|\^/| 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.
| Type ? for help.
#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(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0))));
> end;
exact_soln_y := proc(x)
return sin(sqrt(c(2.0)*c(x) + c(3.0)))
- sqrt(c(2.0)*c(x) + c(3.0))*cos(sqrt(c(2.0)*c(x) + c(3.0)))
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_2D0,
> array_const_3D0,
#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_g,
> 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_2D0,
array_const_3D0, 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_g, 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_2D0,
> array_const_3D0,
#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_g,
> 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_2D0,
array_const_3D0, 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_g, 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_2D0,
> array_const_3D0,
#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_g,
> 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_2D0,
array_const_3D0, 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_g, 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_2D0,
> array_const_3D0,
#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_g,
> 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_2D0,
array_const_3D0, 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_g, 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_2D0,
> array_const_3D0,
#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_g,
> 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_2D0,
array_const_3D0, 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_g, 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_2D0,
> array_const_3D0,
#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_g,
> 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_2D0,
array_const_3D0, 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_g, 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_2D0,
> array_const_3D0,
#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_g,
> 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_2D0,
array_const_3D0, 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_g, 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_2D0,
> array_const_3D0,
#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_g,
> 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_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> array_tmp4_g[1] := cos(array_tmp3[1]);
> array_tmp4[1] := sin(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_2D0[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 sin FULL $eq_no = 1
> array_tmp4_g[2] := (neg(att(1,array_tmp4,array_tmp3,1)));
> array_tmp4[2] := (att(1,array_tmp4_g,array_tmp3,1));
> #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 sin FULL $eq_no = 1
> array_tmp4_g[3] := (neg(att(2,array_tmp4,array_tmp3,1)));
> array_tmp4[3] := (att(2,array_tmp4_g,array_tmp3,1));
> #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 sin FULL $eq_no = 1
> array_tmp4_g[4] := (neg(att(3,array_tmp4,array_tmp3,1)));
> array_tmp4[4] := (att(3,array_tmp4_g,array_tmp3,1));
> #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 sin FULL $eq_no = 1
> array_tmp4_g[5] := (neg(att(4,array_tmp4,array_tmp3,1)));
> array_tmp4[5] := (att(4,array_tmp4_g,array_tmp3,1));
> #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 sin FULL $eq_no = 1
> array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_tmp3,1);
> array_tmp4_g[kkk] := neg(att(kkk-1,array_tmp4,array_tmp3,1));
> #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_2D0,
array_const_3D0, 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_g, 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_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_g[1] := cos(array_tmp3[1]);
array_tmp4[1] := sin(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_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
array_tmp4_g[2] := neg(att(1, array_tmp4, array_tmp3, 1));
array_tmp4[2] := att(1, array_tmp4_g, array_tmp3, 1);
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_g[3] := neg(att(2, array_tmp4, array_tmp3, 1));
array_tmp4[3] := att(2, array_tmp4_g, array_tmp3, 1);
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_g[4] := neg(att(3, array_tmp4, array_tmp3, 1));
array_tmp4[4] := att(3, array_tmp4_g, array_tmp3, 1);
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_g[5] := neg(att(4, array_tmp4, array_tmp3, 1));
array_tmp4[5] := att(4, array_tmp4_g, array_tmp3, 1);
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] := att(kkk - 1, array_tmp4_g, array_tmp3, 1);
array_tmp4_g[kkk] := neg(att(kkk - 1, array_tmp4, array_tmp3, 1));
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_2D0,
> array_const_3D0,
> #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_g,
> 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_g:= 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_g[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_g);
> 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_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_const_3D0);
> array_const_3D0[1] := c(3.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> 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/sin_sqrt_linpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
> 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 := 2.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.0001);");
> omniout_str(ALWAYS,"glob_upper_ratio_limit := c(1.001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit := c(0.999);");
> omniout_str(ALWAYS,"");
> 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(-1.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0))));");
> 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 := 2.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.0001);
> glob_upper_ratio_limit := c(1.001);
> glob_lower_ratio_limit := c(0.999);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-1.5);
> 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 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
> 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,"2017-11-26T16:28:43-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sin_sqrt_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ")
> ;
> 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,"sin_sqrt_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"sin_sqrt_lin 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_2D0,
array_const_3D0, 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_g, 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_g := 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_g[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_g);
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_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_const_3D0);
array_const_3D0[1] := c(3.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
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/sin_sqrt_linpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( sqrt ( 2.0 \
* x + 3.0 ) ) ; ");
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 := 2.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.0001);");
omniout_str(ALWAYS, "glob_upper_ratio_limit := c(1.001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit := c(0.999);");
omniout_str(ALWAYS, "");
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(-1.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)\
*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0))));");
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(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 2.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.0001);
glob_upper_ratio_limit := c(1.001);
glob_lower_ratio_limit := c(0.999);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-1.5);
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 ) = sin ( sqrt ( 2.\
0 * x + 3.0 ) ) ; ");
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, "2017-11-26T16:28:43-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sin_sqrt_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = si\
n ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
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, "sin_sqrt_lin diffeq.mxt");
logitem_str(html_log_file, "sin_sqrt_lin 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=3.8MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sin_sqrt_linpostcpx.cpx#################
diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 2.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.0001);
glob_upper_ratio_limit := c(1.001);
glob_lower_ratio_limit := c(0.999);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-1.5);
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(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0))));
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] = 2.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 2.85047505309 0.0442459135344
y[1] (closed_form) = 2.85047505309 0.0442459135344
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 3.601
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29.5MB, alloc=40.3MB, time=0.38
x[1] = 2.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 2.85068645683 0.0464551154617
y[1] (closed_form) = 2.85069063711 0.0464549678486
absolute error = 4.183e-06
relative error = 0.0001467 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.602
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 2.85083601474 0.047779054587
y[1] (closed_form) = 2.8508416992 0.0477788143246
absolute error = 5.690e-06
relative error = 0.0001995 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.602
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 2.85131457626 0.0481854022673
y[1] (closed_form) = 2.85132026241 0.048184827533
absolute error = 5.715e-06
relative error = 0.0002004 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.603
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=75.0MB, alloc=52.3MB, time=0.97
x[1] = 2.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 2.85186602721 0.0494753244495
y[1] (closed_form) = 2.85187305656 0.0494737525679
absolute error = 7.203e-06
relative error = 0.0002525 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.604
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1023 0.116
h = 0.003 0.006
y[1] (numeric) = 2.8520599999 0.051238747827
y[1] (closed_form) = 2.85206970516 0.0512370557929
absolute error = 9.852e-06
relative error = 0.0003454 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.604
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = 2.85361801751 0.053772978752
y[1] (closed_form) = 2.85363227212 0.0537652875722
absolute error = 1.620e-05
relative error = 0.0005675 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.607
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=120.6MB, alloc=52.3MB, time=1.53
x[1] = 2.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = 2.8538660938 0.0559727578216
y[1] (closed_form) = 2.85388453283 0.0559649229226
absolute error = 2.003e-05
relative error = 0.0007019 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1055 0.13
h = 0.001 0.001
y[1] (numeric) = 2.85403758994 0.057290752862
y[1] (closed_form) = 2.8540575342 0.0572828265509
absolute error = 2.146e-05
relative error = 0.0007518 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1065 0.131
h = 0.001 0.003
y[1] (numeric) = 2.8545217879 0.0576879944432
y[1] (closed_form) = 2.85454173414 0.0576797334445
absolute error = 2.159e-05
relative error = 0.0007562 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=166.0MB, alloc=52.3MB, time=2.09
x[1] = 2.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = 2.85509361943 0.0589653405842
y[1] (closed_form) = 2.85511491058 0.058956082934
absolute error = 2.322e-05
relative error = 0.000813 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.61
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1076 0.138
h = 0.003 0.006
y[1] (numeric) = 2.85531690956 0.0607210902356
y[1] (closed_form) = 2.8553408785 0.0607117146188
absolute error = 2.574e-05
relative error = 0.0009012 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.61
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = 2.85691396992 0.0632228022924
y[1] (closed_form) = 2.85694249634 0.0632074272758
absolute error = 3.241e-05
relative error = 0.001134 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.613
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=211.4MB, alloc=52.3MB, time=2.65
x[1] = 2.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = 2.85719875214 0.0654131838236
y[1] (closed_form) = 2.85723146599 0.0653976684279
absolute error = 3.621e-05
relative error = 0.001267 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1108 0.152
h = 0.001 0.001
y[1] (numeric) = 2.85739220625 0.066725249269
y[1] (closed_form) = 2.85742642647 0.0667096436281
absolute error = 3.761e-05
relative error = 0.001316 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1118 0.153
h = 0.001 0.003
y[1] (numeric) = 2.85788205213 0.0671133832738
y[1] (closed_form) = 2.85791627461 0.0670974427066
absolute error = 3.775e-05
relative error = 0.001321 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.615
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=256.9MB, alloc=52.3MB, time=3.21
x[1] = 2.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = 2.85847428863 0.0683781617744
y[1] (closed_form) = 2.85850985781 0.0683612249262
absolute error = 3.940e-05
relative error = 0.001378 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.616
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1129 0.16
h = 0.003 0.006
y[1] (numeric) = 2.85872692285 0.0701262566308
y[1] (closed_form) = 2.85876517187 0.0701092038788
absolute error = 4.188e-05
relative error = 0.001464 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.616
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = 2.86036308025 0.0725954589567
y[1] (closed_form) = 2.8604058949 0.0725724059494
absolute error = 4.863e-05
relative error = 0.001699 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=302.5MB, alloc=52.3MB, time=3.77
x[1] = 2.116 0.171
h = 0.0001 0.003
y[1] (numeric) = 2.86068460247 0.0747764656916
y[1] (closed_form) = 2.86073160785 0.0747532754542
absolute error = 5.241e-05
relative error = 0.001832 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1161 0.174
h = 0.001 0.001
y[1] (numeric) = 2.8609000355 0.0760826146845
y[1] (closed_form) = 2.8609485485 0.0760593352968
absolute error = 5.381e-05
relative error = 0.00188 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1171 0.175
h = 0.001 0.003
y[1] (numeric) = 2.86139554076 0.0764616387775
y[1] (closed_form) = 2.86144405627 0.0764380242025
absolute error = 5.396e-05
relative error = 0.001885 %
Correct digits = 5
memory used=348.0MB, alloc=52.3MB, time=4.33
Radius of convergence (given) for eq 1 = 3.621
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = 2.86200820749 0.0777138563091
y[1] (closed_form) = 2.86205807152 0.0776892456982
absolute error = 5.561e-05
relative error = 0.001942 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.622
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1182 0.182
h = 0.003 0.006
y[1] (numeric) = 2.86229021408 0.0794543135143
y[1] (closed_form) = 2.86234276018 0.079429588937
absolute error = 5.807e-05
relative error = 0.002028 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=393.5MB, alloc=52.3MB, time=4.89
x[1] = 2.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = 2.863965524 0.0818910113638
y[1] (closed_form) = 2.86402264393 0.081860285076
absolute error = 6.486e-05
relative error = 0.002264 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = 2.86432382232 0.084062663812
y[1] (closed_form) = 2.86438513655 0.0840318032487
absolute error = 6.864e-05
relative error = 0.002395 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1214 0.196
h = 0.001 0.001
y[1] (numeric) = 2.86456125643 0.0853629081349
y[1] (closed_form) = 2.86462407962 0.0853319594433
absolute error = 7.003e-05
relative error = 0.002444 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.627
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=439.1MB, alloc=52.3MB, time=5.45
x[1] = 2.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = 2.86506243251 0.0857328191261
y[1] (closed_form) = 2.86512525846 0.085701534964
absolute error = 7.018e-05
relative error = 0.002449 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.628
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1225 0.201
h = 0.003 0.006
y[1] (numeric) = 2.8653698366 0.087467065055
y[1] (closed_form) = 2.8654353465 0.0874356682843
absolute error = 7.265e-05
relative error = 0.002534 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.628
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = 2.86707928018 0.0898762526803
y[1] (closed_form) = 2.86714937103 0.0898388525658
absolute error = 7.944e-05
relative error = 0.00277 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=484.6MB, alloc=52.3MB, time=6.01
x[1] = 2.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = 2.86746937573 0.0920403066726
y[1] (closed_form) = 2.86754366414 0.0920027747145
absolute error = 8.323e-05
relative error = 0.002901 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.632
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1257 0.215
h = 0.001 0.001
y[1] (numeric) = 2.86772583646 0.0933357392974
y[1] (closed_form) = 2.86780163504 0.0932981200491
absolute error = 8.462e-05
relative error = 0.002949 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.632
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1267 0.216
h = 0.001 0.003
y[1] (numeric) = 2.86823201153 0.0936978705653
y[1] (closed_form) = 2.86830781308 0.0936599155877
absolute error = 8.477e-05
relative error = 0.002954 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.633
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=530.1MB, alloc=52.3MB, time=6.57
x[1] = 2.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = 2.86888291359 0.0949269709874
y[1] (closed_form) = 2.86896006716 0.0948880201186
absolute error = 8.643e-05
relative error = 0.003011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.634
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1278 0.223
h = 0.003 0.006
y[1] (numeric) = 2.86921974663 0.0966536064955
y[1] (closed_form) = 2.86929958684 0.0966145449563
absolute error = 8.888e-05
relative error = 0.003096 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.635
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = 2.87096844902 0.0990302897728
y[1] (closed_form) = 2.87105287843 0.0989852223236
absolute error = 9.570e-05
relative error = 0.003331 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.638
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=575.6MB, alloc=52.3MB, time=7.13
x[1] = 2.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = 2.87139539298 0.101185022116
y[1] (closed_form) = 2.87148402402 0.10113982541
absolute error = 9.949e-05
relative error = 0.003463 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.638
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.131 0.237
h = 0.001 0.001
y[1] (numeric) = 2.87167389905 0.102474568631
y[1] (closed_form) = 2.87176404177 0.10242928552
absolute error = 0.0001009
relative error = 0.003511 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.639
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.132 0.238
h = 0.001 0.003
y[1] (numeric) = 2.87218576616 0.102827578734
y[1] (closed_form) = 2.87227591207 0.10278195957
absolute error = 0.000101
relative error = 0.003515 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.64
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=621.2MB, alloc=52.3MB, time=7.70
x[1] = 2.133 0.241
h = 0.0001 0.004
y[1] (numeric) = 2.87285717499 0.10404412801
y[1] (closed_form) = 2.87294867486 0.10399751284
absolute error = 0.0001027
relative error = 0.003572 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.641
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1331 0.245
h = 0.003 0.006
y[1] (numeric) = 2.87322346994 0.105763165293
y[1] (closed_form) = 2.87331765917 0.105716441023
absolute error = 0.0001051
relative error = 0.003657 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.641
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = 2.87501148977 0.108107338371
y[1] (closed_form) = 2.87511027646 0.108054605031
absolute error = 0.000112
relative error = 0.003892 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.645
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=666.6MB, alloc=52.3MB, time=8.26
x[1] = 2.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = 2.8754753239 0.110252763099
y[1] (closed_form) = 2.87557831656 0.110199902887
absolute error = 0.0001158
relative error = 0.004023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.645
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1363 0.259
h = 0.001 0.001
y[1] (numeric) = 2.87577590078 0.111536431346
y[1] (closed_form) = 2.87588040672 0.111483485537
absolute error = 0.0001172
relative error = 0.004071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.646
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1373 0.26
h = 0.001 0.003
y[1] (numeric) = 2.87629347125 0.111880314669
y[1] (closed_form) = 2.87639798057 0.111827032462
absolute error = 0.0001173
relative error = 0.004075 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.647
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=711.8MB, alloc=52.3MB, time=8.81
x[1] = 2.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = 2.87698541505 0.113084312756
y[1] (closed_form) = 2.87709128033 0.113030034304
absolute error = 0.000119
relative error = 0.004132 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.648
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1384 0.267
h = 0.003 0.006
y[1] (numeric) = 2.87738120624 0.114795761924
y[1] (closed_form) = 2.87748976374 0.114741375808
absolute error = 0.0001214
relative error = 0.004216 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.648
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = 2.87920860312 0.117107415066
y[1] (closed_form) = 2.87932176637 0.117047016127
absolute error = 0.0001283
relative error = 0.004451 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.652
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=757.2MB, alloc=52.3MB, time=9.37
x[1] = 2.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = 2.87970937107 0.119243543905
y[1] (closed_form) = 2.87982674487 0.119183020272
absolute error = 0.0001321
relative error = 0.004582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.652
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1416 0.281
h = 0.001 0.001
y[1] (numeric) = 2.88003204536 0.12052134032
y[1] (closed_form) = 2.88015093413 0.120460731822
absolute error = 0.0001334
relative error = 0.004629 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.652
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1426 0.282
h = 0.001 0.003
y[1] (numeric) = 2.88055533041 0.120856090409
y[1] (closed_form) = 2.88067422274 0.120795145146
absolute error = 0.0001336
relative error = 0.004634 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.653
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=802.4MB, alloc=52.3MB, time=9.92
x[1] = 2.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = 2.88126783808 0.122047535515
y[1] (closed_form) = 2.8813880884 0.121985593642
absolute error = 0.0001353
relative error = 0.00469 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.655
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1437 0.289
h = 0.003 0.006
y[1] (numeric) = 2.88169316133 0.123751404814
y[1] (closed_form) = 2.8818161069 0.12368935658
absolute error = 0.0001377
relative error = 0.004774 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.655
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = 2.88355999579 0.126030524396
y[1] (closed_form) = 2.88368755539 0.125962458995
absolute error = 0.0001446
relative error = 0.005009 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.659
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=847.6MB, alloc=52.3MB, time=10.48
x[1] = 2.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = 2.88409774305 0.128157366746
y[1] (closed_form) = 2.88422951803 0.128089178621
absolute error = 0.0001484
relative error = 0.005139 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.659
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1469 0.303
h = 0.001 0.001
y[1] (numeric) = 2.88444254242 0.129429296352
y[1] (closed_form) = 2.88457583415 0.129361024016
absolute error = 0.0001498
relative error = 0.005187 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.659
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = 2.8849715532 0.129754905916
y[1] (closed_form) = 2.88510484867 0.129686296428
absolute error = 0.0001499
relative error = 0.005191 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.661
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=892.9MB, alloc=52.3MB, time=11.04
x[1] = 2.148 0.308
h = 0.003 0.006
y[1] (numeric) = 2.88542241677 0.131452608512
y[1] (closed_form) = 2.88555841009 0.131383893482
absolute error = 0.0001524
relative error = 0.005275 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.661
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.151 0.314
h = 0.0001 0.005
y[1] (numeric) = 2.88732363476 0.133704181191
y[1] (closed_form) = 2.88746424927 0.133629444884
absolute error = 0.0001592
relative error = 0.005509 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.664
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = 2.88789336089 0.135823477047
y[1] (closed_form) = 2.88803819513 0.135748619603
absolute error = 0.000163
relative error = 0.005639 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.665
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=938.1MB, alloc=52.3MB, time=11.59
x[1] = 2.1512 0.322
h = 0.001 0.001
y[1] (numeric) = 2.88825729759 0.137090623656
y[1] (closed_form) = 2.88840365019 0.137015682524
absolute error = 0.0001644
relative error = 0.005686 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.665
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1522 0.323
h = 0.001 0.003
y[1] (numeric) = 2.88879135476 0.137408427272
y[1] (closed_form) = 2.88893771123 0.13733314864
absolute error = 0.0001646
relative error = 0.005691 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.666
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = 2.88954235585 0.138576749232
y[1] (closed_form) = 2.88969007416 0.138500472996
absolute error = 0.0001662
relative error = 0.005747 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.668
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=983.5MB, alloc=52.3MB, time=12.15
x[1] = 2.1533 0.33
h = 0.003 0.006
y[1] (numeric) = 2.89002282178 0.140266882533
y[1] (closed_form) = 2.8901732414 0.140190502038
absolute error = 0.0001687
relative error = 0.00583 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.668
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = 2.89196359249 0.142485886713
y[1] (closed_form) = 2.89211864156 0.142403479504
absolute error = 0.0001756
relative error = 0.006064 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.672
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = 2.8925703873 0.144595907914
y[1] (closed_form) = 2.8927296614 0.144513381145
absolute error = 0.0001794
relative error = 0.006194 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.672
