|\^/| 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(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2)))); > end; exact_soln_y := proc(x) return c(0.8)*(c(x) + c(2.0))*sqrt(sqrt(c(0.1)*c(x) + c(0.2))) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 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0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > ind_var := array_x[1]; > omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > abserr := float_abs(numeric_val - closed_form_val_y); > if (float_abs(closed_form_val_y) > 0.0) then # if number 3 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 4 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > fi;# end if 4; > else > ; > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 3; > if (glob_good_digits < glob_min_good_digits) then # if number 3 > glob_min_good_digits := glob_good_digits; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,4," "); > omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > #BOTTOM DISPLAY ALOT > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ind_var := array_x[1]; omniout_complex(ALWAYS, "x[1] ", 33, ind_var, 20, " "); term_no := 1; numeric_val := array_y[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_complex(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); abserr := float_abs(numeric_val - closed_form_val_y); if 0. < float_abs(closed_form_val_y) then relerr := abserr/float_abs(closed_form_val_y); if 0. < float_abs(c(relerr)) then glob_good_digits := round(-log10(relerr)) else relerr := 0.; glob_good_digits := Digits - 2 end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 4, " "); omniout_float(ALWAYS, "relative error ", 4, relerr*glob__100, 4, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " ") end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > ; > if (true) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; display_poles() end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre sqrt 1 $eq_no = 1 > array_tmp4[1] := sqrt(array_tmp3[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2; > #emit pre sqrt ID_FULL iii = 2 $eq_no = 1 > #emit pre sqrt 2 $eq_no = 1 > array_tmp4[2] := 0; > array_tmp4[2] := (array_tmp3[2]-ats(2,array_tmp4,array_tmp4,2)) / array_tmp4[1] /glob__2; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0; > array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre sqrt ID_FULL iii = 3 $eq_no = 1 > #emit pre sqrt 3 $eq_no = 1 > array_tmp4[3] := 0; > array_tmp4[3] := (array_tmp3[3]-ats(3,array_tmp4,array_tmp4,2)) / array_tmp4[1] /glob__2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0; > array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre sqrt ID_FULL iii = 4 $eq_no = 1 > #emit pre sqrt 4 $eq_no = 1 > array_tmp4[4] := 0; > array_tmp4[4] := (array_tmp3[4]-ats(4,array_tmp4,array_tmp4,2)) / array_tmp4[1] /glob__2; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0; > array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre sqrt ID_FULL iii = 5 $eq_no = 1 > #emit pre sqrt 5 $eq_no = 1 > array_tmp4[5] := 0; > array_tmp4[5] := (array_tmp3[5]-ats(5,array_tmp4,array_tmp4,2)) / array_tmp4[1] /glob__2; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0; > array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2; > #emit sqrt FULL $eq_no = 1 > array_tmp4[kkk] := 0; > array_tmp4[kkk] := (array_tmp3[kkk] - ats(kkk,array_tmp4,array_tmp4,2)) / array_tmp4[1] / glob__2; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4[1] := sqrt(array_tmp3[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2); array_tmp4[2] := 0; array_tmp4[2] := (array_tmp3[2] - ats(2, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*glob__2); array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[3] := 0; array_tmp3[3] := neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4[3] := 0; array_tmp4[3] := (array_tmp3[3] - ats(3, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*glob__2); array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[4] := 0; array_tmp3[4] := neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4[4] := 0; array_tmp4[4] := (array_tmp3[4] - ats(4, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*glob__2); array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[5] := 0; array_tmp3[5] := neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4[5] := 0; array_tmp4[5] := (array_tmp3[5] - ats(5, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*glob__2); array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp3[kkk] := 0; array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/( array_tmp3[1]*glob__2); array_tmp4[kkk] := 0; array_tmp4[kkk] := ( array_tmp3[kkk] - ats(kkk, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*glob__2); array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=40; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(40),[]); > array_x:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_tmp4:= Array(0..(40),[]); > array_tmp5:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(40) ,(0..40+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 40) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=40) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_0D1); > array_const_0D1[1] := c(0.1); > zero_ats_ar(array_const_0D2); > array_const_0D2[1] := c(0.2); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > array_y_set_initial[1,31] := false; > array_y_set_initial[1,32] := false; > array_y_set_initial[1,33] := false; > array_y_set_initial[1,34] := false; > array_y_set_initial[1,35] := false; > array_y_set_initial[1,36] := false; > array_y_set_initial[1,37] := false; > array_y_set_initial[1,38] := false; > array_y_set_initial[1,39] := false; > array_y_set_initial[1,40] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 40; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sqrt_sqrt_tzeropostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_min_h := c(0.001);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-2.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_min_h := c(0.001); > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(-2.0); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(0.5); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=10000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1 > #left paren 0001C > if (true) then # if number 10 > omniout_str(INFO," "); > fi;# end if 10; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > atomall(); > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10 > display_alot(current_iter); > fi;# end if 10; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (true) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2017-11-26T16:35:40-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sqrt_sqrt_tzero") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ") > ; > logitem_complex(html_log_file,x_start) > ; > logitem_complex(html_log_file,x_end) > ; > logitem_complex(html_log_file,array_x[1]) > ; > logitem_complex(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > glob_desired_digits_correct := 0.0; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > glob_least_ratio_sing := 0; > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > glob_least_6_sing := 0.0; > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 309 ") > ; > logitem_str(html_log_file,"sqrt_sqrt_tzero diffeq.mxt") > ; > logitem_str(html_log_file,"sqrt_sqrt_tzero maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 40; Digits := 32; max_terms := 40; glob_html_log := true; array_y_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 40, []); array_x := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_tmp4 := Array(0 .. 40, []); array_tmp5 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y_higher := Array(0 .. 2, 0 .. 41, []); array_y_higher_work := Array(0 .. 2, 0 .. 41, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y_set_initial := Array(0 .. 2, 0 .. 41, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 40 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 40 do term := 1; while term <= 40 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_0D1); array_const_0D1[1] := c(0.1); zero_ats_ar(array_const_0D2); array_const_0D2[1] := c(0.2); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; array_y_set_initial[1, 31] := false; array_y_set_initial[1, 32] := false; array_y_set_initial[1, 33] := false; array_y_set_initial[1, 34] := false; array_y_set_initial[1, 35] := false; array_y_set_initial[1, 36] := false; array_y_set_initial[1, 37] := false; array_y_set_initial[1, 38] := false; array_y_set_initial[1, 39] := false; array_y_set_initial[1, 40] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 40; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sqrt_sqrt_tzeropostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1\ * x + 0.2 ) ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_min_h := c(0.001);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-2.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.\ 1) * c(x) + c(0.2))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "next_delta := proc()"); omniout_str(ALWAYS, "global glob_nxt, x_delta;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 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* I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.000 + 0.000 * I ];"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;"); omniout_str(ALWAYS, "it := x_delta[glob_nxt];"); omniout_str(ALWAYS, "return it;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 0.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_min_h := c(0.001); glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(-2.0); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(0.5); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 10000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius ; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and (glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do omniout_str(INFO, " "); found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); atomall(); if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sqrt ( sqrt ( 0\ .1 * x + 0.2 ) ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2017-11-26T16:35:40-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sqrt_sqrt_tzero"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sq\ rt ( sqrt ( 0.1 * x + 0.2 ) ) ; "); logitem_complex(html_log_file, x_start); logitem_complex(html_log_file, x_end); logitem_complex(html_log_file, array_x[1]); logitem_complex(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); glob_desired_digits_correct := 0.; logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then glob_least_ratio_sing := 0; logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then glob_least_6_sing := 0.; logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 309 "); logitem_str(html_log_file, "sqrt_sqrt_tzero diffeq.mxt"); logitem_str(html_log_file, "sqrt_sqrt_tzero maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.9MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrt_tzeropostcpx.cpx################# diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_min_h := c(0.001); glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(-2.0); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(0.5); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=10000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2)))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 0.1 h = 0.0001 0.005 y[1] (numeric) = 1.13686852293 0.067699518624 y[1] (closed_form) = 1.13686852293 0.067699518624 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.628 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = 1.13689515458 0.071085844524 y[1] (closed_form) = 1.13689495357 0.0710858559437 absolute error = 2.013e-07 relative error = 1.767e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.262 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=32.1MB, alloc=40.3MB, time=0.41 x[1] = 0.1002 0.108 h = 0.001 0.001 y[1] (numeric) = 1.13693689346 0.0731180867224 y[1] (closed_form) = 1.13693693349 0.0731180808218 absolute error = 4.046e-08 relative error = 3.551e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9908 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1012 0.109 h = 0.001 0.003 y[1] (numeric) = 1.13760521473 0.0738040449107 y[1] (closed_form) = 1.13760536965 0.0738039902229 absolute error = 1.643e-07 relative error = 1.441e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.104 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.705 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = 1.13825602933 0.075844627779 y[1] (closed_form) = 1.13825594625 0.0758446629722 absolute error = 9.023e-08 relative error = 7.910e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.105 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.664 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1023 0.116 h = 0.003 0.006 y[1] (numeric) = 1.13828723543 0.0785549389675 y[1] (closed_form) = 1.13828698228 0.0785548402311 absolute error = 2.717e-07 relative error = 2.381e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.105 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.53 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = 1.14026227443 0.0826474417242 y[1] (closed_form) = 1.14026192872 0.0826482884106 absolute error = 9.145e-07 relative error = 8.000e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.572 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=77.6MB, alloc=44.3MB, time=0.97 x[1] = 0.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = 1.14027983895 0.0860370352948 y[1] (closed_form) = 1.14027965596 0.086037287927 absolute error = 3.119e-07 relative error = 2.728e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.266 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1055 0.13 h = 0.001 0.001 y[1] (numeric) = 1.14031637936 0.0880709538486 y[1] (closed_form) = 1.1403164367 0.0880711873462 absolute error = 2.404e-07 relative error = 2.102e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9939 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1065 0.131 h = 0.001 0.003 y[1] (numeric) = 1.14098345327 0.0887591627282 y[1] (closed_form) = 1.14098362486 0.0887593466696 absolute error = 2.516e-07 relative error = 2.198e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.111 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.719 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = 1.14162952484 0.090802997813 y[1] (closed_form) = 1.14162945967 0.0908032732529 absolute error = 2.830e-07 relative error = 2.471e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.672 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1076 0.138 h = 0.003 0.006 y[1] (numeric) = 1.14165379463 0.0935154980137 y[1] (closed_form) = 1.14165355877 0.0935156411481 absolute error = 2.759e-07 relative error = 2.409e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.541 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=122.9MB, alloc=44.3MB, time=1.52 x[1] = 0.