.595
h = 0.0001 0.004
y[1] (numeric) = 1.65589102036 1.97228524337
y[1] (closed_form) = 1.65589593577 1.97230436097
absolute error = 1.974e-05
relative error = 0.0007665 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.038
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.11
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0941 2.599
h = 0.003 0.006
y[1] (numeric) = 1.65541579732 1.97543955421
y[1] (closed_form) = 1.65542058218 1.9754586475
absolute error = 1.968e-05
relative error = 0.0007637 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.041
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.775
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0971 2.605
h = 0.0001 0.005
y[1] (numeric) = 1.65693962914 1.98056673559
y[1] (closed_form) = 1.65694463236 1.98058636893
absolute error = 2.026e-05
relative error = 0.0007846 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.047
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.017
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0972 2.61
h = 0.0001 0.003
y[1] (numeric) = 1.65632407032 1.98450849552
y[1] (closed_form) = 1.65632899377 1.98452775966
absolute error = 1.988e-05
relative error = 0.0007692 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.05
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.431
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6304.6MB, alloc=52.3MB, time=75.61
x[1] = 1.0973 2.613
h = 0.001 0.001
y[1] (numeric) = 1.65598548832 1.98687928762
y[1] (closed_form) = 1.65599053704 1.98689847342
absolute error = 1.984e-05
relative error = 0.000767 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.052
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] = 1.0983 2.614
h = 0.001 0.003
y[1] (numeric) = 1.65663204008 1.98780410135
y[1] (closed_form) = 1.65663713693 1.98782322793
absolute error = 1.979e-05
relative error = 0.0007649 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.054
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.064
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0993 2.617
h = 0.0001 0.004
y[1] (numeric) = 1.65700049898 1.99030042991
y[1] (closed_form) = 1.65700549287 1.99031967311
absolute error = 1.988e-05
relative error = 0.0007677 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.056
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.133
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0994 2.621
h = 0.003 0.006
y[1] (numeric) = 1.65652212491 1.99345789702
y[1] (closed_form) = 1.65652698863 1.99347711632
absolute error = 1.983e-05
relative error = 0.0007649 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.059
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.805
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1024 2.627
h = 0.0001 0.005
y[1] (numeric) = 1.65804342754 1.99859211097
y[1] (closed_form) = 1.65804851022 1.99861186796
absolute error = 2.040e-05
relative error = 0.0007856 %
Correct digits = 5
memory used=6350.2MB, alloc=52.3MB, time=76.15
Radius of convergence (given) for eq 1 = 4.065
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.031
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1025 2.632
h = 0.0001 0.003
y[1] (numeric) = 1.65742392289 2.00253779289
y[1] (closed_form) = 1.65742892515 2.00255718213
absolute error = 2.002e-05
relative error = 0.0007703 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.069
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.442
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1026 2.635
h = 0.001 0.001
y[1] (numeric) = 1.65708300683 2.00491097141
y[1] (closed_form) = 1.65708813375 2.00493028225
absolute error = 1.998e-05
relative error = 0.0007681 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.071
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.918
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1036 2.636
h = 0.001 0.003
y[1] (numeric) = 1.65772952406 2.00583735707
y[1] (closed_form) = 1.65773469881 2.00585660878
absolute error = 1.994e-05
relative error = 0.0007661 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.072
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.105
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1046 2.639
h = 0.0001 0.004
y[1] (numeric) = 1.65809634177 2.00833679406
y[1] (closed_form) = 1.65810141418 2.00835616225
absolute error = 2.002e-05
relative error = 0.0007688 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.075
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.156
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6395.7MB, alloc=52.3MB, time=76.70
x[1] = 1.1047 2.643
h = 0.003 0.006
y[1] (numeric) = 1.65761483507 2.01149741457
y[1] (closed_form) = 1.6576197777 2.01151675925
absolute error = 1.997e-05
relative error = 0.000766 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.077
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.836
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1077 2.649
h = 0.0001 0.005
y[1] (numeric) = 1.65913363435 2.01663864363
y[1] (closed_form) = 1.65913879651 2.01665852365
absolute error = 2.054e-05
relative error = 0.0007865 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.084
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.044
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1078 2.654