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1028.7MB, alloc=52.3MB, time=12.70
x[1] = 2.1565 0.344
h = 0.001 0.001
y[1] (numeric) = 2.89295650337 0.145857193622
y[1] (closed_form) = 2.89311729777 0.145774583673
absolute error = 0.0001808
relative error = 0.00624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.673
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1575 0.345
h = 0.001 0.003
y[1] (numeric) = 2.89349630686 0.146165841069
y[1] (closed_form) = 2.89365710528 0.146082893194
absolute error = 0.0001809
relative error = 0.006245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.674
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = 2.89426795819 0.147321595598
y[1] (closed_form) = 2.89443012056 0.147237649394
absolute error = 0.0001826
relative error = 0.006301 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.675
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1074.1MB, alloc=52.3MB, time=13.26
x[1] = 2.1586 0.352
h = 0.003 0.006
y[1] (numeric) = 2.89477806651 0.149004162697
y[1] (closed_form) = 2.89494293368 0.148920113144
absolute error = 0.0001851
relative error = 0.006384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.675
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = 2.89675845282 0.15119057366
y[1] (closed_form) = 2.89692795767 0.151100491375
absolute error = 0.000192
relative error = 0.006617 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.679
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = 2.89740236689 0.153291322881
y[1] (closed_form) = 2.89757610231 0.153201122395
absolute error = 0.0001958
relative error = 0.006746 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.68
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1119.4MB, alloc=52.3MB, time=13.82
x[1] = 2.1618 0.366
h = 0.001 0.001
y[1] (numeric) = 2.89781069299 0.154546748625
y[1] (closed_form) = 2.89798595073 0.154456465386
absolute error = 0.0001971
relative error = 0.006793 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.68
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1628 0.367
h = 0.001 0.003
y[1] (numeric) = 2.89835625367 0.154846230246
y[1] (closed_form) = 2.89853151555 0.154755608637
absolute error = 0.0001973
relative error = 0.006797 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.681
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = 2.89914858658 0.155989408776
y[1] (closed_form) = 2.89932521456 0.155897787984
absolute error = 0.000199
relative error = 0.006853 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.682
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1164.7MB, alloc=52.3MB, time=14.38
x[1] = 2.1639 0.374
h = 0.003 0.006
y[1] (numeric) = 2.89968837855 0.157664410621
y[1] (closed_form) = 2.89986771497 0.157572687249
absolute error = 0.0002014
relative error = 0.006936 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.683
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = 2.90170844402 0.159818199778
y[1] (closed_form) = 2.90189242631 0.159720437075
absolute error = 0.0002083
relative error = 0.007169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.687
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.167 0.385
h = 0.0001 0.003
y[1] (numeric) = 2.90238952964 0.161909677305
y[1] (closed_form) = 2.90257774827 0.161811797543
absolute error = 0.0002121
relative error = 0.007298 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.687
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1210.1MB, alloc=52.3MB, time=14.93
x[1] = 2.1671 0.388
h = 0.001 0.001
y[1] (numeric) = 2.90282009741 0.163159242573
y[1] (closed_form) = 2.90300984048 0.163061280403
absolute error = 0.0002135
relative error = 0.007344 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.688
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1681 0.389
h = 0.001 0.003
y[1] (numeric) = 2.90337142601 0.163449547893
y[1] (closed_form) = 2.90356117333 0.163351246888
absolute error = 0.0002137
relative error = 0.007348 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.689
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = 2.9041844724 0.164580140093
y[1] (closed_form) = 2.904375588 0.164480838927
absolute error = 0.0002154
relative error = 0.007404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.69
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1255.3MB, alloc=52.3MB, time=15.49
x[1] = 2.1692 0.396
h = 0.003 0.006
y[1] (numeric) = 2.90475399063 0.166247575706
y[1] (closed_form) = 2.90494781845 0.166148172586
absolute error = 0.0002178
relative error = 0.007486 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.691
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = 2.90681379946 0.168368710601
y[1] (closed_form) = 2.9070122813 0.168263260973
absolute error = 0.0002248
relative error = 0.007719 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.694
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = 2.90753211053 0.17045091432
y[1] (closed_form) = 2.90773483472 0.170345348552
absolute error = 0.0002286
relative error = 0.007847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1300.6MB, alloc=52.3MB, time=16.04
x[1] = 2.1724 0.41
h = 0.001 0.001
y[1] (numeric) = 2.90798495261 0.171694617141
y[1] (closed_form) = 2.90818920344 0.171588969228
absolute error = 0.00023
relative error = 0.007893 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = 2.90854205972 0.171975734873
y[1] (closed_form) = 2.90874631489 0.171869747642
absolute error = 0.0002301
relative error = 0.007897 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.696
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1735 0.415
h = 0.003 0.006
y[1] (numeric) = 2.90913729074 0.173637010505
y[1] (closed_form) = 2.90934426134 0.173530921564
absolute error = 0.0002326
relative error = 0.00798 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.697
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1346.0MB, alloc=52.3MB, time=16.60
x[1] = 2.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = 2.91123175075 0.175730483236
y[1] (closed_form) = 2.91144338245 0.175618341244
absolute error = 0.0002395
relative error = 0.008211 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.701
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = 2.91198225922 0.177805145164
y[1] (closed_form) = 2.91219813863 0.177692887719
absolute error = 0.0002433
relative error = 0.00834 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.701
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1767 0.429
h = 0.001 0.001
y[1] (numeric) = 2.91245437102 0.179044064966
y[1] (closed_form) = 2.91267177901 0.178931725564
absolute error = 0.0002447
relative error = 0.008386 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.702
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1391.5MB, alloc=52.3MB, time=17.16
x[1] = 2.1777 0.43
h = 0.001 0.003
y[1] (numeric) = 2.91301657008 0.179317333676
y[1] (closed_form) = 2.91323398248 0.179204654526
absolute error = 0.0002449
relative error = 0.00839 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.703
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = 2.91386839648 0.180424719784
y[1] (closed_form) = 2.91408718128 0.180311038344
absolute error = 0.0002466
relative error = 0.008445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.704
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1436.9MB, alloc=52.3MB, time=17.72
x[1] = 2.1788 0.437
h = 0.003 0.006
y[1] (numeric) = 2.91449343634 0.182078422521
y[1] (closed_form) = 2.91471494079 0.181964639958
absolute error = 0.000249
relative error = 0.008527 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.705
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = 2.91662776116 0.184139171108
y[1] (closed_form) = 2.91685393476 0.184019327249
absolute error = 0.000256
relative error = 0.008758 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.708
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = 2.91741559978 0.186204549539
y[1] (closed_form) = 2.91764602753 0.18608459073
absolute error = 0.0002598
relative error = 0.008886 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.709
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1482.1MB, alloc=52.3MB, time=18.28
x[1] = 2.182 0.451
h = 0.001 0.001
y[1] (numeric) = 2.91791004914 0.187437599735
y[1] (closed_form) = 2.91814200781 0.187317559079
absolute error = 0.0002612
relative error = 0.008932 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.183 0.452
h = 0.001 0.003
y[1] (numeric) = 2.91847804618 0.187701657832
y[1] (closed_form) = 2.91871000932 0.187581276908
absolute error = 0.0002613
relative error = 0.008936 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.711
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.184 0.455
h = 0.0001 0.004
y[1] (numeric) = 2.91935068041 0.188796418726
y[1] (closed_form) = 2.91958401819 0.188675034176
absolute error = 0.000263
relative error = 0.00899 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.712
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1527.4MB, alloc=52.3MB, time=18.84
x[1] = 2.1841 0.459
h = 0.003 0.006
y[1] (numeric) = 2.92000557549 0.19044254227
y[1] (closed_form) = 2.92024163712 0.190321056808
absolute error = 0.0002655
relative error = 0.009072 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.713
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = 2.92217983086 0.192470523238
y[1] (closed_form) = 2.92242056964 0.192342967666
absolute error = 0.0002724
relative error = 0.009302 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.716
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = 2.92300505811 0.19452660913
y[1] (closed_form) = 2.92325005768 0.194398938884
absolute error = 0.0002763
relative error = 0.00943 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.717
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1572.7MB, alloc=52.3MB, time=19.39
x[1] = 2.1873 0.473
h = 0.001 0.001
y[1] (numeric) = 2.92352188031 0.19575378355
y[1] (closed_form) = 2.92376841323 0.195626031481
absolute error = 0.0002777
relative error = 0.009476 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.718
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1883 0.474
h = 0.001 0.003
y[1] (numeric) = 2.92409568547 0.196008617449
y[1] (closed_form) = 2.92434222289 0.195880524574
absolute error = 0.0002778
relative error = 0.009479 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.719
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = 2.92498916138 0.197090736
y[1] (closed_form) = 2.92523707571 0.196961638036
absolute error = 0.0002795
relative error = 0.009534 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.72
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1618.0MB, alloc=52.3MB, time=19.95
x[1] = 2.1894 0.481
h = 0.003 0.006
y[1] (numeric) = 2.92567395912 0.19872927186
y[1] (closed_form) = 2.92592460164 0.198600073049
absolute error = 0.000282
relative error = 0.009615 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.721
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = 2.92788821121 0.200724437897
y[1] (closed_form) = 2.9281435388 0.200589159595
absolute error = 0.000289
relative error = 0.009845 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.724
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = 2.92875088702 0.202771219758
y[1] (closed_form) = 2.92901048228 0.202635826827
absolute error = 0.0002928
relative error = 0.009972 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.725
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1663.2MB, alloc=52.3MB, time=20.51
x[1] = 2.1926 0.495
h = 0.001 0.001
y[1] (numeric) = 2.92929011821 0.203992510745
y[1] (closed_form) = 2.92955124931 0.20385703593
absolute error = 0.0002942
relative error = 0.01002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.726
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1936 0.496
h = 0.001 0.003
y[1] (numeric) = 2.92986974146 0.204238106069
y[1] (closed_form) = 2.93013087709 0.204102289893
absolute error = 0.0002943
relative error = 0.01002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.727
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = 2.93078409333 0.205307563387
y[1] (closed_form) = 2.93104660815 0.205170740533
absolute error = 0.000296
relative error = 0.01008 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.728
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1708.7MB, alloc=52.3MB, time=21.06
x[1] = 2.1947 0.503
h = 0.003 0.006
y[1] (numeric) = 2.93149884234 0.206938501101
y[1] (closed_form) = 2.93176408983 0.206801577314
absolute error = 0.0002985
relative error = 0.01016 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.729
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = 2.93375315768 0.208900801066
y[1] (closed_form) = 2.93402309808 0.208757787846
absolute error = 0.0003055
relative error = 0.01039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.733
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = 2.93465334347 0.210938264943
y[1] (closed_form) = 2.93492755863 0.210795136906
absolute error = 0.0003093
relative error = 0.01051 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.733
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1754.0MB, alloc=52.3MB, time=21.62
x[1] = 2.1979 0.517
h = 0.001 0.001
y[1] (numeric) = 2.93521502065 0.212153663348
y[1] (closed_form) = 2.93549077422 0.212010453282
absolute error = 0.0003107
relative error = 0.01056 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.734
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = 2.93580047178 0.212390004934
y[1] (closed_form) = 2.93607622988 0.212246452934
absolute error = 0.0003109
relative error = 0.01056 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.735
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.199 0.522
h = 0.003 0.006
y[1] (numeric) = 2.93654113251 0.214014750339
y[1] (closed_form) = 2.93681962708 0.213871097042
absolute error = 0.0003134
relative error = 0.01064 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.736
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1799.4MB, alloc=52.3MB, time=22.18
x[1] = 2.202 0.528
h = 0.0001 0.005
y[1] (numeric) = 2.93883037887 0.215949194735
y[1] (closed_form) = 2.93911357316 0.21579944309
absolute error = 0.0003204
relative error = 0.01087 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.739
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = 2.93976301354 0.21797907278
y[1] (closed_form) = 2.94005048886 0.217829206057
absolute error = 0.0003242
relative error = 0.011 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.74
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2022 0.536
h = 0.001 0.001
y[1] (numeric) = 2.9403441121 0.21918965857
y[1] (closed_form) = 2.94063312811 0.219039709655
absolute error = 0.0003256
relative error = 0.01104 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.741
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1844.6MB, alloc=52.3MB, time=22.74
x[1] = 2.2032 0.537
h = 0.001 0.003
y[1] (numeric) = 2.94093469784 0.219418091685
y[1] (closed_form) = 2.94122371837 0.219267800328
absolute error = 0.0003258
relative error = 0.01105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = 2.94188813905 0.22046418275
y[1] (closed_form) = 2.94217854309 0.220312881456
absolute error = 0.0003275
relative error = 0.0111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.743
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2043 0.544
h = 0.003 0.006
y[1] (numeric) = 2.94265884453 0.22208130565
y[1] (closed_form) = 2.94295198992 0.221929902918
absolute error = 0.0003299
relative error = 0.01118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.744
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1889.9MB, alloc=52.3MB, time=23.29
x[1] = 2.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = 2.94498827943 0.223982779464
y[1] (closed_form) = 2.94528613222 0.223825267401
absolute error = 0.0003369
relative error = 0.01141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.748
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = 2.94595854234 0.226003307744
y[1] (closed_form) = 2.94626068364 0.22584567998
absolute error = 0.0003408
relative error = 0.01153 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.749
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2075 0.558
h = 0.001 0.001
y[1] (numeric) = 2.94656215806 0.227207980406
y[1] (closed_form) = 2.94686584275 0.227050270142
absolute error = 0.0003422
relative error = 0.01158 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.749
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1935.2MB, alloc=52.3MB, time=23.85
x[1] = 2.2085 0.559
h = 0.001 0.003
y[1] (numeric) = 2.94715858954 0.227427129606
y[1] (closed_form) = 2.94746227873 0.227269076295
absolute error = 0.0003424
relative error = 0.01158 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.75
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = 2.94813300723 0.228460496101
y[1] (closed_form) = 2.94843808226 0.228301430909
absolute error = 0.0003441
relative error = 0.01163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.752
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2096 0.566
h = 0.003 0.006
y[1] (numeric) = 2.94893380943 0.230069980585
y[1] (closed_form) = 2.94924163066 0.229910813436
absolute error = 0.0003465
relative error = 0.01171 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.753
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1980.7MB, alloc=52.3MB, time=24.41
x[1] = 2.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = 2.95130350019 0.231938421788
y[1] (closed_form) = 2.9516160364 0.231773133772
absolute error = 0.0003536
relative error = 0.01194 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.756
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = 2.95231145673 0.23394957927
y[1] (closed_form) = 2.95262828913 0.233784174693
absolute error = 0.0003574
relative error = 0.01207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.757
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2128 0.58
h = 0.001 0.001
y[1] (numeric) = 2.95293762893 0.235148325368
y[1] (closed_form) = 2.9532560075 0.234982837896
absolute error = 0.0003588
relative error = 0.01211 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.758
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2026.0MB, alloc=52.3MB, time=24.96
x[1] = 2.2138 0.581
h = 0.001 0.003
y[1] (numeric) = 2.95353991534 0.23535817327
y[1] (closed_form) = 2.95385829836 0.235192342129
absolute error = 0.000359
relative error = 0.01211 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.759
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = 2.95453534526 0.236378789521
y[1] (closed_form) = 2.95485511645 0.236211944431
absolute error = 0.0003607
relative error = 0.01217 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.76
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2149 0.588
h = 0.003 0.006
y[1] (numeric) = 2.95536629702 0.237980617452
y[1] (closed_form) = 2.9556888194 0.237813669731
absolute error = 0.0003632
relative error = 0.01225 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.761
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2071.4MB, alloc=52.3MB, time=25.52
x[1] = 2.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = 2.95777631111 0.239815960232
y[1] (closed_form) = 2.95810355594 0.23964287956
absolute error = 0.0003702
relative error = 0.01247 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.765
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.218 0.599
h = 0.0001 0.003
y[1] (numeric) = 2.95882202798 0.241817723385
y[1] (closed_form) = 2.95915357687 0.241644525051
absolute error = 0.0003741
relative error = 0.0126 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.766
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2181 0.602
h = 0.001 0.001
y[1] (numeric) = 2.95947079673 0.243010527972
y[1] (closed_form) = 2.95980389464 0.24283724626
absolute error = 0.0003755
relative error = 0.01264 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.767
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2116.7MB, alloc=52.3MB, time=26.08
x[1] = 2.2191 0.603
h = 0.001 0.003
y[1] (numeric) = 2.96007894705 0.243211056431
y[1] (closed_form) = 2.96041204934 0.243037430412
absolute error = 0.0003756
relative error = 0.01265 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.768
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = 2.96109542522 0.24421889501
y[1] (closed_form) = 2.96142991804 0.24404425285
absolute error = 0.0003773
relative error = 0.0127 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.769
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2202 0.61
h = 0.003 0.006
y[1] (numeric) = 2.96195658043 0.245813046243
y[1] (closed_form) = 2.96229382953 0.245638300623
absolute error = 0.0003798
relative error = 0.01278 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2162.0MB, alloc=52.3MB, time=26.64
x[1] = 2.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = 2.96440698542 0.247615221017
y[1] (closed_form) = 2.96474896433 0.247434329816
absolute error = 0.0003869
relative error = 0.013 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.774
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = 2.96549053058 0.249607563805
y[1] (closed_form) = 2.96583682162 0.249426553601
absolute error = 0.0003907
relative error = 0.01313 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.775
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2234 0.624
h = 0.001 0.001
y[1] (numeric) = 2.96616193669 0.25079441042
y[1] (closed_form) = 2.96650977966 0.250613316266
absolute error = 0.0003922
relative error = 0.01317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.775
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2207.4MB, alloc=52.3MB, time=27.19
x[1] = 2.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = 2.96677595964 0.250985600533
y[1] (closed_form) = 2.96712380691 0.250804161415
absolute error = 0.0003923
relative error = 0.01318 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.776
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2245 0.629
h = 0.003 0.006
y[1] (numeric) = 2.96766324883 0.252573487144
y[1] (closed_form) = 2.96801385672 0.252391943574
absolute error = 0.0003948
relative error = 0.01325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.777
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = 2.97014887142 0.254347535649
y[1] (closed_form) = 2.97050421552 0.254159835276
absolute error = 0.0004019
relative error = 0.01348 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.781
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2252.7MB, alloc=52.3MB, time=27.75
x[1] = 2.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = 2.97126514595 0.256332198668
y[1] (closed_form) = 2.9716248093 0.256144378043
absolute error = 0.0004058
relative error = 0.0136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.782
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2277 0.643
h = 0.001 0.001
y[1] (numeric) = 2.97195614203 0.257514172847
y[1] (closed_form) = 2.97231735988 0.257326267742
absolute error = 0.0004072
relative error = 0.01365 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.783
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2287 0.644
h = 0.001 0.003
y[1] (numeric) = 2.97257533832 0.257697379203
y[1] (closed_form) = 2.97293656038 0.257509128558
absolute error = 0.0004073
relative error = 0.01365 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.784
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2298.1MB, alloc=52.3MB, time=28.31
x[1] = 2.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = 2.97363123232 0.258681614279
y[1] (closed_form) = 2.97399384932 0.258492343115
absolute error = 0.000409
relative error = 0.0137 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.785
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2298 0.651
h = 0.003 0.006
y[1] (numeric) = 2.97454882792 0.260261781797
y[1] (closed_form) = 2.97491421104 0.260072405279
absolute error = 0.0004115
relative error = 0.01378 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.786
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = 2.97707496819 0.262002523638
y[1] (closed_form) = 2.97744509465 0.261806976682
absolute error = 0.0004186
relative error = 0.01401 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2343.5MB, alloc=52.3MB, time=28.86
x[1] = 2.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = 2.97822920108 0.263977711999
y[1] (closed_form) = 2.97860365521 0.263782042997
absolute error = 0.0004225
relative error = 0.01413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.791
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.233 0.665
h = 0.001 0.001
y[1] (numeric) = 2.97894291258 0.265153694033
y[1] (closed_form) = 2.97931892423 0.264957939813
absolute error = 0.0004239
relative error = 0.01417 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.792
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.234 0.666
h = 0.001 0.003
y[1] (numeric) = 2.97956799732 0.265327524973
y[1] (closed_form) = 2.97994401308 0.265131424528
absolute error = 0.0004241
relative error = 0.01418 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.793
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2388.9MB, alloc=52.3MB, time=29.42
x[1] = 2.235 0.669
h = 0.0001 0.004
y[1] (numeric) = 2.98064504455 0.2662988947
y[1] (closed_form) = 2.98102245763 0.266101771193
absolute error = 0.0004258
relative error = 0.01423 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.794
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2351 0.673
h = 0.003 0.006
y[1] (numeric) = 2.98159300336 0.267871317437
y[1] (closed_form) = 2.98197318799 0.2676740873
absolute error = 0.0004283
relative error = 0.01431 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.795
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = 2.98415972895 0.269578672326
y[1] (closed_form) = 2.98454466392 0.269375257578
absolute error = 0.0004354
relative error = 0.01453 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.799
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2434.3MB, alloc=52.3MB, time=29.98
x[1] = 2.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = 2.9853519916 0.271544352804
y[1] (closed_form) = 2.98574126285 0.271340813971
absolute error = 0.0004393
relative error = 0.01465 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.8
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2383 0.687
h = 0.001 0.001
y[1] (numeric) = 2.9860884613 0.272714321884
y[1] (closed_form) = 2.98647929316 0.272510697004
absolute error = 0.0004407
relative error = 0.0147 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.801
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2393 0.688
h = 0.001 0.003
y[1] (numeric) = 2.98671944252 0.27287875637
y[1] (closed_form) = 2.98711027834 0.272674784565
absolute error = 0.0004409
relative error = 0.0147 %
Correct digits = 4
memory used=2479.8MB, alloc=52.3MB, time=30.54
Radius of convergence (given) for eq 1 = 3.802
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = 2.98781767999 0.273837226589
y[1] (closed_form) = 2.98820991551 0.273632229056
absolute error = 0.0004426
relative error = 0.01475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.804
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2404 0.695
h = 0.003 0.006
y[1] (numeric) = 2.98879605954 0.275401876612
y[1] (closed_form) = 2.98919107217 0.275196771013
absolute error = 0.0004451
relative error = 0.01483 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.804