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = 1.14361987741 0.0976162769036 y[1] (closed_form) = 1.14361955646 0.0976173639111 absolute error = 1.133e-06 relative error = 9.875e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.577 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = 1.14362878454 0.101008593021 y[1] (closed_form) = 1.14362862138 0.10100908616 absolute error = 5.194e-07 relative error = 4.524e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.27 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1108 0.152 h = 0.001 0.001 y[1] (numeric) = 1.14366015174 0.103044223817 y[1] (closed_form) = 1.14366022819 0.10304469603 absolute error = 4.784e-07 relative error = 4.166e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9971 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1118 0.153 h = 0.001 0.003 y[1] (numeric) = 1.14432599856 0.103734687566 y[1] (closed_form) = 1.14432618859 0.10373510947 absolute error = 4.627e-07 relative error = 4.027e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.117 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.735 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = 1.14496736335 0.105781803442 y[1] (closed_form) = 1.14496731791 0.10578231843 absolute error = 5.170e-07 relative error = 4.496e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.119 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.681 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=168.3MB, alloc=44.3MB, time=2.08 x[1] = 0.1129 0.16 h = 0.003 0.006 y[1] (numeric) = 1.14498473028 0.108496540493 y[1] (closed_form) = 1.14498451355 0.108496924802 absolute error = 4.412e-07 relative error = 3.836e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.119 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.552 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = 1.14694194185 0.112605643997 y[1] (closed_form) = 1.14694164744 0.112606970505 absolute error = 1.359e-06 relative error = 0.0001179 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.122 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.582 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.116 0.171 h = 0.0001 0.003 y[1] (numeric) = 1.14694223348 0.116000742036 y[1] (closed_form) = 1.14694209195 0.116001474948 absolute error = 7.465e-07 relative error = 6.475e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.123 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.274 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1161 0.174 h = 0.001 0.001 y[1] (numeric) = 1.14696845325 0.118038120306 y[1] (closed_form) = 1.14696855056 0.118038830522 absolute error = 7.169e-07 relative error = 6.217e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.123 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1171 0.175 h = 0.001 0.003 y[1] (numeric) = 1.14763309317 0.118730842717 y[1] (closed_form) = 1.14763330341 0.118731501888 absolute error = 6.919e-07 relative error = 5.997e-05 % Correct digits = 6 memory used=213.7MB, alloc=44.3MB, time=2.63 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.75 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = 1.14826978777 0.120781267149 y[1] (closed_form) = 1.14826976383 0.120782020958 absolute error = 7.542e-07 relative error = 6.532e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.126 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.689 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1182 0.182 h = 0.003 0.006 y[1] (numeric) = 1.14828028594 0.123498288021 y[1] (closed_form) = 1.14828009015 0.123498912777 absolute error = 6.547e-07 relative error = 5.669e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.126 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.564 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = 1.15022871168 0.12761576283 y[1] (closed_form) = 1.15022844553 0.127617327992 absolute error = 1.588e-06 relative error = 0.0001372 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.588 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = 1.15022043049 0.131013701075 y[1] (closed_form) = 1.15022031236 0.131014672997 absolute error = 9.791e-07 relative error = 8.457e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.278 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=259.0MB, alloc=44.3MB, time=3.19 x[1] = 0.1214 0.196 h = 0.001 0.001 y[1] (numeric) = 1.15024152906 0.133052861386 y[1] (closed_form) = 1.15024164899 0.133053808869 absolute error = 9.550e-07 relative error = 8.248e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.004 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = 1.15090498225 0.133747845876 y[1] (closed_form) = 1.15090521443 0.133748741591 absolute error = 9.253e-07 relative error = 7.986e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.031 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1225 0.201 h = 0.003 0.006 y[1] (numeric) = 1.15090988519 0.136466758074 y[1] (closed_form) = 1.1509096277 0.136467556324 absolute error = 8.388e-07 relative error = 7.237e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.574 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = 1.15285071655 0.140591371385 y[1] (closed_form) = 1.15285039497 0.140593108488 absolute error = 1.767e-06 relative error = 0.0001521 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.136 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.592 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = 1.15283505618 0.143991698806 y[1] (closed_form) = 1.15283487844 0.143992842985 absolute error = 1.158e-06 relative error = 9.967e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.136 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.282 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=304.4MB, alloc=44.3MB, time=3.74 x[1] = 0.1257 0.215 h = 0.001 0.001 y[1] (numeric) = 1.15285174618 0.14603235964 y[1] (closed_form) = 1.15285180582 0.146033477887 absolute error = 1.120e-06 relative error = 9.637e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.137 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.007 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1267 0.216 h = 0.001 0.003 y[1] (numeric) = 1.15351416696 0.146729279887 y[1] (closed_form) = 1.15351433828 0.146730345752 absolute error = 1.080e-06 relative error = 9.284e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.78 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = 1.15414222954 0.148785877305 y[1] (closed_form) = 1.15414216912 0.148787040632 absolute error = 1.165e-06 relative error = 0.0001001 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.139 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.706 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1278 0.223 h = 0.003 0.006 y[1] (numeric) = 1.15414001093 0.15150718899 y[1] (closed_form) = 1.15413977768 0.151508226284 absolute error = 1.063e-06 relative error = 9.134e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.139 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.587 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = 1.1560722156 0.155640256775 y[1] (closed_form) = 1.15607192545 0.15564223091 absolute error = 1.995e-06 relative error = 0.0001711 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.143 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.598 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=349.8MB, alloc=44.3MB, time=4.30 x[1] = 0.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = 1.1560480632 0.159043530452 y[1] (closed_form) = 1.1560479121 0.159044912175 absolute error = 1.390e-06 relative error = 0.0001191 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.144 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.287 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.131 0.237 h = 0.001 0.001 y[1] (numeric) = 1.15605968161 0.161086036189 y[1] (closed_form) = 1.15605976706 0.16108739028 absolute error = 1.357e-06 relative error = 0.0001162 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.144 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.01 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.132 0.238 h = 0.001 0.003 y[1] (numeric) = 1.15672095295 0.161785224113 y[1] (closed_form) = 1.15672114939 0.161786525132 absolute error = 1.316e-06 relative error = 0.0001127 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.145 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.797 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.133 0.241 h = 0.0001 0.004 y[1] (numeric) = 1.1573444511 0.163845205494 y[1] (closed_form) = 1.15734441715 0.163846605436 absolute error = 1.400e-06 relative error = 0.0001198 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.716 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1331 0.245 h = 0.003 0.006 y[1] (numeric) = 1.15733546411 0.166568930908 y[1] (closed_form) = 1.15733525686 0.166570206442 absolute error = 1.292e-06 relative error = 0.0001105 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=395.1MB, alloc=44.3MB, time=4.85 x[1] = 0.