h = 0.0001 0.003
y[1] (numeric) = 1.65851020677 2.02058824403
y[1] (closed_form) = 1.65851528788 2.02060775774
absolute error = 2.016e-05
relative error = 0.0007714 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.087
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.453
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1079 2.657
h = 0.001 0.001
y[1] (numeric) = 1.65816697035 2.02296380664
y[1] (closed_form) = 1.65817217552 2.02298324192
absolute error = 2.012e-05
relative error = 0.0007692 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.089
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.926
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1089 2.658
h = 0.0001 0.004
y[1] (numeric) = 1.65881345701 2.02389175904
y[1] (closed_form) = 1.65881870971 2.02391113526
absolute error = 2.008e-05
relative error = 0.0007672 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.09
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.57
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6441.2MB, alloc=52.3MB, time=77.24
x[1] = 1.109 2.662
h = 0.003 0.006
y[1] (numeric) = 1.65832939707 2.02705495137
y[1] (closed_form) = 1.65833435418 2.02707440757
absolute error = 2.008e-05
relative error = 0.0007666 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.093
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] = 1.112 2.668
h = 0.0001 0.005
y[1] (numeric) = 1.65984597871 2.03220217539
y[1] (closed_form) = 1.65985115587 2.03222216493
absolute error = 2.065e-05
relative error = 0.000787 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.099
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.056
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1121 2.673
h = 0.0001 0.003
y[1] (numeric) = 1.65921914597 2.03615509944
y[1] (closed_form) = 1.65922424154 2.03617472389
absolute error = 2.028e-05
relative error = 0.0007719 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.102
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.462
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1122 2.676
h = 0.001 0.001
y[1] (numeric) = 1.65887389479 2.03853268489
y[1] (closed_form) = 1.65887911388 2.03855223086
absolute error = 2.023e-05
relative error = 0.0007697 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.934
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1132 2.677
h = 0.001 0.003
y[1] (numeric) = 1.65952033969 2.03946198142
y[1] (closed_form) = 1.65952560605 2.03948146841
absolute error = 2.019e-05
relative error = 0.0007677 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.106
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.181
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6486.8MB, alloc=52.3MB, time=77.78
x[1] = 1.1142 2.68
h = 0.0001 0.004
y[1] (numeric) = 1.65988410152 2.04196716613
y[1] (closed_form) = 1.65988926671 2.04198676933
absolute error = 2.027e-05
relative error = 0.0007704 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.109
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.199
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1143 2.684
h = 0.003 0.006
y[1] (numeric) = 1.65939677668 2.04513360966
y[1] (closed_form) = 1.65940181278 2.04515319009
absolute error = 2.022e-05
relative error = 0.0007677 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.111
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.893
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1173 2.69
h = 0.0001 0.005
y[1] (numeric) = 1.66091090243 2.05028781655
y[1] (closed_form) = 1.66091615913 2.05030792801
absolute error = 2.079e-05
relative error = 0.0007878 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.117
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.07
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1174 2.695
h = 0.0001 0.003
y[1] (numeric) = 1.6602801889 2.05424465254
y[1] (closed_form) = 1.6602853634 2.05426440033
absolute error = 2.041e-05
relative error = 0.0007729 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.121
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] = 1.1175 2.698
h = 0.001 0.001
y[1] (numeric) = 1.65993264256 2.05662461778
y[1] (closed_form) = 1.65993793999 2.05664428706
absolute error = 2.037e-05
relative error = 0.0007707 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.123
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.942
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6532.3MB, alloc=52.3MB, time=78.32
x[1] = 1.1185 2.699
h = 0.001 0.003
y[1] (numeric) = 1.66057906418 2.05755547145
y[1] (closed_form) = 1.66058440857 2.05757508183
absolute error = 2.033e-05
relative error = 0.0007687 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.124
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.222
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1195 2.702
h = 0.0001 0.004
y[1] (numeric) = 1.66094122208 2.06006374625
y[1] (closed_form) = 1.66094646592 2.0600834727
absolute error = 2.041e-05
relative error = 0.0007713 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.127
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.222
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1196 2.706
h = 0.003 0.006
y[1] (numeric) = 1.66045081641 2.06323333475
y[1] (closed_form) = 1.66045593154 2.06325303882