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2525.1MB, alloc=52.3MB, time=31.10
x[1] = 2.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = 2.99140343799 0.277075760546
y[1] (closed_form) = 2.99180320781 0.276864455634
absolute error = 0.0004522
relative error = 0.01505 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.808
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = 2.9926338029 0.279031897388
y[1] (closed_form) = 2.99303791779 0.278820466105
absolute error = 0.0004561
relative error = 0.01517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.809
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2436 0.709
h = 0.001 0.001
y[1] (numeric) = 2.99339307424 0.280195831176
y[1] (closed_form) = 2.99379875291 0.279984312927
absolute error = 0.0004575
relative error = 0.01522 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2570.4MB, alloc=52.3MB, time=31.66
x[1] = 2.2446 0.71
h = 0.001 0.003
y[1] (numeric) = 2.99402995968 0.280350847439
y[1] (closed_form) = 2.99443564214 0.28013898155
absolute error = 0.0004577
relative error = 0.01522 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.811
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = 2.9951494246 0.281296382253
y[1] (closed_form) = 2.99555650914 0.281083487849
absolute error = 0.0004594
relative error = 0.01527 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.813
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2457 0.717
h = 0.003 0.006
y[1] (numeric) = 2.99615828327 0.2828532296
y[1] (closed_form) = 2.99656815059 0.282640225533
absolute error = 0.0004619
relative error = 0.01535 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.814
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2615.7MB, alloc=52.3MB, time=32.21
x[1] = 2.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = 2.99880638198 0.284493554879
y[1] (closed_form) = 2.99922101319 0.284274336271
absolute error = 0.000469
relative error = 0.01557 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = 3.00007492274 0.286440109799
y[1] (closed_form) = 3.00049390797 0.286220762285
absolute error = 0.0004729
relative error = 0.01569 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2489 0.731
h = 0.001 0.001
y[1] (numeric) = 3.00085703978 0.287597984428
y[1] (closed_form) = 3.00127759201 0.287378548936
absolute error = 0.0004744
relative error = 0.01573 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2661.0MB, alloc=52.3MB, time=32.77
x[1] = 2.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = 3.00149983689 0.287743559972
y[1] (closed_form) = 3.00192039274 0.287523776112
absolute error = 0.0004745
relative error = 0.01574 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.25 0.736
h = 0.003 0.006
y[1] (numeric) = 3.00253507201 0.28929402973
y[1] (closed_form) = 3.00295841546 0.289074134562
absolute error = 0.000477
relative error = 0.01581 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.253 0.742
h = 0.0001 0.005
y[1] (numeric) = 3.00521867643 0.290905881949
y[1] (closed_form) = 3.00564678961 0.29067975879
absolute error = 0.0004842
relative error = 0.01603 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2706.4MB, alloc=52.3MB, time=33.32
x[1] = 2.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = 3.0065202522 0.292844612435
y[1] (closed_form) = 3.00695272729 0.292618358097
absolute error = 0.0004881
relative error = 0.01616 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2532 0.75
h = 0.001 0.001
y[1] (numeric) = 3.0073221424 0.293997524122
y[1] (closed_form) = 3.00775618731 0.293771180901
absolute error = 0.0004895
relative error = 0.0162 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2542 0.751
h = 0.001 0.003
y[1] (numeric) = 3.00797014667 0.294135025384
y[1] (closed_form) = 3.00840419504 0.293908333153
absolute error = 0.0004897
relative error = 0.0162 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2751.8MB, alloc=52.3MB, time=33.88
x[1] = 2.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = 3.00912936565 0.295056642877
y[1] (closed_form) = 3.00956482055 0.294828916651
absolute error = 0.0004914
relative error = 0.01625 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = 3.01019519099 0.296599249295
y[1] (closed_form) = 3.01063343952 0.296371410078
absolute error = 0.0004939
relative error = 0.01633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2554 0.762
h = 0.003 0.006
y[1] (numeric) = 3.0112666036 0.298141629022
y[1] (closed_form) = 3.01170764677 0.297913676962
absolute error = 0.0004965
relative error = 0.0164 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2797.2MB, alloc=52.3MB, time=34.44
x[1] = 2.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = 3.01399937646 0.299715426438
y[1] (closed_form) = 3.01444519749 0.29948122757
absolute error = 0.0005036
relative error = 0.01662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = 3.01534625949 0.301644247084
y[1] (closed_form) = 3.01579645344 0.301409913841
absolute error = 0.0005075
relative error = 0.01675 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2586 0.776
h = 0.001 0.001
y[1] (numeric) = 3.01617527521 0.302790844954
y[1] (closed_form) = 3.01662704294 0.302556421558
absolute error = 0.000509
relative error = 0.01679 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.838
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2842.6MB, alloc=52.3MB, time=35.00
x[1] = 2.2596 0.777
h = 0.001 0.003
y[1] (numeric) = 3.01683058206 0.302917439705
y[1] (closed_form) = 3.01728235302 0.302682666404
absolute error = 0.0005091
relative error = 0.01679 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = 3.01801531359 0.303824542716
y[1] (closed_form) = 3.01846849399 0.303588731821
absolute error = 0.0005109
relative error = 0.01684 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2607 0.784
h = 0.003 0.006
y[1] (numeric) = 3.01911738916 0.305359019689
y[1] (closed_form) = 3.01957337029 0.305123093599
absolute error = 0.0005134
relative error = 0.01692 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2887.9MB, alloc=52.3MB, time=35.56
x[1] = 2.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = 3.02189109029 0.306898973231
y[1] (closed_form) = 3.02235185553 0.306656783524
absolute error = 0.0005205
relative error = 0.01713 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = 3.0232763809 0.308818084051
y[1] (closed_form) = 3.02374152852 0.308575756679
absolute error = 0.0005245
relative error = 0.01726 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2639 0.798
h = 0.001 0.001
y[1] (numeric) = 3.02412838098 0.309958543231
y[1] (closed_form) = 3.02459510577 0.309716124419
absolute error = 0.0005259
relative error = 0.0173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.848
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2933.3MB, alloc=52.3MB, time=36.12
x[1] = 2.2649 0.799
h = 0.001 0.003
y[1] (numeric) = 3.02478962155 0.310075624968
y[1] (closed_form) = 3.02525634935 0.309832855478
absolute error = 0.0005261
relative error = 0.0173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = 3.02599573415 0.310969632116
y[1] (closed_form) = 3.02646387375 0.310725821758
absolute error = 0.0005278
relative error = 0.01735 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.266 0.806
h = 0.003 0.006
y[1] (numeric) = 3.02712853444 0.312496167917
y[1] (closed_form) = 3.02759948087 0.312252240119
absolute error = 0.0005304
relative error = 0.01743 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.851
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2978.6MB, alloc=52.3MB, time=36.69
x[1] = 2.269 0.812
h = 0.0001 0.005
y[1] (numeric) = 3.02994323036 0.314002175139
y[1] (closed_form) = 3.03041896697 0.313751966406
absolute error = 0.0005375
relative error = 0.01764 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = 3.0313670062 0.315911527637
y[1] (closed_form) = 3.03184713482 0.315661177697
absolute error = 0.0005415
relative error = 0.01776 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2692 0.82
h = 0.001 0.001
y[1] (numeric) = 3.03224203704 0.317045818096
y[1] (closed_form) = 3.03272374628 0.316795375333
absolute error = 0.0005429
relative error = 0.01781 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3024.0MB, alloc=52.3MB, time=37.24
x[1] = 2.2702 0.821
h = 0.001 0.003
y[1] (numeric) = 3.03290921761 0.317153361451
y[1] (closed_form) = 3.0333909296 0.316902567225
absolute error = 0.0005431
relative error = 0.01781 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.859
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = 3.03413674914 0.318034228184
y[1] (closed_form) = 3.0346198753 0.317782389698
absolute error = 0.0005448
relative error = 0.01786 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2713 0.828
h = 0.003 0.006
y[1] (numeric) = 3.03530033653 0.319552782623
y[1] (closed_form) = 3.03578627572 0.319300824289
absolute error = 0.0005474
relative error = 0.01793 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3069.3MB, alloc=52.3MB, time=37.80
x[1] = 2.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = 3.03815609336 0.321024737472
y[1] (closed_form) = 3.03864682862 0.32076648038
absolute error = 0.0005545
relative error = 0.01815 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = 3.03961843297 0.322924280606
y[1] (closed_form) = 3.04011357002 0.322665878507
absolute error = 0.0005585
relative error = 0.01827 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2745 0.842
h = 0.001 0.001
y[1] (numeric) = 3.04051654148 0.324052370771
y[1] (closed_form) = 3.04101326266 0.323793874375
absolute error = 0.00056
relative error = 0.01831 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3114.6MB, alloc=52.3MB, time=38.36
x[1] = 2.2755 0.843
h = 0.001 0.003
y[1] (numeric) = 3.04118966801 0.324150349686
y[1] (closed_form) = 3.04168639166 0.323891501027
absolute error = 0.0005601
relative error = 0.01831 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.868
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = 3.04243865639 0.325018029747
y[1] (closed_form) = 3.04293679656 0.324758133318
absolute error = 0.0005619
relative error = 0.01836 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2766 0.85
h = 0.003 0.006
y[1] (numeric) = 3.04363309394 0.326528560592
y[1] (closed_form) = 3.04413405343 0.326268541742
absolute error = 0.0005644
relative error = 0.01844 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3159.9MB, alloc=52.3MB, time=38.92
x[1] = 2.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = 3.04652997737 0.327966353429
y[1] (closed_form) = 3.04703573864 0.327700017497
absolute error = 0.0005716
relative error = 0.01865 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = 3.04803096013 0.329856033602
y[1] (closed_form) = 3.04854113313 0.32958954861
absolute error = 0.0005756
relative error = 0.01877 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.877
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2798 0.864
h = 0.001 0.001
y[1] (numeric) = 3.0489521937 0.330977890365
y[1] (closed_form) = 3.04946395438 0.330711309507
absolute error = 0.000577
relative error = 0.01881 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.877
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3205.3MB, alloc=52.3MB, time=39.48
x[1] = 2.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = 3.04963127182 0.331066278096
y[1] (closed_form) = 3.05014303467 0.330799344164
absolute error = 0.0005772
relative error = 0.01881 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2809 0.869
h = 0.003 0.006
y[1] (numeric) = 3.05085241163 0.332570235842
y[1] (closed_form) = 3.05136699913 0.332303177013
absolute error = 0.0005798
relative error = 0.01889 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = 3.05378515649 0.333979023594
y[1] (closed_form) = 3.05430455077 0.333705631578
absolute error = 0.000587
relative error = 0.0191 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.884
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3250.7MB, alloc=52.3MB, time=40.04
x[1] = 2.284 0.88
h = 0.0001 0.003
y[1] (numeric) = 3.05531958459 0.335860630814
y[1] (closed_form) = 3.05584339931 0.335587086162
absolute error = 0.0005909
relative error = 0.01922 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.885
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2841 0.883
h = 0.001 0.001
y[1] (numeric) = 3.05626083656 0.336977370624
y[1] (closed_form) = 3.05678624208 0.336703728725
absolute error = 0.0005924
relative error = 0.01926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.886
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2851 0.884
h = 0.001 0.003
y[1] (numeric) = 3.05694515655 0.337057551632
y[1] (closed_form) = 3.05747056397 0.336783555946
absolute error = 0.0005926
relative error = 0.01926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3296.2MB, alloc=52.3MB, time=40.59
x[1] = 2.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = 3.05823433053 0.337900822116
y[1] (closed_form) = 3.0587611589 0.337625771841
absolute error = 0.0005943
relative error = 0.01931 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.889
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2862 0.891
h = 0.003 0.006
y[1] (numeric) = 3.05948643993 0.3393966728
y[1] (closed_form) = 3.06001609959 0.339121494954
absolute error = 0.0005969
relative error = 0.01939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = 3.06246043374 0.340771085821
y[1] (closed_form) = 3.06299490552 0.340489555542
absolute error = 0.0006041
relative error = 0.0196 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.894
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3341.4MB, alloc=52.3MB, time=41.15
x[1] = 2.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = 3.06403365555 0.342642724531
y[1] (closed_form) = 3.06457255798 0.342361037087
absolute error = 0.0006081
relative error = 0.01972 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.895
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2894 0.905
h = 0.001 0.001
y[1] (numeric) = 3.06499812242 0.343753165812
y[1] (closed_form) = 3.0655386193 0.343471379377
absolute error = 0.0006095
relative error = 0.01976 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.896
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2904 0.906
h = 0.001 0.003
y[1] (numeric) = 3.06568840388 0.343823704135
y[1] (closed_form) = 3.06622890233 0.343541563079
absolute error = 0.0006097
relative error = 0.01976 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3386.8MB, alloc=52.3MB, time=41.72
x[1] = 2.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = 3.06699914384 0.344653646723
y[1] (closed_form) = 3.06754106556 0.344370447231
absolute error = 0.0006115
relative error = 0.01981 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2915 0.913
h = 0.003 0.006
y[1] (numeric) = 3.06828228787 0.346141342473
y[1] (closed_form) = 3.06882704744 0.345858012364
absolute error = 0.000614
relative error = 0.01988 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = 3.07129759488 0.347481260973
y[1] (closed_form) = 3.07184717172 0.347191558696
absolute error = 0.0006213
relative error = 0.0201 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.904
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3432.2MB, alloc=52.3MB, time=42.27
x[1] = 2.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = 3.07290969205 0.34934287029
y[1] (closed_form) = 3.07346370988 0.349053006059
absolute error = 0.0006253
relative error = 0.02021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.905
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2947 0.927
h = 0.001 0.001
y[1] (numeric) = 3.07389742248 0.350446975535
y[1] (closed_form) = 3.07445303845 0.350157010477
absolute error = 0.0006267
relative error = 0.02025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.906
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2957 0.928
h = 0.001 0.003
y[1] (numeric) = 3.07459367007 0.350507842508
y[1] (closed_form) = 3.07514928725 0.350217521983
absolute error = 0.0006269
relative error = 0.02025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.907
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3477.5MB, alloc=52.3MB, time=42.83
x[1] = 2.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = 3.0759260139 0.35132440443
y[1] (closed_form) = 3.07648305667 0.351033021505
absolute error = 0.0006286
relative error = 0.0203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.909
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2968 0.935
h = 0.003 0.006
y[1] (numeric) = 3.077240258 0.352803895123
y[1] (closed_form) = 3.07780014526 0.35251237837
absolute error = 0.0006312
relative error = 0.02038 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = 3.08029694186 0.354109195806
y[1] (closed_form) = 3.08086165133 0.353811286668
absolute error = 0.0006385
relative error = 0.02059 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.915
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3523.0MB, alloc=52.3MB, time=43.38
x[1] = 2.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = 3.08194799672 0.355960712296
y[1] (closed_form) = 3.08251715765 0.355662636155
absolute error = 0.0006425
relative error = 0.02071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.916
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3 0.949
h = 0.001 0.001
y[1] (numeric) = 3.08295903979 0.357058442464
y[1] (closed_form) = 3.0835298026 0.356760263563
absolute error = 0.000644
relative error = 0.02075 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.301 0.95
h = 0.001 0.003
y[1] (numeric) = 3.08366125778 0.357109608767
y[1] (closed_form) = 3.08423202144 0.356811073542
absolute error = 0.0006441
relative error = 0.02075 %
Correct digits = 4
memory used=3568.4MB, alloc=52.3MB, time=43.94
Radius of convergence (given) for eq 1 = 3.918
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.302 0.953
h = 0.0001 0.004
y[1] (numeric) = 3.08501524332 0.35791273558
y[1] (closed_form) = 3.08558743486 0.357613133876
absolute error = 0.0006459
relative error = 0.02079 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.92
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3021 0.957
h = 0.003 0.006
y[1] (numeric) = 3.08636065347 0.359383969051
y[1] (closed_form) = 3.08693569621 0.359084230141
absolute error = 0.0006485
relative error = 0.02087 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.921
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3613.8MB, alloc=52.3MB, time=44.50
x[1] = 2.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = 3.08945877718 0.360654525138
y[1] (closed_form) = 3.09003864687 0.360348373147
absolute error = 0.0006557
relative error = 0.02108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.925
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = 3.09114887274 0.362495882817
y[1] (closed_form) = 3.09173320451 0.362189558516
absolute error = 0.0006598
relative error = 0.02119 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.926
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3053 0.971
h = 0.001 0.001
y[1] (numeric) = 3.09218327789 0.36358719733
y[1] (closed_form) = 3.09276921531 0.363280768242
absolute error = 0.0006612
relative error = 0.02123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.927
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3659.3MB, alloc=52.3MB, time=45.06
x[1] = 2.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = 3.09289147021 0.363628632993
y[1] (closed_form) = 3.09347740809 0.363321846711
absolute error = 0.0006614
relative error = 0.02123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.928
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3064 0.976
h = 0.003 0.006
y[1] (numeric) = 3.09426385969 0.365093088119
y[1] (closed_form) = 3.09485265448 0.364786161469
absolute error = 0.000664
relative error = 0.02131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.93
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = 3.09739811937 0.366334127691
y[1] (closed_form) = 3.09799174526 0.36602076982
absolute error = 0.0006713
relative error = 0.02152 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.934
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3704.6MB, alloc=52.3MB, time=45.62
x[1] = 2.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = 3.09912200896 0.368167152632
y[1] (closed_form) = 3.09972010621 0.3678536178
absolute error = 0.0006753
relative error = 0.02163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.935
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3096 0.99
h = 0.001 0.001
y[1] (numeric) = 3.10017664038 0.369253190193
y[1] (closed_form) = 3.1007763466 0.368939548799
absolute error = 0.0006768
relative error = 0.02167 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.936
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3106 0.991
h = 0.001 0.003
y[1] (numeric) = 3.10089009447 0.369286296779
y[1] (closed_form) = 3.10148980081 0.368972297431
absolute error = 0.0006769
relative error = 0.02167 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.937
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3750.0MB, alloc=52.3MB, time=46.18
x[1] = 2.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = 3.10228461223 0.370064532258
y[1] (closed_form) = 3.10288575073 0.369749458565
absolute error = 0.0006787
relative error = 0.02172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.939
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3117 0.998
h = 0.003 0.006
y[1] (numeric) = 3.10368829234 0.37152062826
y[1] (closed_form) = 3.10429229481 0.371205410708
absolute error = 0.0006813
relative error = 0.02179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.94
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = 3.10686410885 0.372726678869
y[1] (closed_form) = 3.10747294675 0.372405008521
absolute error = 0.0006886
relative error = 0.022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.945
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3795.5MB, alloc=52.3MB, time=46.74
x[1] = 2.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = 3.10862719612 0.374549416447
y[1] (closed_form) = 3.10924051623 0.374227563348
absolute error = 0.0006926
relative error = 0.02212 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.946
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3149 1.012
h = 0.001 0.001
y[1] (numeric) = 3.10970528308 0.375628959362
y[1] (closed_form) = 3.11032021602 0.375306997496
absolute error = 0.0006941
relative error = 0.02216 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.947
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3159 1.013
h = 0.001 0.003
y[1] (numeric) = 3.11042471818 0.375652277877
y[1] (closed_form) = 3.11103965079 0.375329957167
absolute error = 0.0006943
relative error = 0.02216 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.948
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3840.9MB, alloc=52.3MB, time=47.30
x[1] = 2.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = 3.11184098606 0.376416913796
y[1] (closed_form) = 3.1124573531 0.376093514335
absolute error = 0.0006961
relative error = 0.0222 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.317 1.02
h = 0.003 0.006
y[1] (numeric) = 3.11327602436 0.377864592876
y[1] (closed_form) = 3.11389526232 0.377541045699
absolute error = 0.0006987
relative error = 0.02227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.951
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.32 1.026
h = 0.0001 0.005
y[1] (numeric) = 3.11649345867 0.379035517897
y[1] (closed_form) = 3.11711753614 0.378705495883
absolute error = 0.000706
relative error = 0.02248 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.955
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3886.2MB, alloc=52.3MB, time=47.85
x[1] = 2.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = 3.11829582838 0.380847894855
y[1] (closed_form) = 3.11892439903 0.380517684038
absolute error = 0.00071
relative error = 0.0226 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.957
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3202 1.034
h = 0.001 0.001
y[1] (numeric) = 3.1193974213 0.381920898164
y[1] (closed_form) = 3.12002760868 0.381590576281
absolute error = 0.0007115
relative error = 0.02264 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.958
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3212 1.035
h = 0.001 0.003
y[1] (numeric) = 3.12012284024 0.381934396817
y[1] (closed_form) = 3.12075302685 0.381603715192
absolute error = 0.0007117
relative error = 0.02264 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.959
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3931.6MB, alloc=52.3MB, time=48.42
x[1] = 2.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = 3.12156089566 0.382685372359
y[1] (closed_form) = 3.12219251892 0.382353607464
absolute error = 0.0007135
relative error = 0.02268 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.961
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3223 1.042
h = 0.003 0.006
y[1] (numeric) = 3.12302735998 0.384124574483
y[1] (closed_form) = 3.12366186117 0.383792657846
absolute error = 0.0007161
relative error = 0.02275 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.962
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = 3.12628647223 0.385260233899
y[1] (closed_form) = 3.12692581681 0.384921819923
absolute error = 0.0007234
relative error = 0.02296 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.966
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3977.0MB, alloc=52.3MB, time=48.97
x[1] = 2.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = 3.12812820968 0.38706217444
y[1] (closed_form) = 3.1287720585 0.386723565345
absolute error = 0.0007275
relative error = 0.02308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.968
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3255 1.056
h = 0.001 0.001
y[1] (numeric) = 3.12925335927 0.388128591653
y[1] (closed_form) = 3.12989882877 0.3877898691
absolute error = 0.0007289
relative error = 0.02311 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.969
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3265 1.057
h = 0.001 0.003
y[1] (numeric) = 3.12998476451 0.388132238036
y[1] (closed_form) = 3.13063023277 0.38779315483
absolute error = 0.0007291
relative error = 0.02311 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4022.2MB, alloc=52.3MB, time=49.53
x[1] = 2.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = 3.13144464473 0.388869490751
y[1] (closed_form) = 3.13209155184 0.388529319645
absolute error = 0.0007309
relative error = 0.02316 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.972
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3276 1.064
h = 0.003 0.006
y[1] (numeric) = 3.13294260326 0.390300153852
y[1] (closed_form) = 3.13359239539 0.389959826809
absolute error = 0.0007335
relative error = 0.02323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.973
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = 3.13624345276 0.391400404274
y[1] (closed_form) = 3.13689809191 0.391053556936
absolute error = 0.0007408
relative error = 0.02344 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.977
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4067.7MB, alloc=52.3MB, time=50.09
x[1] = 2.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = 3.13812464374 0.393191830063
y[1] (closed_form) = 3.13878379832 0.392844781031
absolute error = 0.0007449
relative error = 0.02355 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.979
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3308 1.078