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = 1.15925912825 0.170710494784 y[1] (closed_form) = 1.15925887121 0.170712705036 absolute error = 2.225e-06 relative error = 0.0001899 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.603 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = 1.15922652862 0.174116769839 y[1] (closed_form) = 1.15922640586 0.174118388268 absolute error = 1.623e-06 relative error = 0.0001385 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.291 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1363 0.259 h = 0.001 0.001 y[1] (numeric) = 1.1592331029 0.17616115312 y[1] (closed_form) = 1.15923321584 0.176162742245 absolute error = 1.593e-06 relative error = 0.0001359 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.152 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.014 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1373 0.26 h = 0.001 0.003 y[1] (numeric) = 1.15989324477 0.176862611079 y[1] (closed_form) = 1.15989346799 0.176864146456 absolute error = 1.552e-06 relative error = 0.0001322 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.153 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.814 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = 1.160512216 0.178926001069 y[1] (closed_form) = 1.1605122102 0.178927636799 absolute error = 1.636e-06 relative error = 0.0001393 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.154 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.726 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=440.5MB, alloc=44.3MB, time=5.41 x[1] = 0.1384 0.267 h = 0.003 0.006 y[1] (numeric) = 1.16049649698 0.181652183745 y[1] (closed_form) = 1.16049631744 0.18165369669 absolute error = 1.524e-06 relative error = 0.0001297 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.155 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.613 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = 1.16241170691 0.185802283577 y[1] (closed_form) = 1.1624114846 0.185804729007 absolute error = 2.456e-06 relative error = 0.0002086 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.159 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.609 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = 1.1623707055 0.189211614004 y[1] (closed_form) = 1.16237061275 0.18921346828 absolute error = 1.857e-06 relative error = 0.0001576 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.159 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.296 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1416 0.281 h = 0.001 0.001 y[1] (numeric) = 1.16237226352 0.191257906789 y[1] (closed_form) = 1.16237240559 0.191259730113 absolute error = 1.829e-06 relative error = 0.0001553 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.018 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1426 0.282 h = 0.001 0.003 y[1] (numeric) = 1.16303129577 0.191961636781 y[1] (closed_form) = 1.16303154742 0.191963405699 absolute error = 1.787e-06 relative error = 0.0001516 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.161 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.832 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=486.1MB, alloc=44.3MB, time=5.97 x[1] = 0.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = 1.16364577777 0.194028459222 y[1] (closed_form) = 1.16364580177 0.194030329889 absolute error = 1.871e-06 relative error = 0.0001586 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.162 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.736 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1437 0.289 h = 0.003 0.006 y[1] (numeric) = 1.16362336359 0.196757141787 y[1] (closed_form) = 1.16362321345 0.196758891289 absolute error = 1.756e-06 relative error = 0.0001488 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.163 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.626 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = 1.16553020575 0.200915815697 y[1] (closed_form) = 1.16553001979 0.200918495347 absolute error = 2.686e-06 relative error = 0.0002271 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.167 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.615 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = 1.16548084864 0.20432825436 y[1] (closed_form) = 1.16548078755 0.204330343599 absolute error = 2.090e-06 relative error = 0.0001766 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.168 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.301 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1469 0.303 h = 0.001 0.001 y[1] (numeric) = 1.1654774186 0.20637648792 y[1] (closed_form) = 1.16547759144 0.206378544585 absolute error = 2.064e-06 relative error = 0.0001744 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.168 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.022 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=531.4MB, alloc=44.3MB, time=6.52 x[1] = 0.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = 1.166135361 0.207082491592 y[1] (closed_form) = 1.16613564271 0.207084493209 absolute error = 2.021e-06 relative error = 0.0001707 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.169 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.138 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.148 0.308 h = 0.003 0.006 y[1] (numeric) = 1.16610749521 0.209813239216 y[1] (closed_form) = 1.16610729051 0.209815162109 absolute error = 1.934e-06 relative error = 0.0001632 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.638 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.151 0.314 h = 0.0001 0.005 y[1] (numeric) = 1.16800710122 0.213979224342 y[1] (closed_form) = 1.16800686663 0.213982075371 absolute error = 2.861e-06 relative error = 0.0002409 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.621 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = 1.1679505513 0.217394281159 y[1] (closed_form) = 1.16795043758 0.217396542422 absolute error = 2.264e-06 relative error = 0.0001906 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.175 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.305 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1512 0.322 h = 0.001 0.001 y[1] (numeric) = 1.16794282694 0.219444150835 y[1] (closed_form) = 1.16794294637 0.219446378137 absolute error = 2.231e-06 relative error = 0.0001877 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.175 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.025 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=576.6MB, alloc=44.3MB, time=7.07 x[1] = 0.1522 0.323 h = 0.001 0.003 y[1] (numeric) = 1.16859981989 0.220152100006 y[1] (closed_form) = 1.16860004758 0.220154271712 absolute error = 2.184e-06 relative error = 0.0001836 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.176 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.866 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = 1.16920600778 0.222225317744 y[1] (closed_form) = 1.16920601041 0.222227593729 absolute error = 2.276e-06 relative error = 0.0001912 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.756 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1533 0.33 h = 0.003 0.006 y[1] (numeric) = 1.16917120429 0.224958683654 y[1] (closed_form) = 1.16917103208 0.224960841471 absolute error = 2.165e-06 relative error = 0.0001818 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.652 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = 1.17106260311 0.229133310247 y[1] (closed_form) = 1.17106240779 0.229136393676 absolute error = 3.090e-06 relative error = 0.0002589 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.182 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.627 