absolute error = 2.036e-05
relative error = 0.0007687 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.13
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.924
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1226 2.712
h = 0.0001 0.005
y[1] (numeric) = 1.66196251126 2.06839450701
y[1] (closed_form) = 1.66196784751 2.0684147398
absolute error = 2.092e-05
relative error = 0.0007886 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.136
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.083
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1227 2.717
h = 0.0001 0.003
y[1] (numeric) = 1.66132793926 2.07235525115
y[1] (closed_form) = 1.66133319273 2.07237512167
absolute error = 2.055e-05
relative error = 0.0007738 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.139
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.484
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6577.7MB, alloc=52.3MB, time=78.86
x[1] = 1.1228 2.72
h = 0.001 0.001
y[1] (numeric) = 1.66097811113 2.0747375937
y[1] (closed_form) = 1.66098348693 2.07475738569
absolute error = 2.051e-05
relative error = 0.0007717 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.141
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.951
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1238 2.721
h = 0.001 0.003
y[1] (numeric) = 1.66162451326 2.07566999936
y[1] (closed_form) = 1.66162993572 2.07568973253
absolute error = 2.046e-05
relative error = 0.0007697 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.143
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.263
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1248 2.724
h = 0.0001 0.004
y[1] (numeric) = 1.66198507997 2.07818135775
y[1] (closed_form) = 1.66199040249 2.07820120685
absolute error = 2.055e-05
relative error = 0.0007723 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.145
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.245
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1249 2.728
h = 0.003 0.006
y[1] (numeric) = 1.66149161126 2.08135408804
y[1] (closed_form) = 1.66149680544 2.08137391513
absolute error = 2.050e-05
relative error = 0.0007696 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.148
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.954
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1279 2.734
h = 0.0001 0.005
y[1] (numeric) = 1.66300089988 2.08652220817
y[1] (closed_form) = 1.66300631571 2.0865425617
absolute error = 2.106e-05
relative error = 0.0007894 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.154
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.097
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6623.1MB, alloc=52.3MB, time=79.40
x[1] = 1.128 2.739
h = 0.0001 0.003
y[1] (numeric) = 1.66236249157 2.09048685657
y[1] (closed_form) = 1.66236782403 2.09050684923
absolute error = 2.069e-05
relative error = 0.0007747 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.158
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.496
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1281 2.742
h = 0.001 0.001
y[1] (numeric) = 1.66201039489 2.0928715739
y[1] (closed_form) = 1.66201584909 2.092891488
absolute error = 2.065e-05
relative error = 0.0007726 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.96
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1291 2.743
h = 0.001 0.003
y[1] (numeric) = 1.66265678126 2.09380552641
y[1] (closed_form) = 1.66266228183 2.09382538177
absolute error = 2.060e-05
relative error = 0.0007706 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.161
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.305
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1301 2.746
h = 0.0001 0.004
y[1] (numeric) = 1.66301576938 2.09631996187
y[1] (closed_form) = 1.66302117061 2.09633993301
absolute error = 2.069e-05
relative error = 0.0007732 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.164
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.269
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1302 2.75
h = 0.003 0.006
y[1] (numeric) = 1.66251925526 2.0994958307
y[1] (closed_form) = 1.66252452853 2.09951578022
absolute error = 2.063e-05
relative error = 0.0007705 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.167
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.985
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6668.6MB, alloc=52.3MB, time=79.94
x[1] = 1.1332 2.756
h = 0.0001 0.005
y[1] (numeric) = 1.66402616205 2.1046708812
y[1] (closed_form) = 1.66403165746 2.10469135488
absolute error = 2.120e-05
relative error = 0.0007901 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.173
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.111
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1333 2.761
h = 0.0001 0.003
y[1] (numeric) = 1.66338393937 2.10863942987
y[1] (closed_form) = 1.66338935085 2.10865954408
absolute error = 2.083e-05
relative error = 0.0007756 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.176
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.507
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1334 2.764
h = 0.001 0.001
y[1] (numeric) = 1.66302958727 2.11102651939
y[1] (closed_form) = 1.6630351199 2.11104655501