h = 0.001 0.001
y[1] (numeric) = 3.13927340099 0.394251613166
y[1] (closed_form) = 3.13993418024 0.393904448185
absolute error = 0.0007464
relative error = 0.02359 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = 3.14001079459 0.394245374256
y[1] (closed_form) = 3.14067157209 0.393897847702
absolute error = 0.0007466
relative error = 0.02359 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.981
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4113.1MB, alloc=52.3MB, time=50.64
x[1] = 2.3319 1.083
h = 0.003 0.006
y[1] (numeric) = 3.14153602015 0.395669012463
y[1] (closed_form) = 3.14219968869 0.395321326119
absolute error = 0.0007492
relative error = 0.02366 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.982
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = 3.14487326669 0.396739164746
y[1] (closed_form) = 3.14554178545 0.396384938025
absolute error = 0.0007566
relative error = 0.02386 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.987
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.335 1.094
h = 0.0001 0.003
y[1] (numeric) = 3.14678861356 0.398521946495
y[1] (closed_form) = 3.14746165756 0.398167512342
absolute error = 0.0007607
relative error = 0.02398 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.988
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4158.5MB, alloc=52.3MB, time=51.20
x[1] = 2.3351 1.097
h = 0.001 0.001
y[1] (numeric) = 3.14795781237 0.399576261608
y[1] (closed_form) = 3.14863248451 0.399221709335
absolute error = 0.0007622
relative error = 0.02401 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.989
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3361 1.098
h = 0.001 0.003
y[1] (numeric) = 3.14870048018 0.39956155822
y[1] (closed_form) = 3.14937515015 0.399206643571
absolute error = 0.0007623
relative error = 0.02401 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.99
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = 3.15020123503 0.400273365214
y[1] (closed_form) = 3.15087734797 0.399917353777
absolute error = 0.0007641
relative error = 0.02406 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.992
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4203.9MB, alloc=52.3MB, time=51.76
x[1] = 2.3372 1.105
h = 0.003 0.006
y[1] (numeric) = 3.1517580833 0.401688344131
y[1] (closed_form) = 3.15243709469 0.40133216859
absolute error = 0.0007668
relative error = 0.02413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.993
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = 3.15513717687 0.402722812406
y[1] (closed_form) = 3.15582104166 0.402360072695
absolute error = 0.0007741
relative error = 0.02433 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.998
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = 3.15709213912 0.404494927941
y[1] (closed_form) = 3.15778054053 0.404131973733
absolute error = 0.0007782
relative error = 0.02445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.999
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4249.2MB, alloc=52.3MB, time=52.32
x[1] = 2.3404 1.119
h = 0.001 0.001
y[1] (numeric) = 3.15828504174 0.405542516158
y[1] (closed_form) = 3.15897507535 0.405179441162
absolute error = 0.0007797
relative error = 0.02448 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3414 1.12
h = 0.001 0.003
y[1] (numeric) = 3.15903370106 0.405517864439
y[1] (closed_form) = 3.15972373195 0.40515442613
absolute error = 0.0007799
relative error = 0.02448 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.001
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = 3.16055638699 0.406215761463
y[1] (closed_form) = 3.16124786299 0.405851221418
absolute error = 0.0007817
relative error = 0.02453 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.003
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4294.8MB, alloc=52.3MB, time=52.88
x[1] = 2.3425 1.127
h = 0.003 0.006
y[1] (numeric) = 3.1621449274 0.407622013422
y[1] (closed_form) = 3.16283930913 0.407257304596
absolute error = 0.0007843
relative error = 0.0246 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.004
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = 3.1655659247 0.408620644788
y[1] (closed_form) = 3.16626516276 0.408249347557
absolute error = 0.0007917
relative error = 0.0248 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.009
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = 3.16756058938 0.410382008545
y[1] (closed_form) = 3.16826437555 0.41001048949
absolute error = 0.0007958
relative error = 0.02491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.01
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4340.1MB, alloc=52.3MB, time=53.44
x[1] = 2.3457 1.141
h = 0.001 0.001
y[1] (numeric) = 3.1687772475 0.411422817502
y[1] (closed_form) = 3.16948266995 0.411051174896
absolute error = 0.0007973
relative error = 0.02495 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.011
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3467 1.142
h = 0.001 0.003
y[1] (numeric) = 3.16953189921 0.411388182713
y[1] (closed_form) = 3.17023731839 0.411016175848
absolute error = 0.0007975
relative error = 0.02495 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.013
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = 3.17107655267 0.412072101102
y[1] (closed_form) = 3.17178341908 0.411698987445
absolute error = 0.0007993
relative error = 0.02499 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.014
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4385.5MB, alloc=52.3MB, time=54.00
x[1] = 2.3478 1.149
h = 0.003 0.006
y[1] (numeric) = 3.17269685474 0.41346955622
y[1] (closed_form) = 3.17340663422 0.413096268936
absolute error = 0.000802
relative error = 0.02506 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.016
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = 3.17615981149 0.414432194502
y[1] (closed_form) = 3.17687444997 0.414052294141
absolute error = 0.0008093
relative error = 0.02526 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = 3.17819426602 0.4161827184
y[1] (closed_form) = 3.17891346419 0.415802588625
absolute error = 0.0008135
relative error = 0.02537 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.022
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4430.8MB, alloc=52.3MB, time=54.55
x[1] = 2.351 1.163
h = 0.001 0.001
y[1] (numeric) = 3.17943473152 0.417216694217
y[1] (closed_form) = 3.18015557008 0.416836438031
absolute error = 0.000815
relative error = 0.02541 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.023
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.352 1.164
h = 0.001 0.003
y[1] (numeric) = 3.18019537609 0.417172041037
y[1] (closed_form) = 3.18091621081 0.416791419638
absolute error = 0.0008152
relative error = 0.02541 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.024
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.353 1.167
h = 0.0001 0.004
y[1] (numeric) = 3.18176203327 0.41784191054
y[1] (closed_form) = 3.1824843173 0.417460177183
absolute error = 0.000817
relative error = 0.02545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.026
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4476.1MB, alloc=52.3MB, time=55.11
x[1] = 2.3531 1.171
h = 0.003 0.006
y[1] (numeric) = 3.1834141668 0.419230496919
y[1] (closed_form) = 3.18413937131 0.41884858492
absolute error = 0.0008196
relative error = 0.02552 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.027
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = 3.18691913767 0.420156982693
y[1] (closed_form) = 3.18764920359 0.419768432515
absolute error = 0.000827
relative error = 0.02572 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.032
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = 3.1889934698 0.421896576138
y[1] (closed_form) = 3.1897281071 0.42150778869
absolute error = 0.0008312
relative error = 0.02583 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.033
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4521.5MB, alloc=52.3MB, time=55.66
x[1] = 2.3563 1.185
h = 0.001 0.001
y[1] (numeric) = 3.19025779474 0.422923663424
y[1] (closed_form) = 3.19099407657 0.42253474661
absolute error = 0.0008327
relative error = 0.02587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.034
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = 3.1910244322 0.422868955954
y[1] (closed_form) = 3.1917607096 0.422479672965
absolute error = 0.0008329
relative error = 0.02587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.036
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3574 1.19
h = 0.003 0.006
y[1] (numeric) = 3.1927041283 0.424250229809
y[1] (closed_form) = 3.19344333246 0.423860763626
absolute error = 0.0008355
relative error = 0.02594 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.037
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4566.9MB, alloc=52.3MB, time=56.22
x[1] = 2.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = 3.1962457398 0.425145967925
y[1] (closed_form) = 3.19698980754 0.424749841637
absolute error = 0.0008429
relative error = 0.02614 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.041
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = 3.19835459946 0.426876554788
y[1] (closed_form) = 3.19910324881 0.426480184399
absolute error = 0.0008471
relative error = 0.02625 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.043
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3606 1.204
h = 0.001 0.001
y[1] (numeric) = 3.19963958659 0.427897952208
y[1] (closed_form) = 3.20038988408 0.427501449883
absolute error = 0.0008486
relative error = 0.02628 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.044
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4612.3MB, alloc=52.3MB, time=56.78
x[1] = 2.3616 1.205
h = 0.001 0.003
y[1] (numeric) = 3.2004115026 0.427834632541
y[1] (closed_form) = 3.20116179515 0.4274377632
absolute error = 0.0008488
relative error = 0.02628 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.045
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = 3.20201936833 0.428478431083
y[1] (closed_form) = 3.20277111405 0.42808043991
absolute error = 0.0008506
relative error = 0.02632 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.047
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3627 1.212
h = 0.003 0.006
y[1] (numeric) = 3.2037310271 0.429850697716
y[1] (closed_form) = 3.20448570728 0.429452518206
absolute error = 0.0008533
relative error = 0.02639 %
Correct digits = 4
memory used=4657.8MB, alloc=52.3MB, time=57.34
Radius of convergence (given) for eq 1 = 4.048
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = 3.20731475357 0.430709978741
y[1] (closed_form) = 3.20807429926 0.430305113231
absolute error = 0.0008607
relative error = 0.02659 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.053
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = 3.20946365607 0.432429460957
y[1] (closed_form) = 3.21022779521 0.432024343002
absolute error = 0.0008649
relative error = 0.0267 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.055
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4703.1MB, alloc=52.3MB, time=57.90
x[1] = 2.3659 1.226
h = 0.001 0.001
y[1] (numeric) = 3.21077260058 0.433443863391
y[1] (closed_form) = 3.21153839207 0.433038610366
absolute error = 0.0008664
relative error = 0.02674 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.056
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3669 1.227
h = 0.001 0.003
y[1] (numeric) = 3.21155050886 0.43337042112
y[1] (closed_form) = 3.21231629477 0.432964800102
absolute error = 0.0008666
relative error = 0.02673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.057
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = 3.21318048114 0.433999961543
y[1] (closed_form) = 3.21394772221 0.433593213221
absolute error = 0.0008684
relative error = 0.02678 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.059
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4748.7MB, alloc=52.3MB, time=58.45
x[1] = 2.368 1.234
h = 0.003 0.006
y[1] (numeric) = 3.21492417322 0.435363143507
y[1] (closed_form) = 3.21569435633 0.43495620135
absolute error = 0.0008711
relative error = 0.02684 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.06
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.371 1.24
h = 0.0001 0.005
y[1] (numeric) = 3.21855006624 0.436185798857
y[1] (closed_form) = 3.21932511649 0.435772144387
absolute error = 0.0008785
relative error = 0.02704 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.065
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = 3.22073910013 0.437894078678
y[1] (closed_form) = 3.22151875577 0.437480163154
absolute error = 0.0008827
relative error = 0.02715 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.066
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4794.1MB, alloc=52.3MB, time=59.01
x[1] = 2.3712 1.248
h = 0.001 0.001
y[1] (numeric) = 3.2220720545 0.438901426434
y[1] (closed_form) = 3.22285336672 0.438487372611
absolute error = 0.0008842
relative error = 0.02719 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.067
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3722 1.249
h = 0.001 0.003
y[1] (numeric) = 3.22285595384 0.438817824051
y[1] (closed_form) = 3.22363725982 0.43840340125
absolute error = 0.0008844
relative error = 0.02718 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.069
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = 3.22450806769 0.439433030064
y[1] (closed_form) = 3.22529083081 0.439017474382
absolute error = 0.0008862
relative error = 0.02723 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.071
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4839.5MB, alloc=52.3MB, time=59.57
x[1] = 2.3733 1.256
h = 0.003 0.006
y[1] (numeric) = 3.2262838637 0.440787047729
y[1] (closed_form) = 3.22706957646 0.440371292543
absolute error = 0.0008889
relative error = 0.02729 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.072
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = 3.22995197365 0.441572905674
y[1] (closed_form) = 3.23074255493 0.44115041145
absolute error = 0.0008964
relative error = 0.02749 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.077
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = 3.23218122771 0.44326988286
y[1] (closed_form) = 3.23297642638 0.442847118711
absolute error = 0.0009006
relative error = 0.0276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.078
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4885.0MB, alloc=52.3MB, time=60.13
x[1] = 2.3765 1.27
h = 0.001 0.001
y[1] (numeric) = 3.2335382445 0.444270114751
y[1] (closed_form) = 3.234335104 0.443847208977
absolute error = 0.0009021
relative error = 0.02763 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.079
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3775 1.271
h = 0.001 0.003
y[1] (numeric) = 3.23432813325 0.444176314201
y[1] (closed_form) = 3.23512498584 0.443753038458
absolute error = 0.0009023
relative error = 0.02763 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.08
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = 3.23600242337 0.444777107973
y[1] (closed_form) = 3.23680073502 0.444352693667
absolute error = 0.0009041
relative error = 0.02767 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.082
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4930.4MB, alloc=52.3MB, time=60.68
x[1] = 2.3786 1.278
h = 0.003 0.006
y[1] (numeric) = 3.23781039406 0.446121879719
y[1] (closed_form) = 3.23861166302 0.445697260071
absolute error = 0.0009068
relative error = 0.02774 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.084
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = 3.24152077013 0.44687076541
y[1] (closed_form) = 3.24232690869 0.446439379592
absolute error = 0.0009143
relative error = 0.02794 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.088
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = 3.24379033331 0.44855633724
y[1] (closed_form) = 3.24460110135 0.448124672361
absolute error = 0.0009185
relative error = 0.02804 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.09
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4975.9MB, alloc=52.3MB, time=61.24
x[1] = 2.3818 1.292
h = 0.001 0.001
y[1] (numeric) = 3.24517146517 0.449549390587
y[1] (closed_form) = 3.24598389832 0.449117580663
absolute error = 0.0009201
relative error = 0.02808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.091
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = 3.24596734122 0.449445353277
y[1] (closed_form) = 3.24677976677 0.449013172386
absolute error = 0.0009202
relative error = 0.02808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.092
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3829 1.297
h = 0.003 0.006
y[1] (numeric) = 3.24780317526 0.450782484165
y[1] (closed_form) = 3.24861856461 0.450350092681
absolute error = 0.0009229
relative error = 0.02814 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.094
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5021.2MB, alloc=52.3MB, time=61.80
x[1] = 2.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = 3.25155041433 0.451499907241
y[1] (closed_form) = 3.25237067434 0.451060725918
absolute error = 0.0009304
relative error = 0.02834 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.099
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.386 1.308
h = 0.0001 0.003
y[1] (numeric) = 3.25385488317 0.453176059181
y[1] (closed_form) = 3.25467978323 0.452736590867
absolute error = 0.0009347
relative error = 0.02844 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3861 1.311
h = 0.001 0.001
y[1] (numeric) = 3.25525690126 0.454163170264
y[1] (closed_form) = 3.25608347016 0.453723553936
absolute error = 0.0009362
relative error = 0.02848 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.101
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5066.6MB, alloc=52.3MB, time=62.36
x[1] = 2.3871 1.312
h = 0.001 0.003
y[1] (numeric) = 3.25605805152 0.45405036146
y[1] (closed_form) = 3.25688461221 0.453610373292
absolute error = 0.0009364
relative error = 0.02848 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = 3.25777387147 0.45462439016
y[1] (closed_form) = 3.2586018948 0.454183252602
absolute error = 0.0009382
relative error = 0.02852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3882 1.319
h = 0.003 0.006
y[1] (numeric) = 3.25964201299 0.45595211864
y[1] (closed_form) = 3.26047300807 0.455510764518
absolute error = 0.0009409
relative error = 0.02858 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.106
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5112.1MB, alloc=52.3MB, time=62.92
x[1] = 2.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = 3.26343160854 0.456632236447
y[1] (closed_form) = 3.26426747483 0.456184064607
absolute error = 0.0009484
relative error = 0.02878 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.111
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = 3.26577655368 0.458296786374
y[1] (closed_form) = 3.26661707225 0.457848317918
absolute error = 0.0009527
relative error = 0.02888 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.112
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3914 1.333
h = 0.001 0.001
y[1] (numeric) = 3.26720278575 0.459276598962
y[1] (closed_form) = 3.26804497749 0.458827978893
absolute error = 0.0009542
relative error = 0.02892 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5157.5MB, alloc=52.3MB, time=63.47
x[1] = 2.3924 1.334
h = 0.001 0.003
y[1] (numeric) = 3.26800991866 0.45915348014
y[1] (closed_form) = 3.26885210145 0.45870448722
absolute error = 0.0009544
relative error = 0.02891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.115
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = 3.269748013 0.459712865937
y[1] (closed_form) = 3.27059166025 0.45926271765
absolute error = 0.0009562
relative error = 0.02895 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.117
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3935 1.341
h = 0.003 0.006
y[1] (numeric) = 3.27164853324 0.461031104912
y[1] (closed_form) = 3.27249516004 0.46058073374
absolute error = 0.000959
relative error = 0.02902 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.118
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5203.0MB, alloc=52.3MB, time=64.03
x[1] = 2.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = 3.27548053087 0.46167373381
y[1] (closed_form) = 3.27633202915 0.461216516646
absolute error = 0.0009665
relative error = 0.02921 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.123
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = 3.27786604162 0.463326571946
y[1] (closed_form) = 3.27872220447 0.462869048279
absolute error = 0.0009707
relative error = 0.02932 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.124
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3967 1.355
h = 0.001 0.001
y[1] (numeric) = 3.27931654048 0.464299019123
y[1] (closed_form) = 3.28017438084 0.463841340149
absolute error = 0.0009723
relative error = 0.02935 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5248.4MB, alloc=52.3MB, time=64.59
x[1] = 2.3977 1.356
h = 0.001 0.003
y[1] (numeric) = 3.28012965262 0.464165550184
y[1] (closed_form) = 3.28098748328 0.463707497342
absolute error = 0.0009725
relative error = 0.02935 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.127
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = 3.28189005454 0.4647102094
y[1] (closed_form) = 3.28274935145 0.464250995112
absolute error = 0.0009743
relative error = 0.02939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.129
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3988 1.363
h = 0.003 0.006
y[1] (numeric) = 3.28382302463 0.466018869627
y[1] (closed_form) = 3.2846853089 0.465559425963
absolute error = 0.000977
relative error = 0.02945 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.13
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5293.9MB, alloc=52.3MB, time=65.14
x[1] = 2.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = 3.28769746857 0.466623822961
y[1] (closed_form) = 3.28856462431 0.466157504645
absolute error = 0.0009846
relative error = 0.02964 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.135
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = 3.29012363432 0.468264837077
y[1] (closed_form) = 3.29099546698 0.467798202106
absolute error = 0.0009889
relative error = 0.02975 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.137
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.402 1.377
h = 0.001 0.001
y[1] (numeric) = 3.2915984528 0.469229850455
y[1] (closed_form) = 3.29247196732 0.468763056388
absolute error = 0.0009904
relative error = 0.02978 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.138
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5339.2MB, alloc=52.3MB, time=65.70
x[1] = 2.403 1.378
h = 0.001 0.003
y[1] (numeric) = 3.29241754027 0.469085990793
y[1] (closed_form) = 3.29329104432 0.468618821836
absolute error = 0.0009906
relative error = 0.02978 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.139
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.404 1.381
h = 0.0001 0.004
y[1] (numeric) = 3.29420028254 0.46961583826
y[1] (closed_form) = 3.29507525459 0.469147501678
absolute error = 0.0009924
relative error = 0.02982 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.141
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4041 1.385
h = 0.003 0.006
y[1] (numeric) = 3.29616577359 0.470914828536
y[1] (closed_form) = 3.29704374087 0.47044625592
absolute error = 0.0009952
relative error = 0.02988 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.142
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5384.7MB, alloc=52.3MB, time=66.26
x[1] = 2.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = 3.30008270676 0.471481916666
y[1] (closed_form) = 3.30096554518 0.471006440353
absolute error = 0.001003
relative error = 0.03007 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = 3.30254961691 0.473110992089
y[1] (closed_form) = 3.30343714466 0.472635188707
absolute error = 0.001007
relative error = 0.03018 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.149
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4073 1.399
h = 0.001 0.001
y[1] (numeric) = 3.3040488078 0.474068501816
y[1] (closed_form) = 3.3049380218 0.473592535454
absolute error = 0.001009
relative error = 0.03021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.15
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5430.2MB, alloc=52.3MB, time=66.83
x[1] = 2.4083 1.4
h = 0.003 0.006
y[1] (numeric) = 3.30487386626 0.473914210322
y[1] (closed_form) = 3.30576306898 0.473437868041
absolute error = 0.001009
relative error = 0.03021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = 3.3088190923 0.474454068906
y[1] (closed_form) = 3.30971316446 0.473970802162
absolute error = 0.001016
relative error = 0.0304 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.156
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = 3.31131377762 0.476073834997
y[1] (closed_form) = 3.31221254741 0.475590233552
absolute error = 0.001021
relative error = 0.0305 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.158
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5475.6MB, alloc=52.3MB, time=67.39
x[1] = 2.4115 1.414
h = 0.001 0.001
y[1] (numeric) = 3.31282957345 0.477025526229
y[1] (closed_form) = 3.31373003241 0.476541758966
absolute error = 0.001022
relative error = 0.03053 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4125 1.415
h = 0.001 0.003
y[1] (numeric) = 3.31365847245 0.476863884436
y[1] (closed_form) = 3.31455891955 0.476379740566
absolute error = 0.001022
relative error = 0.03053 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.161
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = 3.31547861779 0.47736796953
y[1] (closed_form) = 3.31638053559 0.476882647338
absolute error = 0.001024
relative error = 0.03057 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.162
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5521.1MB, alloc=52.3MB, time=67.95
x[1] = 2.4136 1.422
h = 0.003 0.006
y[1] (numeric) = 3.31749891309 0.478649602579
y[1] (closed_form) = 3.3184038393 0.478164032529
absolute error = 0.001027
relative error = 0.03063 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.164
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = 3.32148669208 0.479151267579
y[1] (closed_form) = 3.32239648744 0.478658743982
absolute error = 0.001035
relative error = 0.03082 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.169
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = 3.32402226968 0.480758893657
y[1] (closed_form) = 3.32493677517 0.480266024502
absolute error = 0.001039
relative error = 0.03092 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.171
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5566.4MB, alloc=52.3MB, time=68.51
x[1] = 2.4168 1.436
h = 0.001 0.001
y[1] (numeric) = 3.32556252517 0.481702958697
y[1] (closed_form) = 3.32647872423 0.481209919678
absolute error = 0.00104
relative error = 0.03096 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.172
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4178 1.437
h = 0.001 0.003
y[1] (numeric) = 3.32639738563 0.481530814704
y[1] (closed_form) = 3.327313572 0.481037398041
absolute error = 0.001041
relative error = 0.03095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.173
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = 3.32823995484 0.482019851056