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = 1.17099778416 0.232551571203 y[1] (closed_form) = 1.17099770512 0.232554065746 absolute error = 2.496e-06 relative error = 0.0002091 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.31 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=622.0MB, alloc=44.3MB, time=7.62 x[1] = 0.1565 0.344 h = 0.001 0.001 y[1] (numeric) = 1.17098512478 0.234603438352 y[1] (closed_form) = 1.17098527794 0.234605897361 absolute error = 2.464e-06 relative error = 0.0002063 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.184 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.029 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1575 0.345 h = 0.001 0.003 y[1] (numeric) = 1.17164106437 0.235313663583 y[1] (closed_form) = 1.17164132507 0.235316066386 absolute error = 2.417e-06 relative error = 0.0002022 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.185 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.886 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = 1.17224287137 0.237390378026 y[1] (closed_form) = 1.17224290844 0.23739288641 absolute error = 2.509e-06 relative error = 0.0002097 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.186 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.766 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1586 0.352 h = 0.003 0.006 y[1] (numeric) = 1.17220148028 0.240126361183 y[1] (closed_form) = 1.17220134218 0.240128753006 absolute error = 2.396e-06 relative error = 0.0002002 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.187 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.667 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = 1.17408475845 0.244309662476 y[1] (closed_form) = 1.17408460393 0.244312977291 absolute error = 3.318e-06 relative error = 0.0002767 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.633 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=667.5MB, alloc=44.3MB, time=8.18 x[1] = 0.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = 1.17401171815 0.247731177181 y[1] (closed_form) = 1.17401167535 0.247733904061 absolute error = 2.727e-06 relative error = 0.0002273 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.192 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.316 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1618 0.366 h = 0.001 0.001 y[1] (numeric) = 1.17399415287 0.249785071103 y[1] (closed_form) = 1.17399434132 0.249787760901 absolute error = 2.696e-06 relative error = 0.0002246 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.193 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.033 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1628 0.367 h = 0.001 0.003 y[1] (numeric) = 1.17464905855 0.250497573068 y[1] (closed_form) = 1.17464935381 0.250500206066 absolute error = 2.650e-06 relative error = 0.0002206 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.194 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.905 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = 1.17524652284 0.252577804995 y[1] (closed_form) = 1.1752465959 0.252580544844 absolute error = 2.741e-06 relative error = 0.000228 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.195 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.778 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1639 0.374 h = 0.003 0.006 y[1] (numeric) = 1.17519858271 0.255316444498 y[1] (closed_form) = 1.17519848032 0.255319069385 absolute error = 2.627e-06 relative error = 0.0002184 % Correct digits = 6 memory used=713.1MB, alloc=52.3MB, time=8.75 Radius of convergence (given) for eq 1 = 2.196 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.682 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = 1.17707382671 0.259508452047 y[1] (closed_form) = 1.17707371449 0.259511997215 absolute error = 3.547e-06 relative error = 0.0002943 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.64 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.167 0.385 h = 0.0001 0.003 y[1] (numeric) = 1.17699261322 0.26293326897 y[1] (closed_form) = 1.17699260822 0.262936227222 absolute error = 2.958e-06 relative error = 0.0002453 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.201 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.321 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1671 0.388 h = 0.001 0.001 y[1] (numeric) = 1.17697017145 0.264989218271 y[1] (closed_form) = 1.17697039672 0.264992137922 absolute error = 2.928e-06 relative error = 0.0002427 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.202 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.037 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1681 0.389 h = 0.001 0.003 y[1] (numeric) = 1.17762406254 0.265703997318 y[1] (closed_form) = 1.17762439389 0.265706859589 absolute error = 2.881e-06 relative error = 0.0002387 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.203 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.925 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=758.5MB, alloc=52.3MB, time=9.30 x[1] = 0.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = 1.17821722236 0.267787766726 y[1] (closed_form) = 1.17821733296 0.267790737086 absolute error = 2.972e-06 relative error = 0.000246 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.204 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.789 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1692 0.396 h = 0.003 0.006 y[1] (numeric) = 1.17816277215 0.270529100756 y[1] (closed_form) = 1.17816270702 0.270531957749 absolute error = 2.858e-06 relative error = 0.0002364 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.205 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.697 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = 1.18003006834 0.274729844467 y[1] (closed_form) = 1.18002999988 0.274733618939 absolute error = 3.775e-06 relative error = 0.0003116 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.647 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = 1.17994073025 0.278158010932 y[1] (closed_form) = 1.17994076457 0.278161199573 absolute error = 3.189e-06 relative error = 0.000263 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.327 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1724 0.41 h = 0.001 0.001 y[1] (numeric) = 1.17991344166 0.28021604353 y[1] (closed_form) = 1.17991370526 0.280219192078 absolute error = 3.160e-06 relative error = 0.0002605 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.211 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.042 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=804.1MB, alloc=52.3MB, time=9.85 x[1] = 0.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = 1.18056633734 0.280933099685 y[1] (closed_form) = 1.18056670628 0.28093619029 absolute error = 3.113e-06 relative error = 0.0002565 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.212 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.258 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1735 0.415 h = 0.003 0.006 y[1] (numeric) = 1.18050658801 0.283676654938 y[1] (closed_form) = 1.1805064752 0.283679684639 absolute error = 3.032e-06 relative error = 0.0002497 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.71 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = 1.18236700753 0.287884847867 y[1] (closed_form) = 1.18236689695 0.287888792645 absolute error = 3.946e-06 relative error = 0.0003243 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.217 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.653 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = 1.18227067466 0.291315838549 y[1] (closed_form) = 1.18227066305 0.29131919843 absolute error = 3.360e-06 relative error = 0.0002759 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.218 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.331 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1767 0.429 h = 0.001 0.001 y[1] (numeric) = 1.18223921276 