absolute error = 2.079e-05
relative error = 0.0007734 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.969
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1344 2.765
h = 0.0001 0.004
y[1] (numeric) = 1.66367596156 2.11196201363
y[1] (closed_form) = 1.66368154027 2.11198199061
absolute error = 2.074e-05
relative error = 0.0007715 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.18
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.83
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1345 2.769
h = 0.003 0.006
y[1] (numeric) = 1.66317696497 2.11514044201
y[1] (closed_form) = 1.66318225378 2.11516050105
absolute error = 2.074e-05
relative error = 0.000771 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.182
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.012
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6714.2MB, alloc=52.3MB, time=80.49
x[1] = 1.1375 2.775
h = 0.0001 0.005
y[1] (numeric) = 1.66468175862 2.12032141595
y[1] (closed_form) = 1.66468727001 2.12034199721
absolute error = 2.131e-05
relative error = 0.0007904 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.189
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.123
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1376 2.78
h = 0.0001 0.003
y[1] (numeric) = 1.66403622369 2.1242932735
y[1] (closed_form) = 1.66404165066 2.12431349648
absolute error = 2.094e-05
relative error = 0.0007759 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.516
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1377 2.783
h = 0.001 0.001
y[1] (numeric) = 1.66367991241 2.12668237615
y[1] (closed_form) = 1.66368546002 2.12670252052
absolute error = 2.089e-05
relative error = 0.0007738 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.194
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.976
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1387 2.784
h = 0.001 0.003
y[1] (numeric) = 1.66432626091 2.12761919331
y[1] (closed_form) = 1.66433185435 2.1276392791
absolute error = 2.085e-05
relative error = 0.0007719 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.195
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.381
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1397 2.787
h = 0.0001 0.004
y[1] (numeric) = 1.66468230826 2.13013931858
y[1] (closed_form) = 1.66468780348 2.13015951988
absolute error = 2.094e-05
relative error = 0.0007744 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.312
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6759.7MB, alloc=52.3MB, time=81.03
x[1] = 1.1398 2.791
h = 0.003 0.006
y[1] (numeric) = 1.66418013645 2.13332098286
y[1] (closed_form) = 1.6641855044 2.13334116321
absolute error = 2.088e-05
relative error = 0.0007718 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.201
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.043
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1428 2.797
h = 0.0001 0.005
y[1] (numeric) = 1.66568259312 2.1385088549
y[1] (closed_form) = 1.66568818412 2.13852955523
absolute error = 2.144e-05
relative error = 0.000791 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.207
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] = 1.1429 2.802
h = 0.0001 0.003
y[1] (numeric) = 1.66503328421 2.14248460532
y[1] (closed_form) = 1.66503879023 2.14250494876
absolute error = 2.108e-05
relative error = 0.0007767 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.211
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.527
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.143 2.805
h = 0.001 0.001
y[1] (numeric) = 1.66467474165 2.14487607536
y[1] (closed_form) = 1.66468036774 2.14489634017
absolute error = 2.103e-05
relative error = 0.0007746 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.985
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.144 2.806
h = 0.001 0.003
y[1] (numeric) = 1.66532108483 2.14581442484
y[1] (closed_form) = 1.66532675646 2.14583463116
absolute error = 2.099e-05
relative error = 0.0007727 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.214
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.423
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6805.1MB, alloc=52.3MB, time=81.57
x[1] = 1.145 2.809
h = 0.0001 0.004
y[1] (numeric) = 1.66567558899 2.14833760856
y[1] (closed_form) = 1.66568116299 2.14835793022
absolute error = 2.107e-05
relative error = 0.0007752 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.217
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.336
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1451 2.813
h = 0.003 0.006
y[1] (numeric) = 1.66517042139 2.15152240192
y[1] (closed_form) = 1.6651758685 2.151542703
absolute error = 2.102e-05
relative error = 0.0007726 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.22
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.074
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1481 2.819
h = 0.0001 0.005
y[1] (numeric) = 1.66667056468 2.15671715457
y[1] (closed_form) = 1.66667623529 2.1567379734
absolute error = 2.158e-05
relative error = 0.0007916 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.226
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.15
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1482 2.824