y[1] (closed_form) = 3.32915761355 0.481525249627
absolute error = 0.001042
relative error = 0.03099 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.175
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5611.8MB, alloc=52.3MB, time=69.06
x[1] = 2.4189 1.444
h = 0.003 0.006
y[1] (numeric) = 3.33029295979 0.483291557572
y[1] (closed_form) = 3.33121363486 0.482796701174
absolute error = 0.001045
relative error = 0.03105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.176
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = 3.33432333128 0.48375483208
y[1] (closed_form) = 3.33524887436 0.483252992095
absolute error = 0.001053
relative error = 0.03124 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.181
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.422 1.455
h = 0.0001 0.003
y[1] (numeric) = 3.33689989046 0.485350196956
y[1] (closed_form) = 3.3378301562 0.484848000291
absolute error = 0.001057
relative error = 0.03134 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.183
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5657.2MB, alloc=52.3MB, time=69.62
x[1] = 2.4221 1.458
h = 0.001 0.001
y[1] (numeric) = 3.33846465826 0.48628656204
y[1] (closed_form) = 3.339396622 0.485784191372
absolute error = 0.001059
relative error = 0.03137 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.184
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4231 1.459
h = 0.001 0.003
y[1] (numeric) = 3.33930547453 0.48610387344
y[1] (closed_form) = 3.34023742472 0.485601124088
absolute error = 0.001059
relative error = 0.03137 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.186
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = 3.3411704986 0.486577770505
y[1] (closed_form) = 3.34210392273 0.486073829845
absolute error = 0.001061
relative error = 0.03141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.188
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5702.5MB, alloc=52.3MB, time=70.18
x[1] = 2.4242 1.466
h = 0.003 0.006
y[1] (numeric) = 3.34325628417 0.48783945213
y[1] (closed_form) = 3.34419273263 0.487335249221
absolute error = 0.001064
relative error = 0.03147 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.189
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = 3.3473292857 0.488264135769
y[1] (closed_form) = 3.34827060071 0.487752918869
absolute error = 0.001071
relative error = 0.03166 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.194
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = 3.34994691565 0.489847115844
y[1] (closed_form) = 3.35089296592 0.489335530882
absolute error = 0.001076
relative error = 0.03176 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.196
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5747.9MB, alloc=52.3MB, time=70.73
x[1] = 2.4274 1.48
h = 0.001 0.001
y[1] (numeric) = 3.35153624839 0.490775705766
y[1] (closed_form) = 3.35248400109 0.490263942566
absolute error = 0.001077
relative error = 0.03179 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.197
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = 3.35238301428 0.490582429678
y[1] (closed_form) = 3.35333075256 0.490070286748
absolute error = 0.001077
relative error = 0.03179 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4285 1.485
h = 0.003 0.006
y[1] (numeric) = 3.35449719434 0.49183579378
y[1] (closed_form) = 3.35544796373 0.491323382125
absolute error = 0.00108
relative error = 0.03185 %
Correct digits = 3
memory used=5793.4MB, alloc=52.3MB, time=71.29
Radius of convergence (given) for eq 1 = 4.2
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = 3.35860738231 0.492227605438
y[1] (closed_form) = 3.35956301709 0.491708153312
absolute error = 0.001088
relative error = 0.03203 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.205
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = 3.36126058554 0.493800314962
y[1] (closed_form) = 3.3622209666 0.493280484918
absolute error = 0.001092
relative error = 0.03214 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.207
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5838.9MB, alloc=52.3MB, time=71.85
x[1] = 2.4317 1.499
h = 0.001 0.001
y[1] (numeric) = 3.36287119886 0.49472244443
y[1] (closed_form) = 3.36383328623 0.49420243248
absolute error = 0.001094
relative error = 0.03217 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.208
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4327 1.5
h = 0.001 0.003
y[1] (numeric) = 3.36372320752 0.494520091054
y[1] (closed_form) = 3.36468527972 0.493999698461
absolute error = 0.001094
relative error = 0.03216 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.209
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = 3.36563027856 0.494965839871
y[1] (closed_form) = 3.36659382763 0.494444243561
absolute error = 0.001096
relative error = 0.0322 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.211
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5884.2MB, alloc=52.3MB, time=72.41
x[1] = 2.4338 1.507
h = 0.003 0.006
y[1] (numeric) = 3.36777737208 0.496208991622
y[1] (closed_form) = 3.36874396049 0.495687119165
absolute error = 0.001098
relative error = 0.03226 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = 3.37193025838 0.496561832387
y[1] (closed_form) = 3.37290171014 0.496032888387
absolute error = 0.001106
relative error = 0.03245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.218
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = 3.37462469962 0.498121921808
y[1] (closed_form) = 3.37560091033 0.497592588024
absolute error = 0.00111
relative error = 0.03255 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.219
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5929.6MB, alloc=52.3MB, time=72.96
x[1] = 2.437 1.521
h = 0.001 0.001
y[1] (numeric) = 3.37625997645 0.499036132974
y[1] (closed_form) = 3.37723789793 0.498506612874
absolute error = 0.001112
relative error = 0.03258 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.221
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.438 1.522
h = 0.001 0.003
y[1] (numeric) = 3.37711792249 0.498823110997
y[1] (closed_form) = 3.37809582789 0.4982932092
absolute error = 0.001112
relative error = 0.03257 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.222
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.439 1.525
h = 0.0001 0.004
y[1] (numeric) = 3.37904753536 0.499253453961
y[1] (closed_form) = 3.38002691909 0.498722341632
absolute error = 0.001114
relative error = 0.03261 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.224
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5975.0MB, alloc=52.3MB, time=73.52
x[1] = 2.4391 1.529
h = 0.003 0.006
y[1] (numeric) = 3.38122761324 0.500486289693
y[1] (closed_form) = 3.38221004436 0.499954893457
absolute error = 0.001117
relative error = 0.03267 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.225
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = 3.38542323107 0.500799951078
y[1] (closed_form) = 3.38641052319 0.50026145188
absolute error = 0.001125
relative error = 0.03285 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.23
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = 3.38815899918 0.502347289966
y[1] (closed_form) = 3.38915106296 0.501808388856
absolute error = 0.001129
relative error = 0.03295 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.232
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6020.4MB, alloc=52.3MB, time=74.08
x[1] = 2.4423 1.543
h = 0.001 0.001
y[1] (numeric) = 3.38981899184 0.503253503528
y[1] (closed_form) = 3.39081277086 0.502714411597
absolute error = 0.001131
relative error = 0.03298 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.234
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4433 1.544
h = 0.001 0.003
y[1] (numeric) = 3.3906828677 0.50302976875
y[1] (closed_form) = 3.3916766297 0.502490294066
absolute error = 0.001131
relative error = 0.03298 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.235
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = 3.39263505137 0.50344460983
y[1] (closed_form) = 3.39363029312 0.502903917704
absolute error = 0.001133
relative error = 0.03301 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.237
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6065.7MB, alloc=52.3MB, time=74.63
x[1] = 2.4444 1.551
h = 0.003 0.006
y[1] (numeric) = 3.39484818417 0.504667023807
y[1] (closed_form) = 3.39584648139 0.504126039849
absolute error = 0.001135
relative error = 0.03307 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.238
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = 3.39908656515 0.504941294556
y[1] (closed_form) = 3.40008972068 0.504393175869
absolute error = 0.001143
relative error = 0.03326 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.243
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = 3.40186374881 0.50647575011
y[1] (closed_form) = 3.40287168875 0.505927217125
absolute error = 0.001148
relative error = 0.03336 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.245
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6111.1MB, alloc=52.3MB, time=75.19
x[1] = 2.4476 1.565
h = 0.001 0.001
y[1] (numeric) = 3.4035485095 0.507373885346
y[1] (closed_form) = 3.40455816916 0.506825156942
absolute error = 0.001149
relative error = 0.03338 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.247
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4486 1.566
h = 0.001 0.003
y[1] (numeric) = 3.40441830709 0.507139393122
y[1] (closed_form) = 3.40542794878 0.506590280905
absolute error = 0.001149
relative error = 0.03338 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.248
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = 3.40639308998 0.507538634898
y[1] (closed_form) = 3.40740421279 0.506988298237
absolute error = 0.001151
relative error = 0.03342 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6156.5MB, alloc=52.3MB, time=75.75
x[1] = 2.4497 1.573
h = 0.003 0.006
y[1] (numeric) = 3.40863934807 0.508750519494
y[1] (closed_form) = 3.40965353445 0.508199882909
absolute error = 0.001154
relative error = 0.03348 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.251
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = 3.41292052222 0.508985185604
y[1] (closed_form) = 3.41393956389 0.508427382185
absolute error = 0.001162
relative error = 0.03366 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.256
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = 3.41573920989 0.510506622669
y[1] (closed_form) = 3.41676304876 0.509948392306
absolute error = 0.001166
relative error = 0.03376 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.258
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6201.8MB, alloc=52.3MB, time=76.31
x[1] = 2.4529 1.587
h = 0.001 0.001
y[1] (numeric) = 3.41744879066 0.511396597444
y[1] (closed_form) = 3.41847435373 0.51083816697
absolute error = 0.001168
relative error = 0.03378 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = 3.41832450141 0.511151302693
y[1] (closed_form) = 3.41935004553 0.510592487341
absolute error = 0.001168
relative error = 0.03378 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.261
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.454 1.592
h = 0.003 0.006
y[1] (numeric) = 3.42059945629 0.512354432217
y[1] (closed_form) = 3.42162807084 0.511795309777
absolute error = 0.001171
relative error = 0.03384 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6247.3MB, alloc=52.3MB, time=76.87
x[1] = 2.457 1.598
h = 0.0001 0.005
y[1] (numeric) = 3.42491796344 0.512555344739
y[1] (closed_form) = 3.42595143082 0.511989027521
absolute error = 0.001178
relative error = 0.03402 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.267
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = 3.42777260436 0.514065961726
y[1] (closed_form) = 3.4288108801 0.513499206624
absolute error = 0.001183
relative error = 0.03412 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4572 1.606
h = 0.001 0.001
y[1] (numeric) = 3.42950368954 0.5149491419
y[1] (closed_form) = 3.43054369342 0.514382182627
absolute error = 0.001185
relative error = 0.03415 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.271
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6292.8MB, alloc=52.3MB, time=77.43
x[1] = 2.4582 1.607
h = 0.001 0.003
y[1] (numeric) = 3.43038461229 0.514694582555
y[1] (closed_form) = 3.43142459637 0.514127237474
absolute error = 0.001185
relative error = 0.03414 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.272
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = 3.43240170932 0.515064803634
y[1] (closed_form) = 3.43344317704 0.51449622085
absolute error = 0.001187
relative error = 0.03418 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.274
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4593 1.614
h = 0.003 0.006
y[1] (numeric) = 3.43470992106 0.51625719918
y[1] (closed_form) = 3.43575446755 0.515688301072
absolute error = 0.001189
relative error = 0.03424 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.276
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6338.2MB, alloc=52.3MB, time=77.99
x[1] = 2.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = 3.43907127548 0.51641810196
y[1] (closed_form) = 3.44012067118 0.515841976346
absolute error = 0.001197
relative error = 0.03441 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.281
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = 3.44196758606 0.517915443775
y[1] (closed_form) = 3.44302180295 0.51733886715
absolute error = 0.001202
relative error = 0.03451 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.283
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4625 1.628
h = 0.001 0.001
y[1] (numeric) = 3.44372358873 0.518790307535
y[1] (closed_form) = 3.44477953826 0.518213521874
absolute error = 0.001203
relative error = 0.03454 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.284
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6383.6MB, alloc=52.3MB, time=78.54
x[1] = 2.4635 1.629
h = 0.001 0.003
y[1] (numeric) = 3.44461040785 0.518524860522
y[1] (closed_form) = 3.44566633657 0.517947687984
absolute error = 0.001203
relative error = 0.03454 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.285
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = 3.44665018338 0.518879196336
y[1] (closed_form) = 3.44770759697 0.518300778831
absolute error = 0.001205
relative error = 0.03457 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.287
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4646 1.636
h = 0.003 0.006
y[1] (numeric) = 3.448991722 0.520060745084
y[1] (closed_form) = 3.4500522225 0.519482003689
absolute error = 0.001208
relative error = 0.03463 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.289
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6429.0MB, alloc=52.3MB, time=79.10
x[1] = 2.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = 3.45339594899 0.520181416406
y[1] (closed_form) = 3.45446129475 0.519595414453
absolute error = 0.001216
relative error = 0.03481 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.294
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = 3.45633401698 0.521665341207
y[1] (closed_form) = 3.45740419679 0.521078874859
absolute error = 0.00122
relative error = 0.0349 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.296
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4678 1.65
h = 0.001 0.001
y[1] (numeric) = 3.4581149887 0.522531802415
y[1] (closed_form) = 3.45918690565 0.521945122072
absolute error = 0.001222
relative error = 0.03493 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.297
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6474.5MB, alloc=52.3MB, time=79.66
x[1] = 2.4688 1.651
h = 0.001 0.003
y[1] (numeric) = 3.45900769414 0.522255421438
y[1] (closed_form) = 3.46007958925 0.521668353146
absolute error = 0.001222
relative error = 0.03493 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.299
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = 3.4610701743 0.522593769297
y[1] (closed_form) = 3.46214355545 0.522005448686
absolute error = 0.001224
relative error = 0.03496 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.301
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4699 1.658
h = 0.003 0.006
y[1] (numeric) = 3.46344510935 0.523764356407
y[1] (closed_form) = 3.46452158557 0.523175703175
absolute error = 0.001227
relative error = 0.03502 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.302
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6519.9MB, alloc=52.3MB, time=80.22
x[1] = 2.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = 3.46789223252 0.523844571923
y[1] (closed_form) = 3.46897354971 0.523248624759
absolute error = 0.001235
relative error = 0.03519 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.307
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.473 1.669
h = 0.0001 0.003
y[1] (numeric) = 3.47087214535 0.525314935556
y[1] (closed_form) = 3.47195830947 0.524718510356
absolute error = 0.001239
relative error = 0.03529 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.309
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4731 1.672
h = 0.001 0.001
y[1] (numeric) = 3.47267813746 0.526172906688
y[1] (closed_form) = 3.47376604323 0.525576262443
absolute error = 0.001241
relative error = 0.03532 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6565.2MB, alloc=52.3MB, time=80.77
x[1] = 2.4741 1.673
h = 0.001 0.003
y[1] (numeric) = 3.47357671866 0.525885545041
y[1] (closed_form) = 3.47466460154 0.525288511773
absolute error = 0.001241
relative error = 0.03531 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.312
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = 3.47566192896 0.526207800923
y[1] (closed_form) = 3.476751299 0.525609507893
absolute error = 0.001243
relative error = 0.03535 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.314
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4752 1.68
h = 0.003 0.006
y[1] (numeric) = 3.47807032973 0.527367309709
y[1] (closed_form) = 3.47916280301 0.526768675165
absolute error = 0.001246
relative error = 0.0354 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.316
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6610.6MB, alloc=52.3MB, time=81.33
x[1] = 2.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = 3.48256037095 0.527406842466
y[1] (closed_form) = 3.48365768057 0.526800880299
absolute error = 0.001254
relative error = 0.03558 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.321
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = 3.48558221573 0.528863498473
y[1] (closed_form) = 3.48668438516 0.528257044375
absolute error = 0.001258
relative error = 0.03567 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.323
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4784 1.694
h = 0.001 0.001
y[1] (numeric) = 3.48741327933 0.529712890628
y[1] (closed_form) = 3.48851719494 0.529106212341
absolute error = 0.00126
relative error = 0.0357 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.324
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6656.0MB, alloc=52.3MB, time=81.89
x[1] = 2.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = 3.48831772522 0.529414501205
y[1] (closed_form) = 3.48942161686 0.528807432819
absolute error = 0.00126
relative error = 0.0357 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.325
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4795 1.699
h = 0.003 0.006
y[1] (numeric) = 3.49075512155 0.530564779216
y[1] (closed_form) = 3.49186212333 0.52995736147
absolute error = 0.001263
relative error = 0.03575 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.327
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = 3.49528260971 0.530569621464
y[1] (closed_form) = 3.496394444 0.529954846788
absolute error = 0.00127
relative error = 0.03593 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.332
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6701.4MB, alloc=52.3MB, time=82.44
x[1] = 2.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = 3.49834078328 0.532014860275
y[1] (closed_form) = 3.49945748865 0.531399581655
absolute error = 0.001275
relative error = 0.03602 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.334
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4827 1.713
h = 0.001 0.001
y[1] (numeric) = 3.50019357201 0.532857095171
y[1] (closed_form) = 3.50131202751 0.532241587914
absolute error = 0.001277
relative error = 0.03605 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.335
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4837 1.714
h = 0.001 0.003
y[1] (numeric) = 3.50110318888 0.532549245054
y[1] (closed_form) = 3.50222161948 0.531933346757
absolute error = 0.001277
relative error = 0.03604 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.337
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6746.8MB, alloc=52.3MB, time=83.00
x[1] = 2.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = 3.50323095499 0.532841547585
y[1] (closed_form) = 3.50435087481 0.532224375458
absolute error = 0.001279
relative error = 0.03608 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.339
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4848 1.721
h = 0.003 0.006
y[1] (numeric) = 3.5057019464 0.533980525932
y[1] (closed_form) = 3.50682498476 0.533362995401
absolute error = 0.001282
relative error = 0.03613 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.341
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = 3.51027239141 0.53394425649
y[1] (closed_form) = 3.51140025701 0.533319334763
absolute error = 0.001289
relative error = 0.0363 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.346
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6792.2MB, alloc=52.3MB, time=83.56
x[1] = 2.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = 3.51337265982 0.535375510096
y[1] (closed_form) = 3.51450540943 0.534750070053
absolute error = 0.001294
relative error = 0.0364 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.348
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.488 1.735
h = 0.001 0.001
y[1] (numeric) = 3.51525061563 0.53620899755
y[1] (closed_form) = 3.51638511988 0.535583323556
absolute error = 0.001296
relative error = 0.03642 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.349
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.489 1.736
h = 0.001 0.003
y[1] (numeric) = 3.51616607573 0.535890030813
y[1] (closed_form) = 3.51730055397 0.535263964699
absolute error = 0.001296
relative error = 0.03642 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.35
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6837.7MB, alloc=52.3MB, time=84.12
x[1] = 2.49 1.739
h = 0.0001 0.004
y[1] (numeric) = 3.51831664264 0.536165936797
y[1] (closed_form) = 3.51945261107 0.535538589161
absolute error = 0.001298
relative error = 0.03645 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.352
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4901 1.743
h = 0.003 0.006
y[1] (numeric) = 3.52082129778 0.53729349372
y[1] (closed_form) = 3.52196039294 0.53666577832
absolute error = 0.001301
relative error = 0.03651 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.354
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = 3.52543471647 0.537215878321
y[1] (closed_form) = 3.52657863327 0.536580737156
absolute error = 0.001308
relative error = 0.03668 %
Correct digits = 3
memory used=6883.1MB, alloc=52.3MB, time=84.67
Radius of convergence (given) for eq 1 = 4.359
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = 3.52857716575 0.538632993742
y[1] (closed_form) = 3.52972597948 0.537997319637
absolute error = 0.001313
relative error = 0.03677 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.361
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4933 1.757
h = 0.001 0.001
y[1] (numeric) = 3.53048033905 0.539457640948
y[1] (closed_form) = 3.53163091193 0.538821727486
absolute error = 0.001315
relative error = 0.0368 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.363
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6928.5MB, alloc=52.3MB, time=85.23
x[1] = 2.4943 1.758
h = 0.001 0.003
y[1] (numeric) = 3.5314016298 0.539127509372
y[1] (closed_form) = 3.53255217554 0.538491202708
absolute error = 0.001315
relative error = 0.03679 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.364
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = 3.53357502047 0.539386909738
y[1] (closed_form) = 3.53472705733 0.538749313776
absolute error = 0.001317
relative error = 0.03683 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.366
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4954 1.765
h = 0.003 0.006
y[1] (numeric) = 3.53611340743 0.540502921515
y[1] (closed_form) = 3.5372685792 0.539864948265
absolute error = 0.00132
relative error = 0.03688 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.368
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6973.8MB, alloc=52.3MB, time=85.78
x[1] = 2.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = 3.54076981481 0.540383723399
y[1] (closed_form) = 3.54192980227 0.539738289518
absolute error = 0.001327
relative error = 0.03705 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.373
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = 3.54395453056 0.5417865454
y[1] (closed_form) = 3.54511942788 0.541140563701
absolute error = 0.001332
relative error = 0.03714 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4986 1.779
h = 0.001 0.001
y[1] (numeric) = 3.54588297147 0.542602258204
y[1] (closed_form) = 3.54704963247 0.541956031651
absolute error = 0.001334
relative error = 0.03717 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.376
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7019.2MB, alloc=52.3MB, time=86.34
x[1] = 2.4996 1.78
h = 0.001 0.003
y[1] (numeric) = 3.54681007976 0.542260913196
y[1] (closed_form) = 3.54797671246 0.541614292358
absolute error = 0.001334
relative error = 0.03716 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.378
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = 3.54900631649 0.542503697596
y[1] (closed_form) = 3.55017444116 0.5418557796
absolute error = 0.001336
relative error = 0.0372 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5007 1.787
h = 0.003 0.006
y[1] (numeric) = 3.55157850298 0.543608038709
y[1] (closed_form) = 3.55274977075 0.542959733739
absolute error = 0.001339
relative error = 0.03725 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.382
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7064.7MB, alloc=52.3MB, time=86.90
x[1] = 2.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = 3.55627791223 0.543447018648
y[1] (closed_form) = 3.5574539894 0.542791217891
absolute error = 0.001347
relative error = 0.03742 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.387
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = 3.55950497959 0.544835389752
y[1] (closed_form) = 3.56068597955 0.544179026046
absolute error = 0.001351
relative error = 0.03751 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.389
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5039 1.801
h = 0.001 0.001
y[1] (numeric) = 3.56145873796 0.54564207266
y[1] (closed_form) = 3.56264150611 0.544985458511
absolute error = 0.001353
relative error = 0.03754 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7110.1MB, alloc=52.3MB, time=87.46
x[1] = 2.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = 3.56239165013 0.545289465259
y[1] (closed_form) = 3.56357438882 0.544632455743