0.293375628957 y[1] (closed_form) = 1.18223942958 0.293378947469 absolute error = 3.326e-06 relative error = 0.000273 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.219 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.045 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=849.5MB, alloc=52.3MB, time=10.39 x[1] = 0.1777 0.43 h = 0.001 0.003 y[1] (numeric) = 1.18289123977 0.294094633405 y[1] (closed_form) = 1.1828915613 0.294097893495 absolute error = 3.276e-06 relative error = 0.0002688 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.964 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = 1.18347644928 0.296184985629 y[1] (closed_form) = 1.18347655274 0.29618835604 absolute error = 3.372e-06 relative error = 0.0002764 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.221 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.811 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1788 0.437 h = 0.003 0.006 y[1] (numeric) = 1.18340995697 0.298931355591 y[1] (closed_form) = 1.18340988427 0.298934615577 absolute error = 3.261e-06 relative error = 0.0002672 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.222 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.726 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = 1.18526258867 0.303148337021 y[1] (closed_form) = 1.18526252454 0.303152509127 absolute error = 4.173e-06 relative error = 0.0003411 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.226 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = 1.18515822219 0.306582762865 y[1] (closed_form) = 1.18515825267 0.306586351277 absolute error = 3.589e-06 relative error = 0.0002931 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.227 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.337 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=894.8MB, alloc=52.3MB, time=10.93 x[1] = 0.182 0.451 h = 0.001 0.001 y[1] (numeric) = 1.18512196897 0.308644687041 y[1] (closed_form) = 1.18512222685 0.308648232643 absolute error = 3.555e-06 relative error = 0.0002903 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.228 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.183 0.452 h = 0.001 0.003 y[1] (numeric) = 1.1857730359 0.309365968047 y[1] (closed_form) = 1.18577339775 0.309369454694 absolute error = 3.505e-06 relative error = 0.000286 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.229 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.985 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.184 0.455 h = 0.0001 0.004 y[1] (numeric) = 1.18635405035 0.311459911177 y[1] (closed_form) = 1.1863541956 0.311463509291 absolute error = 3.601e-06 relative error = 0.0002936 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.231 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.823 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1841 0.459 h = 0.003 0.006 y[1] (numeric) = 1.18628116073 0.314209080317 y[1] (closed_form) = 1.18628112963 0.314212569577 absolute error = 3.489e-06 relative error = 0.0002843 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.232 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.742 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = 1.18812609049 0.318434875541 y[1] (closed_form) = 1.18812607419 0.318439273885 absolute error = 4.398e-06 relative error = 0.0003576 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.667 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=940.3MB, alloc=52.3MB, time=11.48 x[1] = 0.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = 1.18801374012 0.321872780623 y[1] (closed_form) = 1.18801381412 0.321876596536 absolute error = 3.817e-06 relative error = 0.0003101 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.237 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.343 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1873 0.473 h = 0.001 0.001 y[1] (numeric) = 1.18797272585 0.32393686452 y[1] (closed_form) = 1.18797302622 0.323940636209 absolute error = 3.784e-06 relative error = 0.0003073 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.238 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.054 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1883 0.474 h = 0.001 0.003 y[1] (numeric) = 1.18862285147 0.324660421234 y[1] (closed_form) = 1.18862325506 0.324664133451 absolute error = 3.734e-06 relative error = 0.0003031 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.239 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.007 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = 1.18919970921 0.326757972331 y[1] (closed_form) = 1.18919989767 0.326761797127 absolute error = 3.829e-06 relative error = 0.0003105 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.241 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.835 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1894 0.481 h = 0.003 0.006 y[1] (numeric) = 1.18912046239 0.329509975308 y[1] (closed_form) = 1.18912047435 0.329513692811 absolute error = 3.718e-06 relative error = 0.0003013 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.242 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.758 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=985.6MB, alloc=52.3MB, time=12.02 x[1] = 0.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = 1.19095777583 0.333744608054 y[1] (closed_form) = 1.19095780873 0.333749231529 absolute error = 4.624e-06 relative error = 0.0003738 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.246 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.674 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = 1.19083749159 0.337186035319 y[1] (closed_form) = 1.19083761053 0.337190077688 absolute error = 4.044e-06 relative error = 0.0003268 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.247 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.349 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1926 0.495 h = 0.001 0.001 y[1] (numeric) = 1.19079174676 0.339252304208 y[1] (closed_form) = 1.19079209102 0.339256300964 absolute error = 4.012e-06 relative error = 0.000324 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.248 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.059 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1936 0.496 h = 0.001 0.003 y[1] (numeric) = 1.19144094967 0.33997813549 y[1] (closed_form) = 1.19144139641 0.339982072273 absolute error = 3.962e-06 relative error = 0.0003198 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.249 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.029 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = 1.192013689 0.342079310871 y[1] (closed_form) = 1.19201392209 0.342083361314 absolute error = 4.057e-06 relative error = 0.0003272 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.251 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.848 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1031.1MB, alloc=52.3MB, time=12.56 x[1] = 0.1947 0.503 h = 0.003 0.006 y[1] (numeric) = 1.19192812535 0.344834181441 y[1] (closed_form) = 1.1919281818 0.344838126143 absolute error = 3.945e-06 relative error = 0.0003179 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.252 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.775 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = 1.19375790779 0.349077673897 y[1] (closed_form) = 1.19375799122 0.349082521388 absolute error = 4.848e-06 relative error = 0.0003898 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.256 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.682 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = 1.19362974 0.35252266517 y[1] (closed_form) = 1.19362990528 0.352526932932 absolute error = 4.271e-06 relative error = 0.0003432 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.257 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.355 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1979 0.517 h = 0.001 0.001 y[1] (numeric) = 1.19357929524 