h = 0.0001 0.003
y[1] (numeric) = 1.66601750319 2.16069679364
y[1] (closed_form) = 1.66602308829 2.16071725695
absolute error = 2.121e-05
relative error = 0.0007774 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.229
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.538
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1483 2.827
h = 0.001 0.001
y[1] (numeric) = 1.66565674215 2.16309062834
y[1] (closed_form) = 1.66566244674 2.16311101301
absolute error = 2.117e-05
relative error = 0.0007753 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.231
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.994
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6850.6MB, alloc=52.3MB, time=82.12
x[1] = 1.1493 2.828
h = 0.001 0.003
y[1] (numeric) = 1.66630308353 2.16403050507
y[1] (closed_form) = 1.66630883338 2.16405083134
absolute error = 2.112e-05
relative error = 0.0007734 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.233
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.465
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1503 2.831
h = 0.0001 0.004
y[1] (numeric) = 1.66665605658 2.16655674066
y[1] (closed_form) = 1.66666170938 2.16657718211
absolute error = 2.121e-05
relative error = 0.0007759 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.235
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.359
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1504 2.835
h = 0.003 0.006
y[1] (numeric) = 1.66614791026 2.16974465959
y[1] (closed_form) = 1.66615343654 2.16976508081
absolute error = 2.116e-05
relative error = 0.0007733 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.238
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.105
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1534 2.841
h = 0.0001 0.005
y[1] (numeric) = 1.66764576348 2.17494627537
y[1] (closed_form) = 1.66765151369 2.17496721213
absolute error = 2.171e-05
relative error = 0.0007922 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.244
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.164
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1535 2.846
h = 0.0001 0.003
y[1] (numeric) = 1.66698897063 2.17892979878
y[1] (closed_form) = 1.66699463481 2.17895038138
absolute error = 2.135e-05
relative error = 0.0007781 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.248
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.55
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6896.1MB, alloc=52.3MB, time=82.66
x[1] = 1.1536 2.849
h = 0.001 0.001
y[1] (numeric) = 1.6666260038 2.18132599536
y[1] (closed_form) = 1.6666317869 2.18134649931
absolute error = 2.130e-05
relative error = 0.0007761 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.002
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1546 2.85
h = 0.001 0.003
y[1] (numeric) = 1.66727234683 2.18226739431
y[1] (closed_form) = 1.66727817491 2.18228783996
absolute error = 2.126e-05
relative error = 0.0007741 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.251
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.506
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1556 2.853
h = 0.0001 0.004
y[1] (numeric) = 1.66762380074 2.18479667515
y[1] (closed_form) = 1.66762953236 2.18481723582
absolute error = 2.134e-05
relative error = 0.0007766 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.254
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.383
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1557 2.857
h = 0.003 0.006
y[1] (numeric) = 1.66711269258 2.18798771608
y[1] (closed_form) = 1.66711829805 2.18800825687
absolute error = 2.129e-05
relative error = 0.000774 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.257
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.137
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1587 2.863
h = 0.0001 0.005
y[1] (numeric) = 1.66860827877 2.19319617753
y[1] (closed_form) = 1.66861410859 2.19321723165
absolute error = 2.185e-05
relative error = 0.0007927 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.263
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.178
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=6941.6MB, alloc=52.3MB, time=83.21
x[1] = 1.1588 2.868
h = 0.0001 0.003
y[1] (numeric) = 1.6679477756 2.19718358088
y[1] (closed_form) = 1.66795351888 2.1972042822
absolute error = 2.148e-05
relative error = 0.0007788 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.267
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.561
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1589 2.871
h = 0.001 0.001
y[1] (numeric) = 1.66758261555 2.19958213652
y[1] (closed_form) = 1.66758847718 2.19960275919
absolute error = 2.144e-05
relative error = 0.0007767 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.011
Order of pole (three term test) = 1.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1599 2.872
h = 0.001 0.003
y[1] (numeric) = 1.66822896365 2.20052505267
y[1] (closed_form) = 1.66823486998 2.20054561712
absolute error = 2.140e-05
relative error = 0.0007748 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.27
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.548
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=6978.0MB, alloc=52.3MB, time=83.62