absolute error = 0.001353
relative error = 0.03753 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.392
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.505 1.806
h = 0.003 0.006
y[1] (numeric) = 3.56499312538 0.546384062632
y[1] (closed_form) = 3.56617901411 0.545726657625
absolute error = 0.001356
relative error = 0.03758 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.393
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.508 1.812
h = 0.0001 0.005
y[1] (numeric) = 3.56973006045 0.546187362628
y[1] (closed_form) = 3.57092075329 0.545522431261
absolute error = 0.001364
relative error = 0.03775 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.399
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7155.6MB, alloc=52.3MB, time=88.02
x[1] = 2.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = 3.57299382521 0.547563672937
y[1] (closed_form) = 3.57418945215 0.54689816555
absolute error = 0.001368
relative error = 0.03784 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.401
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5082 1.82
h = 0.001 0.001
y[1] (numeric) = 3.57496952481 0.548362808104
y[1] (closed_form) = 3.57616692391 0.547697045446
absolute error = 0.00137
relative error = 0.03787 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5092 1.821
h = 0.001 0.003
y[1] (numeric) = 3.57590755639 0.548000535838
y[1] (closed_form) = 3.57710492501 0.547334376865
absolute error = 0.00137
relative error = 0.03786 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.403
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7201.1MB, alloc=52.3MB, time=88.58
x[1] = 2.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = 3.57814656228 0.548212376528
y[1] (closed_form) = 3.57934542442 0.547544905556
absolute error = 0.001372
relative error = 0.03789 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.406
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5103 1.828
h = 0.003 0.006
y[1] (numeric) = 3.58078196336 0.54929506557
y[1] (closed_form) = 3.58198398395 0.548627189271
absolute error = 0.001375
relative error = 0.03795 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.407
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = 3.58556192277 0.549056092122
y[1] (closed_form) = 3.58676874052 0.548380653772
absolute error = 0.001383
relative error = 0.03811 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.412
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7246.5MB, alloc=52.3MB, time=89.14
x[1] = 2.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = 3.58886819822 0.550417653581
y[1] (closed_form) = 3.59007996301 0.549741623613
absolute error = 0.001388
relative error = 0.03821 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.415
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5135 1.842
h = 0.001 0.001
y[1] (numeric) = 3.59086930836 0.551207578198
y[1] (closed_form) = 3.59208284981 0.550531287202
absolute error = 0.001389
relative error = 0.03823 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.416
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5145 1.843
h = 0.001 0.003
y[1] (numeric) = 3.59181311759 0.550833951312
y[1] (closed_form) = 3.59302662736 0.550157262917
absolute error = 0.001389
relative error = 0.03822 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.417
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7292.0MB, alloc=52.3MB, time=89.69
x[1] = 2.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = 3.59407503074 0.551028853658
y[1] (closed_form) = 3.59529003472 0.550350845167
absolute error = 0.001391
relative error = 0.03825 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.419
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5156 1.85
h = 0.003 0.006
y[1] (numeric) = 3.59674442447 0.552099503908
y[1] (closed_form) = 3.59796259507 0.551421079943
absolute error = 0.001394
relative error = 0.03831 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = 3.60156741605 0.551818010876
y[1] (closed_form) = 3.60279037653 0.551131988893
absolute error = 0.001402
relative error = 0.03847 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.426
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7337.4MB, alloc=52.3MB, time=90.25
x[1] = 2.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = 3.60491628593 0.553164659657
y[1] (closed_form) = 3.60614420636 0.552478030206
absolute error = 0.001407
relative error = 0.03856 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.429
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5188 1.864
h = 0.001 0.001
y[1] (numeric) = 3.60694285554 0.553945274431
y[1] (closed_form) = 3.60817255715 0.553258378106
absolute error = 0.001409
relative error = 0.03859 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.43
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5198 1.865
h = 0.001 0.003
y[1] (numeric) = 3.60789242724 0.553560242953
y[1] (closed_form) = 3.60912209594 0.552872948144
absolute error = 0.001409
relative error = 0.03858 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.431
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7382.8MB, alloc=52.3MB, time=90.81
x[1] = 2.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = 3.61017726717 0.553738091786
y[1] (closed_form) = 3.61140843072 0.553049468703
absolute error = 0.001411
relative error = 0.03861 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.434
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5209 1.872
h = 0.003 0.006
y[1] (numeric) = 3.6128807197 0.554796570875
y[1] (closed_form) = 3.61411505805 0.554107522012
absolute error = 0.001414
relative error = 0.03866 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.435
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = 3.61774674938 0.554472309766
y[1] (closed_form) = 3.61898586994 0.553775626643
absolute error = 0.001422
relative error = 0.03883 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.441
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7428.2MB, alloc=52.3MB, time=91.36
x[1] = 2.524 1.883
h = 0.0001 0.003
y[1] (numeric) = 3.62113829688 0.555803879846
y[1] (closed_form) = 3.62238239032 0.555106573159
absolute error = 0.001426
relative error = 0.03892 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.443
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5241 1.886
h = 0.001 0.001
y[1] (numeric) = 3.62319037456 0.556575084174
y[1] (closed_form) = 3.62443625367 0.555877504677
absolute error = 0.001428
relative error = 0.03894 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.444
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5251 1.887
h = 0.001 0.003
y[1] (numeric) = 3.624145693 0.556178597792
y[1] (closed_form) = 3.62539153795 0.555480618726
absolute error = 0.001428
relative error = 0.03894 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.445
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7473.6MB, alloc=52.3MB, time=91.92
x[1] = 2.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = 3.6264534785 0.556339276726
y[1] (closed_form) = 3.62770081889 0.555639961127
absolute error = 0.00143
relative error = 0.03896 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.448
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5262 1.894
h = 0.003 0.006
y[1] (numeric) = 3.62919105554 0.557385450537
y[1] (closed_form) = 3.63044157889 0.556685698695
absolute error = 0.001433
relative error = 0.03902 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.449
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = 3.6341001273 0.557018170532
y[1] (closed_form) = 3.63535542484 0.55631074792
absolute error = 0.001441
relative error = 0.03918 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.455
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7519.0MB, alloc=52.3MB, time=92.48
x[1] = 2.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = 3.63753443505 0.558334493711
y[1] (closed_form) = 3.63879471837 0.557626431189
absolute error = 0.001446
relative error = 0.03927 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.457
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5294 1.908
h = 0.001 0.001
y[1] (numeric) = 3.63961206902 0.559096185687
y[1] (closed_form) = 3.64087414251 0.55838784433
absolute error = 0.001447
relative error = 0.03929 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.458
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = 3.64057311794 0.558688193759
y[1] (closed_form) = 3.641835156 0.557979451747
absolute error = 0.001447
relative error = 0.03929 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7564.6MB, alloc=52.3MB, time=93.04
x[1] = 2.5305 1.913
h = 0.003 0.006
y[1] (numeric) = 3.6433402695 0.559724074563
y[1] (closed_form) = 3.64460549744 0.559014887129
absolute error = 0.00145
relative error = 0.03934 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.461
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = 3.64828690868 0.559320075468
y[1] (closed_form) = 3.64955690406 0.558603185525
absolute error = 0.001458
relative error = 0.0395 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.467
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = 3.65175827314 0.560623648964
y[1] (closed_form) = 3.6530332656 0.559906104997
absolute error = 0.001463
relative error = 0.03959 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.469
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7610.0MB, alloc=52.3MB, time=93.60
x[1] = 2.5337 1.927
h = 0.001 0.001
y[1] (numeric) = 3.65385805844 0.561377375633
y[1] (closed_form) = 3.65513484501 0.560659547626
absolute error = 0.001465
relative error = 0.03961 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5347 1.928
h = 0.001 0.003
y[1] (numeric) = 3.6548241644 0.560959507301
y[1] (closed_form) = 3.65610091445 0.56024127769
absolute error = 0.001465
relative error = 0.03961 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.472
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = 3.65717490149 0.561088196988
y[1] (closed_form) = 3.658453148 0.560368615276
absolute error = 0.001467
relative error = 0.03963 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.474
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7655.4MB, alloc=52.3MB, time=94.15
x[1] = 2.5358 1.935
h = 0.003 0.006
y[1] (numeric) = 3.65997629997 0.562111518972
y[1] (closed_form) = 3.66125774474 0.561391481219
absolute error = 0.00147
relative error = 0.03968 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.476
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = 3.66496598646 0.561664028168
y[1] (closed_form) = 3.66625218998 0.560936250906
absolute error = 0.001478
relative error = 0.03985 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = 3.66848026542 0.562952036991
y[1] (closed_form) = 3.6697714789 0.5622235889
absolute error = 0.001483
relative error = 0.03993 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.483
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7700.8MB, alloc=52.3MB, time=94.71
x[1] = 2.539 1.949
h = 0.001 0.001
y[1] (numeric) = 3.670605697 0.563696058808
y[1] (closed_form) = 3.67189870908 0.562967320486
absolute error = 0.001484
relative error = 0.03995 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.485
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.54 1.95
h = 0.001 0.003
y[1] (numeric) = 3.67157750233 0.563266589628
y[1] (closed_form) = 3.67287047658 0.562537448618
absolute error = 0.001484
relative error = 0.03995 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.486
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.541 1.953
h = 0.0001 0.004
y[1] (numeric) = 3.67395123594 0.563377770037
y[1] (closed_form) = 3.67524570705 0.562647268444
absolute error = 0.001486
relative error = 0.03998 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.488
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7746.2MB, alloc=52.3MB, time=95.27
x[1] = 2.5411 1.957
h = 0.003 0.006
y[1] (numeric) = 3.67678694591 0.564388394281
y[1] (closed_form) = 3.67808462342 0.56365742573
absolute error = 0.001489
relative error = 0.04003 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.49
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = 3.68181967808 0.563897154432
y[1] (closed_form) = 3.68312210529 0.563158409117
absolute error = 0.001497
relative error = 0.04019 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.495
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = 3.68537695245 0.56516942421
y[1] (closed_form) = 3.68668440249 0.564429991016
absolute error = 0.001502
relative error = 0.04027 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.498
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7791.6MB, alloc=52.3MB, time=95.82
x[1] = 2.5443 1.971
h = 0.001 0.001
y[1] (numeric) = 3.68752807746 0.565903635585
y[1] (closed_form) = 3.68883733057 0.565163905881
absolute error = 0.001504
relative error = 0.0403 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.499
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5453 1.972
h = 0.001 0.003
y[1] (numeric) = 3.68850556433 0.565462513998
y[1] (closed_form) = 3.68981477828 0.564722380522
absolute error = 0.001504
relative error = 0.04029 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.5
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = 3.69090231029 0.565556064145
y[1] (closed_form) = 3.69221302145 0.564814561528
absolute error = 0.001506
relative error = 0.04032 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.503
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7837.0MB, alloc=52.3MB, time=96.38
x[1] = 2.5464 1.979
h = 0.003 0.006
y[1] (numeric) = 3.69377239556 0.566553849882
y[1] (closed_form) = 3.69508632123 0.565811869233
absolute error = 0.001509
relative error = 0.04037 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = 3.69884816976 0.566018601439
y[1] (closed_form) = 3.70016683573 0.565268806521
absolute error = 0.001517
relative error = 0.04053 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = 3.70244851982 0.567274955673
y[1] (closed_form) = 3.70377222146 0.566524455581
absolute error = 0.001522
relative error = 0.04061 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.512
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7882.5MB, alloc=52.3MB, time=96.95
x[1] = 2.5496 1.993
h = 0.001 0.001
y[1] (numeric) = 3.70462538499 0.567999249742
y[1] (closed_form) = 3.70595089417 0.567248446773
absolute error = 0.001523
relative error = 0.04063 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.513
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5506 1.994
h = 0.001 0.003
y[1] (numeric) = 3.70560853502 0.567546423884
y[1] (closed_form) = 3.70693400369 0.566795216061
absolute error = 0.001524
relative error = 0.04063 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = 3.70802830834 0.567622221628
y[1] (closed_form) = 3.70935527451 0.566869636029
absolute error = 0.001526
relative error = 0.04065 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.517
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7927.9MB, alloc=52.3MB, time=97.51
x[1] = 2.5517 2.001
h = 0.003 0.006
y[1] (numeric) = 3.71093283219 0.568607026396
y[1] (closed_form) = 3.71226302098 0.567853951537
absolute error = 0.001529
relative error = 0.0407 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.519
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = 3.71605164276 0.568027507621
y[1] (closed_form) = 3.71738656206 0.567266580742
absolute error = 0.001537
relative error = 0.04086 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.524
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = 3.71969514811 0.569267767698
y[1] (closed_form) = 3.7210351159 0.568506118106
absolute error = 0.001541
relative error = 0.04095 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.527
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7973.3MB, alloc=52.3MB, time=98.06
x[1] = 2.5549 2.015
h = 0.001 0.001
y[1] (numeric) = 3.72189779977 0.569982036335
y[1] (closed_form) = 3.72323957954 0.569220077413
absolute error = 0.001543
relative error = 0.04097 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.528
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = 3.72288659402 0.569517454045
y[1] (closed_form) = 3.72422833192 0.568755089186
absolute error = 0.001543
relative error = 0.04096 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.529
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.556 2.02
h = 0.003 0.006
y[1] (numeric) = 3.7258209689 0.570491381243
y[1] (closed_form) = 3.72716593629 0.569728517296
absolute error = 0.001546
relative error = 0.04101 %
Correct digits = 3
memory used=8018.8MB, alloc=52.3MB, time=98.62
Radius of convergence (given) for eq 1 = 4.531
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.559 2.026
h = 0.0001 0.005
y[1] (numeric) = 3.73097734928 0.569874057321
y[1] (closed_form) = 3.73232703892 0.569103308545
absolute error = 0.001554
relative error = 0.04117 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.537
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = 3.73465825913 0.571100834791
y[1] (closed_form) = 3.73601300848 0.570329348163
absolute error = 0.001559
relative error = 0.04125 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.539
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8064.3MB, alloc=52.3MB, time=99.18
x[1] = 2.5592 2.034
h = 0.001 0.001
y[1] (numeric) = 3.73688326488 0.57180669424
y[1] (closed_form) = 3.73823983012 0.571034892709
absolute error = 0.001561
relative error = 0.04127 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.54
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5602 2.035
h = 0.001 0.003
y[1] (numeric) = 3.73787704281 0.571332017329
y[1] (closed_form) = 3.739233565 0.570559808915
absolute error = 0.001561
relative error = 0.04127 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = 3.74033991687 0.571374727673
y[1] (closed_form) = 3.74169793703 0.570601125223
absolute error = 0.001563
relative error = 0.04129 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.544
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8109.6MB, alloc=52.3MB, time=99.74
x[1] = 2.5613 2.042
h = 0.003 0.006
y[1] (numeric) = 3.7433088481 0.572335404948
y[1] (closed_form) = 3.74467010606 0.571561292023
absolute error = 0.001566
relative error = 0.04134 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = 3.74850825203 0.571673317816
y[1] (closed_form) = 3.74987422177 0.570891281864
absolute error = 0.001574
relative error = 0.0415 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.551
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = 3.75223246563 0.572883664117
y[1] (closed_form) = 3.75360350786 0.572100872324
absolute error = 0.001579
relative error = 0.04158 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.553
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8155.1MB, alloc=52.3MB, time=100.30
x[1] = 2.5645 2.056
h = 0.001 0.001
y[1] (numeric) = 3.7544833442 0.573579294147
y[1] (closed_form) = 3.75585620675 0.572796180834
absolute error = 0.001581
relative error = 0.0416 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.555
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5655 2.057
h = 0.001 0.003
y[1] (numeric) = 3.75548273029 0.573092762731
y[1] (closed_form) = 3.75685554839 0.572309241456
absolute error = 0.001581
relative error = 0.04159 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.556
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = 3.75796867173 0.573117365106
y[1] (closed_form) = 3.75934298789 0.57233244095
absolute error = 0.001583
relative error = 0.04162 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.559
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8200.5MB, alloc=52.3MB, time=100.86
x[1] = 2.5666 2.064
h = 0.003 0.006
y[1] (numeric) = 3.76097222122 0.574064645335
y[1] (closed_form) = 3.76234978323 0.573279199032
absolute error = 0.001586
relative error = 0.04167 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.56
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = 3.76621463717 0.573357527136
y[1] (closed_form) = 3.76759690014 0.572564119374
absolute error = 0.001594
relative error = 0.04182 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.566
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = 3.76998223213 0.574551257671
y[1] (closed_form) = 3.77136958033 0.573757075839
absolute error = 0.001599
relative error = 0.04191 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.568
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8245.9MB, alloc=52.3MB, time=101.42
x[1] = 2.5698 2.078
h = 0.001 0.001
y[1] (numeric) = 3.77225902858 0.575236546585
y[1] (closed_form) = 3.77364820151 0.574442036531
absolute error = 0.0016
relative error = 0.04192 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.57
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5708 2.079
h = 0.001 0.003
y[1] (numeric) = 3.77326400231 0.574738107681
y[1] (closed_form) = 3.77465312937 0.573943188587
absolute error = 0.0016
relative error = 0.04192 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.571
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = 3.775773023 0.574744475576
y[1] (closed_form) = 3.77716364816 0.573948144683
absolute error = 0.001602
relative error = 0.04194 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.573
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8291.4MB, alloc=52.3MB, time=101.97
x[1] = 2.5719 2.086
h = 0.003 0.006
y[1] (numeric) = 3.77881125183 0.575678209851
y[1] (closed_form) = 3.78020513087 0.574881344985
absolute error = 0.001606
relative error = 0.04199 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.575
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = 3.7840966662 0.574925790647
y[1] (closed_form) = 3.785495235 0.574120925664
absolute error = 0.001614
relative error = 0.04214 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.581
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.575 2.097
h = 0.0001 0.003
y[1] (numeric) = 3.78790771936 0.57610271876
y[1] (closed_form) = 3.7893113861 0.575297061236
absolute error = 0.001618
relative error = 0.04223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.583
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8336.8MB, alloc=52.3MB, time=102.54
x[1] = 2.5751 2.1
h = 0.001 0.001
y[1] (numeric) = 3.79021047828 0.576777553632
y[1] (closed_form) = 3.79161597416 0.575971561098
absolute error = 0.00162
relative error = 0.04225 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.584
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5761 2.101
h = 0.001 0.003
y[1] (numeric) = 3.79122101859 0.576267153983
y[1] (closed_form) = 3.79262646715 0.575460751334
absolute error = 0.00162
relative error = 0.04224 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.586
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = 3.79375312956 0.576255159786
y[1] (closed_form) = 3.7951600762 0.57544733635
absolute error = 0.001622
relative error = 0.04227 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.588
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8382.2MB, alloc=52.3MB, time=103.09
x[1] = 2.5772 2.108
h = 0.003 0.006
y[1] (numeric) = 3.79682609819 0.57717519756
y[1] (closed_form) = 3.79823630672 0.576366828171
absolute error = 0.001625
relative error = 0.04231 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = 3.80215449525 0.576377205365
y[1] (closed_form) = 3.80356938196 0.575560796978
absolute error = 0.001634
relative error = 0.04246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.595
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = 3.80600908273 0.577537142351
y[1] (closed_form) = 3.80742908004 0.576719922714
absolute error = 0.001638
relative error = 0.04255 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.598
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8427.6MB, alloc=52.3MB, time=103.65
x[1] = 2.5804 2.122
h = 0.001 0.001
y[1] (numeric) = 3.80833784823 0.578201409034
y[1] (closed_form) = 3.80975967907 0.577383847513
absolute error = 0.00164
relative error = 0.04256 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.599
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = 3.80935393349 0.57767899512
y[1] (closed_form) = 3.81077571556 0.576861022412
absolute error = 0.00164
relative error = 0.04256 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.601
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5815 2.127
h = 0.003 0.006
y[1] (numeric) = 3.81245701878 0.578587536515
y[1] (closed_form) = 3.81388206952 0.577769007392
absolute error = 0.001643
relative error = 0.0426 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.602
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8473.1MB, alloc=52.3MB, time=104.21
x[1] = 2.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = 3.81782294702 0.577750608982
y[1] (closed_form) = 3.81925266614 0.576924007073
absolute error = 0.001651
relative error = 0.04276 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.608
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = 3.82171527321 0.578896287707
y[1] (closed_form) = 3.82315011404 0.578068858405
absolute error = 0.001656
relative error = 0.04284 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.61
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5847 2.141
h = 0.001 0.001
y[1] (numeric) = 3.82406658702 0.579551675809
y[1] (closed_form) = 3.82550326522 0.57872389869
absolute error = 0.001658
relative error = 0.04286 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.612
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8518.5MB, alloc=52.3MB, time=104.76
x[1] = 2.5857 2.142
h = 0.001 0.003
y[1] (numeric) = 3.82508757142 0.57901894305
y[1] (closed_form) = 3.8265241996 0.578190753804
absolute error = 0.001658
relative error = 0.04285 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.613
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = 3.82766289684 0.578972713243
y[1] (closed_form) = 3.82910102297 0.578143086295
absolute error = 0.00166
relative error = 0.04287 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.615
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5868 2.149
h = 0.003 0.006
y[1] (numeric) = 3.83080083435 0.579867274251
y[1] (closed_form) = 3.83224223736 0.579037078751
absolute error = 0.001663
relative error = 0.04292 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.617
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8563.9MB, alloc=52.3MB, time=105.32
x[1] = 2.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = 3.8362097137 0.57898426202
y[1] (closed_form) = 3.83765577281 0.578145954446
absolute error = 0.001671
relative error = 0.04307 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.623
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = 3.84014571599 0.580112593966
y[1] (closed_form) = 3.84159690942 0.579273439849
absolute error = 0.001676
relative error = 0.04315 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.625
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.59 2.163
h = 0.001 0.001
y[1] (numeric) = 3.84252311854 0.580757198768
y[1] (closed_form) = 3.84397615371 0.579917689802
absolute error = 0.001678
relative error = 0.04317 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.627
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8609.4MB, alloc=52.3MB, time=105.88
x[1] = 2.591 2.164
h = 0.001 0.003
y[1] (numeric) = 3.84354960681 0.580212351196
y[1] (closed_form) = 3.84500259045 0.579372429033
absolute error = 0.001678
relative error = 0.04316 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.628
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.592 2.167