0.354591143643 y[1] (closed_form) = 1.19357968476 0.354595364433 absolute error = 4.239e-06 relative error = 0.0003404 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.258 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.064 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = 1.19422759389 0.355319248068 y[1] (closed_form) = 1.19422808514 0.355323408401 absolute error = 4.189e-06 relative error = 0.0003362 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.259 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.392 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1076.6MB, alloc=52.3MB, time=13.10 x[1] = 0.199 0.522 h = 0.003 0.006 y[1] (numeric) = 1.19413688987 0.358076478425 y[1] (closed_form) = 1.1941369052 0.35808059464 absolute error = 4.116e-06 relative error = 0.0003302 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.789 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.202 0.528 h = 0.0001 0.005 y[1] (numeric) = 1.1959601521 0.362327525304 y[1] (closed_form) = 1.19596019958 0.362332541582 absolute error = 5.017e-06 relative error = 0.0004014 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.264 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.688 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = 1.19582519578 0.365775523904 y[1] (closed_form) = 1.19582532152 0.365779961635 absolute error = 4.440e-06 relative error = 0.000355 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.266 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.36 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2022 0.536 h = 0.001 0.001 y[1] (numeric) = 1.1957707034 0.367845868006 y[1] (closed_form) = 1.19577105247 0.367850257604 absolute error = 4.403e-06 relative error = 0.000352 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.266 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.068 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2032 0.537 h = 0.001 0.003 y[1] (numeric) = 1.19641821129 0.36857591725 y[1] (closed_form) = 1.19641866145 0.368580245976 absolute error = 4.352e-06 relative error = 0.0003476 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.268 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.071 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1122.0MB, alloc=52.3MB, time=13.64 x[1] = 0.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = 1.19698334543 0.370683829534 y[1] (closed_form) = 1.1969835847 0.370688273863 absolute error = 4.451e-06 relative error = 0.0003552 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.269 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.871 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2043 0.544 h = 0.003 0.006 y[1] (numeric) = 1.19688610068 0.373444048689 y[1] (closed_form) = 1.1968861631 0.373448390138 absolute error = 4.342e-06 relative error = 0.0003463 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.806 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = 1.19870198958 0.377703993566 y[1] (closed_form) = 1.19870209 0.377709231767 absolute error = 5.239e-06 relative error = 0.0004169 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.275 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.696 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = 1.19855924353 0.381155631636 y[1] (closed_form) = 1.19855941812 0.381160292768 absolute error = 4.664e-06 relative error = 0.0003709 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.276 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.366 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2075 0.558 h = 0.001 0.001 y[1] (numeric) = 1.1985001083 0.383228229664 y[1] (closed_form) = 1.19850050513 0.383232841354 absolute error = 4.629e-06 relative error = 0.0003679 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.277 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.073 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1167.5MB, alloc=52.3MB, time=14.18 x[1] = 0.2085 0.559 h = 0.001 0.003 y[1] (numeric) = 1.19914674582 0.383960548886 y[1] (closed_form) = 1.19914724298 0.383965099248 absolute error = 4.577e-06 relative error = 0.0003635 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.278 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.094 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = 1.19970787068 0.386072128592 y[1] (closed_form) = 1.19970815845 0.386076795548 absolute error = 4.676e-06 relative error = 0.000371 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.885 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2096 0.566 h = 0.003 0.006 y[1] (numeric) = 1.19960442527 0.388835307451 y[1] (closed_form) = 1.19960453613 0.388839873049 absolute error = 4.567e-06 relative error = 0.0003622 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.281 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.824 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = 1.20141302517 0.393104168253 y[1] (closed_form) = 1.2014131798 0.393109627228 absolute error = 5.461e-06 relative error = 0.000432 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.285 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.704 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = 1.20126254036 0.396559484444 y[1] (closed_form) = 1.20126276512 0.39656436788 absolute error = 4.889e-06 relative error = 0.0003864 % Correct digits = 5 memory used=1212.9MB, alloc=52.3MB, time=14.73 Radius of convergence (given) for eq 1 = 2.287 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.373 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2128 0.58 h = 0.001 0.001 y[1] (numeric) = 1.20119879327 0.39863435908 y[1] (closed_form) = 1.20119923916 0.398639191793 absolute error = 4.853e-06 relative error = 0.0003835 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.288 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.078 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2138 0.581 h = 0.001 0.003 y[1] (numeric) = 1.20184457838 0.399368946083 y[1] (closed_form) = 1.20184512385 0.399373717027 absolute error = 4.802e-06 relative error = 0.0003792 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.289 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.118 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = 1.20240173202 0.401484206766 y[1] (closed_form) = 1.20240206959 0.401489095264 absolute error = 4.900e-06 relative error = 0.0003865 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.291 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.898 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2149 0.588 h = 0.003 0.006 y[1] (numeric) = 1.20229212701 0.404250375652 y[1] (closed_form) = 1.20229228764 0.404255164301 absolute error = 4.791e-06 relative error = 0.0003777 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.292 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.842 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1258.4MB, alloc=52.3MB, time=15.27 x[1] = 0.