h = 0.0001 0.004
y[1] (numeric) = 3.84614805092 0.580147388358
y[1] (closed_form) = 3.8476025323 0.579306019306
absolute error = 0.00168
relative error = 0.04318 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.63
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5921 2.171
h = 0.003 0.006
y[1] (numeric) = 3.84932089954 0.581027813916
y[1] (closed_form) = 3.85077866572 0.5801858639
absolute error = 0.001683
relative error = 0.04323 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.632
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8654.9MB, alloc=52.3MB, time=106.44
x[1] = 2.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = 3.85477270819 0.58009843927
y[1] (closed_form) = 3.85623511784 0.57924833768
absolute error = 0.001692
relative error = 0.04338 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.638
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = 3.85875246041 0.581209229942
y[1] (closed_form) = 3.86022001693 0.580358262424
absolute error = 0.001696
relative error = 0.04346 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.64
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5953 2.185
h = 0.001 0.001
y[1] (numeric) = 3.86115599441 0.581842933844
y[1] (closed_form) = 3.86262539701 0.580991604361
absolute error = 0.001698
relative error = 0.04348 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.642
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8700.3MB, alloc=52.3MB, time=107.00
x[1] = 2.5963 2.186
h = 0.001 0.003
y[1] (numeric) = 3.86218796331 0.581285917208
y[1] (closed_form) = 3.86365731287 0.580434173462
absolute error = 0.001698
relative error = 0.04347 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.643
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = 3.86480953383 0.581202089583
y[1] (closed_form) = 3.86628038084 0.580348889692
absolute error = 0.0017
relative error = 0.04349 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.645
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5974 2.193
h = 0.003 0.006
y[1] (numeric) = 3.86801735152 0.582068222909
y[1] (closed_form) = 3.86949149125 0.58121442949
absolute error = 0.001704
relative error = 0.04354 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.647
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8745.6MB, alloc=52.3MB, time=107.55
x[1] = 2.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = 3.87351206554 0.581092206186
y[1] (closed_form) = 3.8749908357 0.58023022149
absolute error = 0.001712
relative error = 0.04368 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.653
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = 3.87753564067 0.582185259097
y[1] (closed_form) = 3.87901957023 0.581322388854
absolute error = 0.001717
relative error = 0.04376 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.655
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6006 2.207
h = 0.001 0.001
y[1] (numeric) = 3.8799653483 0.582807943313
y[1] (closed_form) = 3.88145112825 0.581944703903
absolute error = 0.001718
relative error = 0.04378 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.657
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8791.0MB, alloc=52.3MB, time=108.11
x[1] = 2.6016 2.208
h = 0.001 0.003
y[1] (numeric) = 3.88100277404 0.582238703121
y[1] (closed_form) = 3.88248849942 0.581375048385
absolute error = 0.001719
relative error = 0.04378 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.658
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = 3.8836474778 0.58213587791
y[1] (closed_form) = 3.88513470028 0.581270757708
absolute error = 0.001721
relative error = 0.0438 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6027 2.215
h = 0.003 0.006
y[1] (numeric) = 3.88689032186 0.582987560634
y[1] (closed_form) = 3.88838084493 0.582121834192
absolute error = 0.001724
relative error = 0.04384 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.662
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8836.5MB, alloc=52.3MB, time=108.67
x[1] = 2.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = 3.89242791511 0.58196462026
y[1] (closed_form) = 3.89392305521 0.581090662634
absolute error = 0.001732
relative error = 0.04399 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.668
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = 3.8964953853 0.583039736945
y[1] (closed_form) = 3.89799569726 0.58216487392
absolute error = 0.001737
relative error = 0.04407 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6059 2.229
h = 0.001 0.001
y[1] (numeric) = 3.89895130819 0.583651281507
y[1] (closed_form) = 3.90045347486 0.582776042031
absolute error = 0.001739
relative error = 0.04408 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.672
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8881.7MB, alloc=52.3MB, time=109.22
x[1] = 2.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = 3.89999416642 0.583069763034
y[1] (closed_form) = 3.90149627697 0.582194107171
absolute error = 0.001739
relative error = 0.04408 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.673
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.607 2.234
h = 0.003 0.006
y[1] (numeric) = 3.90326738033 0.583909297407
y[1] (closed_form) = 3.90477279813 0.583033024218
absolute error = 0.001742
relative error = 0.04412 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.675
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.61 2.24
h = 0.0001 0.005
y[1] (numeric) = 3.90884242357 0.582846250111
y[1] (closed_form) = 3.91035244703 0.581961711066
absolute error = 0.00175
relative error = 0.04427 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.681
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8927.1MB, alloc=52.3MB, time=109.78
x[1] = 2.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = 3.91294795116 0.583906291495
y[1] (closed_form) = 3.91446315743 0.583020829924
absolute error = 0.001755
relative error = 0.04434 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.683
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6102 2.248
h = 0.001 0.001
y[1] (numeric) = 3.91542660688 0.584508463394
y[1] (closed_form) = 3.91694367162 0.583622619087
absolute error = 0.001757
relative error = 0.04436 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.685
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6112 2.249
h = 0.001 0.003
y[1] (numeric) = 3.91647426844 0.583916396497
y[1] (closed_form) = 3.91799127572 0.583030134873
absolute error = 0.001757
relative error = 0.04435 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.686
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=8972.6MB, alloc=52.3MB, time=110.34
x[1] = 2.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = 3.91916226296 0.583778139961
y[1] (closed_form) = 3.92068076662 0.582890395345
absolute error = 0.001759
relative error = 0.04438 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.688
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6123 2.256
h = 0.003 0.006
y[1] (numeric) = 3.92247060965 0.584602925409
y[1] (closed_form) = 3.92399242862 0.583714550595
absolute error = 0.001762
relative error = 0.04442 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.69
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = 3.9280884811 0.583492425144
y[1] (closed_form) = 3.92961489163 0.582595744201
absolute error = 0.00177
relative error = 0.04456 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.696
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9018.1MB, alloc=52.3MB, time=110.90
x[1] = 2.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = 3.93223803805 0.584534156622
y[1] (closed_form) = 3.93376964377 0.583636532868
absolute error = 0.001775
relative error = 0.04464 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.698
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6155 2.27
h = 0.001 0.001
y[1] (numeric) = 3.93474298655 0.585124963008
y[1] (closed_form) = 3.936276455 0.58422694908
absolute error = 0.001777
relative error = 0.04466 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.7
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6165 2.271
h = 0.001 0.003
y[1] (numeric) = 3.93579603444 0.584520515091
y[1] (closed_form) = 3.93732944385 0.583622082792
absolute error = 0.001777
relative error = 0.04465 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.701
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9063.6MB, alloc=52.3MB, time=111.46
x[1] = 2.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = 3.93850717843 0.584362875467
y[1] (closed_form) = 3.94004208366 0.583462950666
absolute error = 0.001779
relative error = 0.04467 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.704
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6176 2.278
h = 0.003 0.006
y[1] (numeric) = 3.9418507134 0.585172749257
y[1] (closed_form) = 3.94338894173 0.584272181123
absolute error = 0.001782
relative error = 0.04471 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.706
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = 3.94751138068 0.584014509097
y[1] (closed_form) = 3.94905418608 0.583105594372
absolute error = 0.001791
relative error = 0.04486 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.711
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9109.0MB, alloc=52.3MB, time=112.02
x[1] = 2.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = 3.95170503661 0.585037726611
y[1] (closed_form) = 3.95325304952 0.584127848561
absolute error = 0.001796
relative error = 0.04493 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.714
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6208 2.292
h = 0.001 0.001
y[1] (numeric) = 3.95423631796 0.585617044185
y[1] (closed_form) = 3.95578619786 0.58470676844
absolute error = 0.001797
relative error = 0.04495 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6218 2.293
h = 0.001 0.003
y[1] (numeric) = 3.95529472623 0.585000159884
y[1] (closed_form) = 3.95684454548 0.584089464716
absolute error = 0.001798
relative error = 0.04494 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.717
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9154.5MB, alloc=52.3MB, time=112.58
x[1] = 2.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = 3.95802902303 0.584823000452
y[1] (closed_form) = 3.95958033749 0.583910803211
absolute error = 0.0018
relative error = 0.04496 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.719
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6229 2.3
h = 0.003 0.006
y[1] (numeric) = 3.96140780083 0.585617798194
y[1] (closed_form) = 3.96296244612 0.584704944337
absolute error = 0.001803
relative error = 0.045 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.721
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9199.9MB, alloc=52.3MB, time=113.14
x[1] = 2.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = 3.96711122932 0.584411529406
y[1] (closed_form) = 3.96867043682 0.583490288312
absolute error = 0.001811
relative error = 0.04515 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.727
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.626 2.311
h = 0.0001 0.003
y[1] (numeric) = 3.97134905293 0.585416026975
y[1] (closed_form) = 3.97291348021 0.584493801812
absolute error = 0.001816
relative error = 0.04522 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.729
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6261 2.314
h = 0.001 0.001
y[1] (numeric) = 3.97390670664 0.585983731293
y[1] (closed_form) = 3.97547300513 0.585061100833
absolute error = 0.001818
relative error = 0.04524 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.731
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9245.3MB, alloc=52.3MB, time=113.70
x[1] = 2.6271 2.315
h = 0.001 0.003
y[1] (numeric) = 3.97497044876 0.58535435503
y[1] (closed_form) = 3.97653668498 0.5844313041
absolute error = 0.001818
relative error = 0.04523 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.732
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = 3.97772790082 0.58515753809
y[1] (closed_form) = 3.97929563155 0.584232975451
absolute error = 0.00182
relative error = 0.04525 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.734
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6282 2.322
h = 0.003 0.006
y[1] (numeric) = 3.98114197522 0.585937093862
y[1] (closed_form) = 3.9827130445 0.58501186118
absolute error = 0.001823
relative error = 0.04529 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.736
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9290.8MB, alloc=52.3MB, time=114.26
x[1] = 2.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = 3.98688812808 0.584682505931
y[1] (closed_form) = 3.98846374431 0.583748845185
absolute error = 0.001831
relative error = 0.04544 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = 3.99117018712 0.585668075665
y[1] (closed_form) = 3.99275103535 0.58473340988
absolute error = 0.001836
relative error = 0.04551 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.745
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6314 2.336
h = 0.001 0.001
y[1] (numeric) = 3.99375425213 0.586224041145
y[1] (closed_form) = 3.99533697577 0.585288962379
absolute error = 0.001838
relative error = 0.04553 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.746
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9336.2MB, alloc=52.3MB, time=114.83
x[1] = 2.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = 3.994823301 0.585582117141
y[1] (closed_form) = 3.99640596072 0.584646616862
absolute error = 0.001838
relative error = 0.04552 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.747
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6325 2.341
h = 0.003 0.006
y[1] (numeric) = 3.99826798454 0.586348840529
y[1] (closed_form) = 3.99985398933 0.585412658515
absolute error = 0.001842
relative error = 0.04556 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.75
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = 4.00405146222 0.585052935406
y[1] (closed_form) = 4.00564200102 0.584108289858
absolute error = 0.00185
relative error = 0.0457 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.755
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9381.7MB, alloc=52.3MB, time=115.38
x[1] = 2.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = 4.00837188005 0.586022572782
y[1] (closed_form) = 4.00996766156 0.585076904107
absolute error = 0.001855
relative error = 0.04577 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.758
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6357 2.355
h = 0.001 0.001
y[1] (numeric) = 4.01097885163 0.586568647669
y[1] (closed_form) = 4.01257651224 0.585622559383
absolute error = 0.001857
relative error = 0.04579 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.759
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6367 2.356
h = 0.001 0.003
y[1] (numeric) = 4.01205259663 0.585915940935
y[1] (closed_form) = 4.01365019191 0.584969430222
absolute error = 0.001857
relative error = 0.04578 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.761
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9427.1MB, alloc=52.3MB, time=115.94
x[1] = 2.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = 4.0148533766 0.585682451989
y[1] (closed_form) = 4.01645246505 0.584734411465
absolute error = 0.001859
relative error = 0.0458 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.763
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6378 2.363
h = 0.003 0.006
y[1] (numeric) = 4.01833345653 0.58643362115
y[1] (closed_form) = 4.01993589793 0.5854848853
absolute error = 0.001862
relative error = 0.04584 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.765
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = 4.02415958755 0.585088851152
y[1] (closed_form) = 4.02576654699 0.584131610613
absolute error = 0.00187
relative error = 0.04598 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.771
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9472.5MB, alloc=52.3MB, time=116.50
x[1] = 2.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = 4.02852436688 0.586039169606
y[1] (closed_form) = 4.03013658114 0.58508088455
absolute error = 0.001876
relative error = 0.04605 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.773
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.641 2.377
h = 0.001 0.001
y[1] (numeric) = 4.03115782215 0.586573269429
y[1] (closed_form) = 4.03277191966 0.585614556927
absolute error = 0.001877
relative error = 0.04607 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.775
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.642 2.378
h = 0.001 0.003
y[1] (numeric) = 4.03223682264 0.585907910303
y[1] (closed_form) = 4.03385085315 0.584948774337
absolute error = 0.001878
relative error = 0.04606 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.776
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9518.0MB, alloc=52.3MB, time=117.06
x[1] = 2.643 2.381
h = 0.0001 0.004
y[1] (numeric) = 4.03506076138 0.58565436458
y[1] (closed_form) = 4.03667628416 0.584693688994
absolute error = 0.00188
relative error = 0.04608 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.778
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6431 2.385
h = 0.003 0.006
y[1] (numeric) = 4.03857628952 0.586389809381
y[1] (closed_form) = 4.04019517284 0.585428424628
absolute error = 0.001883
relative error = 0.04612 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.781
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = 4.0444450306 0.584995879018
y[1] (closed_form) = 4.04606841562 0.584025948254
absolute error = 0.001891
relative error = 0.04626 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.786
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9563.4MB, alloc=52.3MB, time=117.62
x[1] = 2.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = 4.04885423642 0.585926665268
y[1] (closed_form) = 4.05048288831 0.58495566837
absolute error = 0.001896
relative error = 0.04633 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.789
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6463 2.399
h = 0.001 0.001
y[1] (numeric) = 4.05151421261 0.586448661236
y[1] (closed_form) = 4.05314475188 0.585477228977
absolute error = 0.001898
relative error = 0.04635 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6473 2.4
h = 0.001 0.003
y[1] (numeric) = 4.05259843989 0.585770593383
y[1] (closed_form) = 4.05422891046 0.584798736629
absolute error = 0.001898
relative error = 0.04634 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.792
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9608.8MB, alloc=52.3MB, time=118.18
x[1] = 2.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = 4.05544553622 0.585496849482
y[1] (closed_form) = 4.0570774981 0.584523443238
absolute error = 0.0019
relative error = 0.04636 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.794
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6484 2.407
h = 0.003 0.006
y[1] (numeric) = 4.05899656333 0.586216398198
y[1] (closed_form) = 4.06063189331 0.585242268804
absolute error = 0.001903
relative error = 0.0464 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.796
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = 4.06490786893 0.584773010304
y[1] (closed_form) = 4.06654768387 0.583790293412
absolute error = 0.001912
relative error = 0.04653 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.802
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9654.3MB, alloc=52.3MB, time=118.73
x[1] = 2.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = 4.06936156526 0.585684049213
y[1] (closed_form) = 4.07100665904 0.584700244347
absolute error = 0.001917
relative error = 0.04661 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.804
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6516 2.421
h = 0.001 0.001
y[1] (numeric) = 4.07204809898 0.586193811429
y[1] (closed_form) = 4.07369508425 0.58520956321
absolute error = 0.001919
relative error = 0.04662 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.806
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6526 2.422
h = 0.001 0.003
y[1] (numeric) = 4.07313752377 0.585502978335
y[1] (closed_form) = 4.07478443863 0.584518304593
absolute error = 0.001919
relative error = 0.04661 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.807
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9699.7MB, alloc=52.3MB, time=119.29
x[1] = 2.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = 4.07600777555 0.58520889393
y[1] (closed_form) = 4.07765618069 0.58422266077
absolute error = 0.001921
relative error = 0.04663 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6537 2.429
h = 0.003 0.006
y[1] (numeric) = 4.0795943516 0.585912373364
y[1] (closed_form) = 4.08124613234 0.584925402928
absolute error = 0.001924
relative error = 0.04667 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.812
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = 4.08554817387 0.584419229118
y[1] (closed_form) = 4.08720442246 0.583423629539
absolute error = 0.001932
relative error = 0.04681 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.817
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9745.1MB, alloc=52.3MB, time=119.85
x[1] = 2.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = 4.0900464237 0.585310303711
y[1] (closed_form) = 4.09170796304 0.584313594097
absolute error = 0.001938
relative error = 0.04688 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.82
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6569 2.443
h = 0.001 0.001
y[1] (numeric) = 4.09275955093 0.585807701188
y[1] (closed_form) = 4.09442298583 0.584810540146
absolute error = 0.001939
relative error = 0.04689 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.822
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = 4.09385414338 0.585104046165
y[1] (closed_form) = 4.09551750614 0.584106458578
absolute error = 0.00194
relative error = 0.04688 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.823
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9790.4MB, alloc=52.3MB, time=120.41
x[1] = 2.658 2.448
h = 0.003 0.006
y[1] (numeric) = 4.09747155263 0.58579397824
y[1] (closed_form) = 4.09913829735 0.584795641093
absolute error = 0.001943
relative error = 0.04692 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.825
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.661 2.454
h = 0.0001 0.005
y[1] (numeric) = 4.10346252934 0.584258270498
y[1] (closed_form) = 4.10513372736 0.583251268025
absolute error = 0.001951
relative error = 0.04706 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.831
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = 4.10799942036 0.585132517054
y[1] (closed_form) = 4.10967591959 0.584124385522
absolute error = 0.001956
relative error = 0.04713 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.833
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9835.9MB, alloc=52.3MB, time=120.97
x[1] = 2.6612 2.462
h = 0.001 0.001
y[1] (numeric) = 4.11073561616 0.585619483008
y[1] (closed_form) = 4.11241401455 0.584610893083
absolute error = 0.001958
relative error = 0.04714 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.835
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6622 2.463
h = 0.001 0.003
y[1] (numeric) = 4.11183478608 0.584904806835
y[1] (closed_form) = 4.11351311084 0.583895789468
absolute error = 0.001958
relative error = 0.04713 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.836
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = 4.11474836216 0.584572767284
y[1] (closed_form) = 4.11642817519 0.58356217186
absolute error = 0.00196
relative error = 0.04715 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.839
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9881.3MB, alloc=52.3MB, time=121.53
x[1] = 2.6633 2.47
h = 0.003 0.006
y[1] (numeric) = 4.11840141294 0.585246304388
y[1] (closed_form) = 4.1200846156 0.584234945116
absolute error = 0.001964
relative error = 0.04719 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.841
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = 4.12443481479 0.583660279323
y[1] (closed_form) = 4.12612245292 0.582640212788
absolute error = 0.001972
relative error = 0.04732 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.847
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = 4.12901637641 0.5845141537
y[1] (closed_form) = 4.13070932752 0.583492935634
absolute error = 0.001977
relative error = 0.04739 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.849
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9926.8MB, alloc=52.3MB, time=122.09
x[1] = 2.6665 2.484
h = 0.001 0.001
y[1] (numeric) = 4.13177923258 0.584988508705
y[1] (closed_form) = 4.13347408688 0.583966824026
absolute error = 0.001979
relative error = 0.04741 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.851
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6675 2.485
h = 0.001 0.003
y[1] (numeric) = 4.13288351378 0.584260904304
y[1] (closed_form) = 4.13457829269 0.583238791169
absolute error = 0.001979
relative error = 0.0474 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.852
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = 4.13582023563 0.583908112006
y[1] (closed_form) = 4.13751650157 0.582884410725
absolute error = 0.001981
relative error = 0.04742 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.855
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=9972.1MB, alloc=52.3MB, time=122.64
x[1] = 2.6686 2.492
h = 0.003 0.006
y[1] (numeric) = 4.13950897578 0.584565076882
y[1] (closed_form) = 4.14120863872 0.583540597224
absolute error = 0.001985
relative error = 0.04745 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.857
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = 4.14558474834 0.582928431069
y[1] (closed_form) = 4.14728882853 0.581895202064
absolute error = 0.001993
relative error = 0.04759 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.862
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = 4.15021104058 0.583761711099
y[1] (closed_form) = 4.15192044546 0.582727307873
absolute error = 0.001998
relative error = 0.04766 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.865
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10017.4MB, alloc=52.3MB, time=123.20
x[1] = 2.6718 2.506
h = 0.001 0.001
y[1] (numeric) = 4.15300059127 0.584223321078
y[1] (closed_form) = 4.15471190335 0.58318844294
absolute error = 0.002
relative error = 0.04767 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.867
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6728 2.507
h = 0.001 0.003
y[1] (numeric) = 4.15410995229 0.583482731289
y[1] (closed_form) = 4.15582118719 0.582447423688
absolute error = 0.002
relative error = 0.04766 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.868
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = 4.15706981405 0.583109040437
y[1] (closed_form) = 4.15878253467 0.582072134544
absolute error = 0.002002
relative error = 0.04768 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10062.8MB, alloc=52.3MB, time=123.76
x[1] = 2.6739 2.514
h = 0.003 0.006
y[1] (numeric) = 4.16079429027 0.583749254301
y[1] (closed_form) = 4.16251041522 0.582711555363
absolute error = 0.002005
relative error = 0.04771 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.873
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = 4.1669123768 0.582061682764
y[1] (closed_form) = 4.16863290038 0.58101519225
absolute error = 0.002014
relative error = 0.04785 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.878
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.677 2.525
h = 0.0001 0.003
y[1] (numeric) = 4.17158345861 0.582874144497
y[1] (closed_form) = 4.17330931853 0.581826456856
absolute error = 0.002019
relative error = 0.04791 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.881
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10108.2MB, alloc=52.3MB, time=124.31
x[1] = 2.6771 2.528
h = 0.001 0.001
y[1] (numeric) = 4.17439973734 0.583322874312
y[1] (closed_form) = 4.17612750841 0.582274703384
absolute error = 0.002021
relative error = 0.04793 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.883
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6781 2.529
h = 0.001 0.003
y[1] (numeric) = 4.17551414612 0.582569241823
y[1] (closed_form) = 4.17724183823 0.581520640429
absolute error = 0.002021
relative error = 0.04792 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.884
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = 4.17849714095 0.58217450574
y[1] (closed_form) = 4.18022631737 0.581124295854
absolute error = 0.002023
relative error = 0.04794 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.886
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10153.6MB, alloc=52.3MB, time=124.87
x[1] = 2.6792 2.536
h = 0.003 0.006
y[1] (numeric) = 4.18225739908 0.582797788391
y[1] (closed_form) = 4.18398998712 0.581746770653
absolute error = 0.002026
relative error = 0.04797 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.888
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = 4.1884177405 0.58105898463
y[1] (closed_form) = 4.19015470817 0.579999132949
absolute error = 0.002035
relative error = 0.0481 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.894
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = 4.19313366976 0.581850402347
y[1] (closed_form) = 4.19487598532 0.580789330416
absolute error = 0.00204
relative error = 0.04817 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.897
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10199.0MB, alloc=52.3MB, time=125.42
x[1] = 2.6824 2.55
h = 0.001 0.001
y[1] (numeric) = 4.19597670933 0.582286115811
y[1] (closed_form) = 4.19772093999 0.581224552142
absolute error = 0.002042
relative error = 0.04818 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.898
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = 4.19709613328 0.581519383165
y[1] (closed_form) = 4.19884028316 0.580457388032
absolute error = 0.002042
relative error = 0.04818 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.9
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6835 2.555
h = 0.003 0.006
y[1] (numeric) = 4.20088743221 0.582128373671
y[1] (closed_form) = 4.20263499986 0.581065557827
absolute error = 0.002045
relative error = 0.04821 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.902
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10244.4MB, alloc=52.3MB, time=125.98
x[1] = 2.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = 4.20708471141 0.580345726676
y[1] (closed_form) = 4.20883664253 0.579274040078
absolute error = 0.002054
relative error = 0.04834 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.908
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = 4.21183954371 0.581119383456
y[1] (closed_form) = 4.21359683289 0.580046456669
absolute error = 0.002059
relative error = 0.04841 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10289.9MB, alloc=52.3MB, time=126.54
x[1] = 2.6867 2.569
h = 0.001 0.001
y[1] (numeric) = 4.21470580119 0.581544102322
y[1] (closed_form) = 4.21646500893 0.580470676505
absolute error = 0.002061
relative error = 0.04842 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.912
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6877 2.57
h = 0.001 0.003
y[1] (numeric) = 4.21582967246 0.580766106582
y[1] (closed_form) = 4.21758879786 0.579692248425
absolute error = 0.002061
relative error = 0.04841 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.913
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = 4.21885594574 0.580332092233
y[1] (closed_form) = 4.22061655279 0.579256606444
absolute error = 0.002063
relative error = 0.04843 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.916
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10335.3MB, alloc=52.3MB, time=127.11
x[1] = 2.6888 2.577
h = 0.003 0.006
y[1] (numeric) = 4.22268311146 0.580923812915
y[1] (closed_form) = 4.22444714372 0.579847491446
absolute error = 0.002066
relative error = 0.04846 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.918
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = 4.22892253307 0.579089358632
y[1] (closed_form) = 4.23069090908 0.578004123787
absolute error = 0.002075
relative error = 0.04859 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.924
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = 4.23372232028 0.579841547389
y[1] (closed_form) = 4.23549606576 0.578755048833
absolute error = 0.00208
relative error = 0.04866 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.926
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10380.8MB, alloc=52.3MB, time=127.67
x[1] = 2.692 2.591
h = 0.001 0.001
y[1] (numeric) = 4.23661539954 0.580252994095
y[1] (closed_form) = 4.23839106748 0.579165987914
absolute error = 0.002082
relative error = 0.04867 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.928
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.693 2.592
h = 0.001 0.003
y[1] (numeric) = 4.23774422447 0.579461790511
y[1] (closed_form) = 4.23951980822 0.578374351003
absolute error = 0.002082
relative error = 0.04866 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.929
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.694 2.595
h = 0.0001 0.004
y[1] (numeric) = 4.2407936075 0.579006306493
y[1] (closed_form) = 4.24257067129 0.577917229002
absolute error = 0.002084
relative error = 0.04868 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.932
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10426.1MB, alloc=52.3MB, time=128.22
x[1] = 2.6941 2.599
h = 0.003 0.006
y[1] (numeric) = 4.24465668357 0.579580573246
y[1] (closed_form) = 4.2464371797 0.578490644877
absolute error = 0.002088
relative error = 0.04871 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.934
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = 4.2509381818 0.577694000929
y[1] (closed_form) = 4.25272300157 0.576595116433
absolute error = 0.002096
relative error = 0.04884 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.94
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = 4.25578297863 0.578424490953
y[1] (closed_form) = 4.2575731792 0.577324319011
absolute error = 0.002101
relative error = 0.04891 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.943
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10471.5MB, alloc=52.3MB, time=128.78
x[1] = 2.6973 2.613
h = 0.001 0.001
y[1] (numeric) = 4.25870291055 0.578822526345
y[1] (closed_form) = 4.26049503743 0.577721838108
absolute error = 0.002103
relative error = 0.04892 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.944
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6983 2.614
h = 0.001 0.003
y[1] (numeric) = 4.25983665492 0.578018057067
y[1] (closed_form) = 4.26162869574 0.576916934523
absolute error = 0.002103
relative error = 0.04891 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.946
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = 4.26290913699 0.577540953438
y[1] (closed_form) = 4.26470265619 0.576438182508
absolute error = 0.002105
relative error = 0.04892 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.948
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10516.9MB, alloc=52.3MB, time=129.34
x[1] = 2.6994 2.621
h = 0.003 0.006
y[1] (numeric) = 4.2668081658 0.578097580692
y[1] (closed_form) = 4.26860512441 0.576993943552
absolute error = 0.002109
relative error = 0.04896 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = 4.2731316725 0.576158578168
y[1] (closed_form) = 4.27493293425 0.575045942026
absolute error = 0.002117
relative error = 0.04908 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.956
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = 4.2780215325 0.576867137037
y[1] (closed_form) = 4.2798281863 0.575753189503
absolute error = 0.002122
relative error = 0.04915 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.959
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10562.3MB, alloc=52.3MB, time=129.90
x[1] = 2.7026 2.635
h = 0.001 0.001
y[1] (numeric) = 4.28096834727 0.577251620944
y[1] (closed_form) = 4.2827769312 0.57613714837
absolute error = 0.002124
relative error = 0.04916 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.96
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7036 2.636
h = 0.001 0.003
y[1] (numeric) = 4.28210697626 0.576433828
y[1] (closed_form) = 4.28391547225 0.575318920143
absolute error = 0.002125
relative error = 0.04915 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.962
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = 4.28520254567 0.575934954002
y[1] (closed_form) = 4.28701251828 0.574818387306
absolute error = 0.002127
relative error = 0.04917 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.964
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10607.7MB, alloc=52.3MB, time=130.46
x[1] = 2.7047 2.643
h = 0.003 0.006
y[1] (numeric) = 4.28913756869 0.576473754829
y[1] (closed_form) = 4.29095098773 0.575356306456
absolute error = 0.00213
relative error = 0.0492 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.966
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = 4.29550301332 0.574482008525
y[1] (closed_form) = 4.29732071462 0.573355518156
absolute error = 0.002138
relative error = 0.04933 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.972
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = 4.3004379889 0.575168402119
y[1] (closed_form) = 4.30226109341 0.574040576201
absolute error = 0.002144
relative error = 0.04939 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.975
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10653.2MB, alloc=52.3MB, time=131.01
x[1] = 2.7079 2.657
h = 0.001 0.001
y[1] (numeric) = 4.30341171599 0.575539193363
y[1] (closed_form) = 4.30523675442 0.574410833585
absolute error = 0.002146
relative error = 0.0494 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.977
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = 4.30455519424 0.574708018661
y[1] (closed_form) = 4.30638014283 0.573579222631
absolute error = 0.002146
relative error = 0.04939 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.978
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.709 2.662
h = 0.003 0.006
y[1] (numeric) = 4.308521448 0.575231753877
y[1] (closed_form) = 4.31034984896 0.57410206275
absolute error = 0.002149
relative error = 0.04943 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10698.5MB, alloc=52.3MB, time=131.57
x[1] = 2.712 2.668
h = 0.0001 0.005
y[1] (numeric) = 4.31492356651 0.573194853711
y[1] (closed_form) = 4.31675623194 0.572056083229
absolute error = 0.002158
relative error = 0.04955 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.986
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = 4.31989768501 0.573862517655
y[1] (closed_form) = 4.32173576349 0.572722390798
absolute error = 0.002163
relative error = 0.04961 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.989
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7122 2.676
h = 0.001 0.001
y[1] (numeric) = 4.3228947658 0.574221729939
y[1] (closed_form) = 4.32473478154 0.573081061614
absolute error = 0.002165
relative error = 0.04962 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.99
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10743.8MB, alloc=52.3MB, time=132.13
x[1] = 2.7132 2.677
h = 0.001 0.003
y[1] (numeric) = 4.32404254971 0.573379047243
y[1] (closed_form) = 4.32588247397 0.572237941813
absolute error = 0.002165
relative error = 0.04962 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.992
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = 4.32718130822 0.572839534312
y[1] (closed_form) = 4.32902270576 0.57169675044
absolute error = 0.002167
relative error = 0.04963 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.994
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7143 2.684
h = 0.003 0.006
y[1] (numeric) = 4.33118363286 0.573345092077
y[1] (closed_form) = 4.33302848993 0.572201397478
absolute error = 0.002171
relative error = 0.04966 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 4.996
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10789.4MB, alloc=52.3MB, time=132.69
x[1] = 2.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = 4.33762755549 0.571254860098
y[1] (closed_form) = 4.33947665543 0.570102042929
absolute error = 0.002179
relative error = 0.04979 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.002
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = 4.34264688681 0.571899919248
y[1] (closed_form) = 4.34450141079 0.570745721159
absolute error = 0.002184
relative error = 0.04985 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.005
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7175 2.698
h = 0.001 0.001
y[1] (numeric) = 4.34567093456 0.572245173845
y[1] (closed_form) = 4.34752739953 0.571090425329
absolute error = 0.002186
relative error = 0.04986 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.007
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10834.8MB, alloc=52.3MB, time=133.24
x[1] = 2.7185 2.699
h = 0.001 0.003
y[1] (numeric) = 4.3468235011 0.571389000564
y[1] (closed_form) = 4.34867987266 0.570233813987
absolute error = 0.002186
relative error = 0.04985 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.008
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = 4.34998530963 0.570827281399
y[1] (closed_form) = 4.35184315249 0.569670405785
absolute error = 0.002189
relative error = 0.04987 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.01
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7196 2.706
h = 0.003 0.006
y[1] (numeric) = 4.35402374417 0.571314471033
y[1] (closed_form) = 4.35588505343 0.570156668845
absolute error = 0.002192
relative error = 0.0499 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.013
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10880.3MB, alloc=52.3MB, time=133.80
x[1] = 2.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = 4.36050939358 0.569170589771
y[1] (closed_form) = 4.3623749237 0.56800362169
absolute error = 0.0022
relative error = 0.05002 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.018
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = 4.36557398676 0.569792805215
y[1] (closed_form) = 4.36744495184 0.568624431465
absolute error = 0.002206
relative error = 0.05008 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.021
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7228 2.72
h = 0.001 0.001
y[1] (numeric) = 4.36862502891 0.570123958102
y[1] (closed_form) = 4.37049793866 0.568955024893
absolute error = 0.002208
relative error = 0.05009 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.023
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10925.7MB, alloc=52.3MB, time=134.36
x[1] = 2.7238 2.721
h = 0.001 0.003
y[1] (numeric) = 4.36978234107 0.569254235831
y[1] (closed_form) = 4.37165515547 0.568084863609
absolute error = 0.002208
relative error = 0.05008 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.024
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = 4.37296718397 0.568670156618
y[1] (closed_form) = 4.37484146762 0.567499084721
absolute error = 0.00221
relative error = 0.0501 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.027
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7249 2.728
h = 0.003 0.006
y[1] (numeric) = 4.37704176621 0.569138786043
y[1] (closed_form) = 4.37891952306 0.567966771593
absolute error = 0.002214
relative error = 0.05013 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.029
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=10971.2MB, alloc=52.3MB, time=134.92
x[1] = 2.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = 4.38356906265 0.566940936726
y[1] (closed_form) = 4.38545101796 0.565759712954
absolute error = 0.002222
relative error = 0.05025 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.035
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.728 2.739
h = 0.0001 0.003
y[1] (numeric) = 4.38867896556 0.567540067913
y[1] (closed_form) = 4.39056636665 0.566357413515
absolute error = 0.002227
relative error = 0.05031 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.038
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7281 2.742
h = 0.001 0.001
y[1] (numeric) = 4.39175702876 0.567856974093
y[1] (closed_form) = 4.39364637818 0.566673751132
absolute error = 0.002229
relative error = 0.05032 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.039
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11016.6MB, alloc=52.3MB, time=135.48
x[1] = 2.7291 2.743
h = 0.001 0.003
y[1] (numeric) = 4.392919049 0.566973644327
y[1] (closed_form) = 4.3948083011 0.56578998141
absolute error = 0.002229
relative error = 0.05031 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.041
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = 4.39612690956 0.566367050494
y[1] (closed_form) = 4.39801762879 0.565181677214
absolute error = 0.002232
relative error = 0.05033 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.043
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7302 2.75
h = 0.003 0.006
y[1] (numeric) = 4.40023767634 0.566816926328
y[1] (closed_form) = 4.40213187551 0.565630594388
absolute error = 0.002235
relative error = 0.05036 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.046
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11062.0MB, alloc=52.3MB, time=136.04
x[1] = 2.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = 4.40680653766 0.564564788905
y[1] (closed_form) = 4.4087049125 0.563369204109
absolute error = 0.002243
relative error = 0.05048 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.051
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = 4.41196179692 0.565140593653
y[1] (closed_form) = 4.41386562827 0.563943553074
absolute error = 0.002249
relative error = 0.05054 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.054
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7334 2.764
h = 0.001 0.001
y[1] (numeric) = 4.41506690712 0.565443107164
y[1] (closed_form) = 4.41697269043 0.564245488844
absolute error = 0.002251
relative error = 0.05055 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.056
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11107.5MB, alloc=52.3MB, time=136.60
x[1] = 2.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = 4.4162335973 0.564546111309
y[1] (closed_form) = 4.4181392813 0.563348052096
absolute error = 0.002251
relative error = 0.05054 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.057
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7345 2.769
h = 0.003 0.006
y[1] (numeric) = 4.42037576608 0.564980120518
y[1] (closed_form) = 4.42228493572 0.563781088682
absolute error = 0.002254
relative error = 0.05057 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.059
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = 4.42698098931 0.562681490198
y[1] (closed_form) = 4.42889431522 0.561473167678
absolute error = 0.002263
relative error = 0.05069 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.065
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11152.9MB, alloc=52.3MB, time=137.15
x[1] = 2.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = 4.43217560804 0.56323756218
y[1] (closed_form) = 4.43409439991 0.562027762185
absolute error = 0.002268
relative error = 0.05075 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.068
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7377 2.783
h = 0.001 0.001
y[1] (numeric) = 4.43530419343 0.563527891937
y[1] (closed_form) = 4.43722494045 0.562317506287
absolute error = 0.00227
relative error = 0.05076 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7387 2.784
h = 0.001 0.003
y[1] (numeric) = 4.43647503611 0.562619140781
y[1] (closed_form) = 4.43839568212 0.561408313412
absolute error = 0.00227
relative error = 0.05075 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.071
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11198.3MB, alloc=52.3MB, time=137.71
x[1] = 2.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = 4.43972595173 0.561970512196
y[1] (closed_form) = 4.44164806084 0.560757954431
absolute error = 0.002273
relative error = 0.05076 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.074
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7398 2.791
h = 0.003 0.006
y[1] (numeric) = 4.44390437306 0.562385404886
y[1] (closed_form) = 4.44582997468 0.561171858223
absolute error = 0.002276
relative error = 0.05079 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.076
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = 4.45055100569 0.560031886547
y[1] (closed_form) = 4.45248074007 0.558809005485
absolute error = 0.002285
relative error = 0.05091 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.082
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11243.7MB, alloc=52.3MB, time=138.27
x[1] = 2.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = 4.45579106721 0.560564177691
y[1] (closed_form) = 4.45772627811 0.559339793617
absolute error = 0.00229
relative error = 0.05097 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.085
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.743 2.805
h = 0.001 0.001
y[1] (numeric) = 4.45894674762 0.560839840925
y[1] (closed_form) = 4.46088391722 0.559614861885
absolute error = 0.002292
relative error = 0.05098 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.086
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.744 2.806
h = 0.001 0.003
y[1] (numeric) = 4.46012218849 0.559917313951
y[1] (closed_form) = 4.46205925507 0.558691892268
absolute error = 0.002292
relative error = 0.05097 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.088
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11289.2MB, alloc=52.3MB, time=138.83
x[1] = 2.745 2.809
h = 0.0001 0.004
y[1] (numeric) = 4.46339607011 0.559245724202
y[1] (closed_form) = 4.46533459744 0.558018561308
absolute error = 0.002294
relative error = 0.05098 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.09
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7451 2.813
h = 0.003 0.006
y[1] (numeric) = 4.46761077824 0.559641303391
y[1] (closed_form) = 4.46955280465 0.558413135121
absolute error = 0.002298
relative error = 0.05101 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.093
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = 4.47429873121 0.557232573429
y[1] (closed_form) = 4.47624486647 0.555995026952
absolute error = 0.002306
relative error = 0.05113 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.098
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11334.6MB, alloc=52.3MB, time=139.39
x[1] = 2.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = 4.47958427863 0.557740836963
y[1] (closed_form) = 4.48153590086 0.556501761739
absolute error = 0.002312
relative error = 0.05119 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.101
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7483 2.827
h = 0.001 0.001
y[1] (numeric) = 4.48276707785 0.558001684989
y[1] (closed_form) = 4.48472066229 0.556762005415
absolute error = 0.002314
relative error = 0.0512 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7493 2.828
h = 0.001 0.003
y[1] (numeric) = 4.48394707716 0.557065323362
y[1] (closed_form) = 4.48590055656 0.555825200229
absolute error = 0.002314
relative error = 0.05119 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11380.1MB, alloc=52.3MB, time=139.95
x[1] = 2.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = 4.48724390403 0.556370615028
y[1] (closed_form) = 4.48919884176 0.555128739825
absolute error = 0.002316
relative error = 0.0512 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.107
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7504 2.835
h = 0.003 0.006
y[1] (numeric) = 4.49149493197 0.5567466824
y[1] (closed_form) = 4.49345337527 0.555503785219
absolute error = 0.00232
relative error = 0.05123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.109
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11425.4MB, alloc=52.3MB, time=140.50
x[1] = 2.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = 4.49822411378 0.554282416023
y[1] (closed_form) = 4.50018664163 0.553030096738
absolute error = 0.002328
relative error = 0.05135 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.115
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = 4.50355518895 0.554766403605
y[1] (closed_form) = 4.50552321412 0.553512529638
absolute error = 0.002334
relative error = 0.05141 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.118
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7536 2.849
h = 0.001 0.001
y[1] (numeric) = 4.50676512997 0.555012286805
y[1] (closed_form) = 4.50873512084 0.553757799036
absolute error = 0.002336
relative error = 0.05141 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.12
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11470.8MB, alloc=52.3MB, time=141.06
x[1] = 2.7546 2.85
h = 0.001 0.003
y[1] (numeric) = 4.50794964741 0.554062031618
y[1] (closed_form) = 4.5099195312 0.55280709938
absolute error = 0.002336
relative error = 0.0514 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.121
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = 4.51126939775 0.553344046571
y[1] (closed_form) = 4.51324073736 0.55208735136
absolute error = 0.002338
relative error = 0.05142 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.123
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7557 2.857
h = 0.003 0.006
y[1] (numeric) = 4.51555677747 0.553700402566
y[1] (closed_form) = 4.51753162908 0.552442668647
absolute error = 0.002341
relative error = 0.05144 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11516.0MB, alloc=52.3MB, time=141.62
x[1] = 2.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = 4.52232709417 0.55118027382
y[1] (closed_form) = 4.52430600565 0.549913073818
absolute error = 0.00235
relative error = 0.05156 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.132
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = 4.52770373767 0.551639735549
y[1] (closed_form) = 4.52968815672 0.550370954733
absolute error = 0.002355
relative error = 0.05162 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.134
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7589 2.871
h = 0.001 0.001
y[1] (numeric) = 4.53094084273 0.551870503384
y[1] (closed_form) = 4.53292723092 0.550601099243
absolute error = 0.002357
relative error = 0.05163 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.136
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=11561.4MB, alloc=52.3MB, time=142.18
x[1] = 2.7599 2.872
h = 0.001 0.003
y[1] (numeric) = 4.53212983742 0.550906295663
y[1] (closed_form) = 4.53411611647 0.549636446151
absolute error = 0.002358
relative error = 0.05162 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 5.138
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ;
Iterations = 754
Total Elapsed Time = 2 Minutes 22 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 2 Minutes 22 Seconds
> quit
memory used=11579.9MB, alloc=52.3MB, time=142.40