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = 1.20409352182 0.408528168869 y[1] (closed_form) = 1.20409373188 0.408533847462 absolute error = 5.682e-06 relative error = 0.0004469 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.296 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.712 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.218 0.599 h = 0.0001 0.003 y[1] (numeric) = 1.20393534941 0.411987200742 y[1] (closed_form) = 1.20393562561 0.411992305374 absolute error = 5.112e-06 relative error = 0.0004017 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.297 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.379 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2181 0.602 h = 0.001 0.001 y[1] (numeric) = 1.20386702155 0.414064374009 y[1] (closed_form) = 1.20386751776 0.414069426664 absolute error = 5.077e-06 relative error = 0.0003988 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.298 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.083 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2191 0.603 h = 0.001 0.003 y[1] (numeric) = 1.20451197201 0.414801226342 y[1] (closed_form) = 1.20451256706 0.414806216802 absolute error = 5.026e-06 relative error = 0.0003945 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.142 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = 1.20506519238 0.416920180868 y[1] (closed_form) = 1.20506558103 0.41692528981 absolute error = 5.124e-06 relative error = 0.0004018 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.301 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.912 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1303.8MB, alloc=52.3MB, time=15.81 x[1] = 0.2202 0.61 h = 0.003 0.006 y[1] (numeric) = 1.20494946895 0.419689369229 y[1] (closed_form) = 1.20494968064 0.419694379822 absolute error = 5.015e-06 relative error = 0.000393 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.302 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.86 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = 1.20674374215 0.423976109949 y[1] (closed_form) = 1.20674400882 0.423982006995 absolute error = 5.903e-06 relative error = 0.0004615 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.307 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.72 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = 1.20657793342 0.42743889398 y[1] (closed_form) = 1.20657826232 0.42744421869 absolute error = 5.335e-06 relative error = 0.0004168 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.308 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.386 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2234 0.624 h = 0.001 0.001 y[1] (numeric) = 1.20650505593 0.429518387252 y[1] (closed_form) = 1.20650560373 0.429523658758 absolute error = 5.300e-06 relative error = 0.0004138 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.309 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.088 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = 1.20714918934 0.430257502216 y[1] (closed_form) = 1.20714983521 0.430262711116 absolute error = 5.249e-06 relative error = 0.0004096 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.311 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.537 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1349.3MB, alloc=52.3MB, time=16.36 x[1] = 0.2245 0.629 h = 0.003 0.006 y[1] (numeric) = 1.2070284881 0.433029171715 y[1] (closed_form) = 1.20702866489 0.433034352181 absolute error = 5.183e-06 relative error = 0.0004042 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.312 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.876 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = 1.20881659092 0.437323541684 y[1] (closed_form) = 1.20881682746 0.437329605622 absolute error = 6.069e-06 relative error = 0.0004721 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.316 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.727 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = 1.20864420502 0.440789493711 y[1] (closed_form) = 1.20864450041 0.440794986701 absolute error = 5.501e-06 relative error = 0.0004276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.318 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.391 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2277 0.643 h = 0.001 0.001 y[1] (numeric) = 1.20856740839 0.4428709469 y[1] (closed_form) = 1.20856792172 0.442876385637 absolute error = 5.463e-06 relative error = 0.0004244 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.319 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.092 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2287 0.644 h = 0.001 0.003 y[1] (numeric) = 1.20921082553 0.443611997666 y[1] (closed_form) = 1.2092114363 0.443617373446 absolute error = 5.410e-06 relative error = 0.0004201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.187 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1394.8MB, alloc=52.3MB, time=16.90 x[1] = 0.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = 1.20975678325 0.445737811708 y[1] (closed_form) = 1.2097571904 0.445743307637 absolute error = 5.511e-06 relative error = 0.0004275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.322 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.938 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2298 0.651 h = 0.003 0.006 y[1] (numeric) = 1.20962974804 0.44851262232 y[1] (closed_form) = 1.20962997824 0.448518022655 absolute error = 5.405e-06 relative error = 0.000419 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.323 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.894 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = 1.21141088314 0.452815965199 y[1] (closed_form) = 1.21141117847 0.452822245416 absolute error = 6.287e-06 relative error = 0.0004861 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.327 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.735 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = 1.21123095625 0.456285735032 y[1] (closed_form) = 1.21123130661 0.456291446008 absolute error = 5.722e-06 relative error = 0.0004421 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.329 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.398 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.233 0.665 h = 0.001 0.001 y[1] (numeric) = 1.21114966787 0.458369546659 y[1] (closed_form) = 1.21115023504 0.458375202206 absolute error = 5.684e-06 relative error = 0.0004389 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.098 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1440.1MB, alloc=52.3MB, time=17.44 x[1] = 0.234 0.666 h = 0.001 0.003 y[1] (numeric) = 1.21179230022 0.459112854608 y[1] (closed_form) = 1.21179296407 0.459118446813 absolute error = 5.631e-06 relative error = 0.0004346 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.331 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.213 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.235 0.669 h = 0.0001 0.004 y[1] (numeric) = 1.21233443239 0.461242396041 y[1] (closed_form) = 1.21233489412 0.461248109239 absolute error = 5.732e-06 relative error = 0.0004419 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.333 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.952 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2351 0.673 h = 0.003 0.006 y[1] (numeric) = 1.21220139671 0.464020306134 y[1] (closed_form) = 1.21220168154 0.464025925201 absolute error = 5.626e-06 relative error = 0.0004335 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.334 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.913 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = 1.21397564617 0.468332633139 y[1] (closed_form) = 1.2139760014 0.46833912845 absolute error = 6.505e-06 relative error = 0.0004999 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.339 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.744 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = 1.21378822985 0.471806254223 y[1] (closed_form) = 1.21378863637 0.471812182041 absolute error = 5.942e-06 relative error = 0.0004563 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.405 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1485.5MB, alloc=52.3MB, time=17.98 x[1] = 0.2383 0.687 h = 0.001 0.001 y[1] (numeric) = 1.21370248102 0.473892443837 y[1] (closed_form) = 1.21370310319 0.473898315077 absolute error = 5.904e-06 relative error = 0.0004531 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.341 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.103 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2393 0.688 h = 0.001 0.003 y[1] (numeric) = 1.21434434561 0.474638005604 y[1] (closed_form) = 1.21434506371 0.474643813132 absolute error = 5.852e-06 relative error = 0.0004488 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.343 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.238 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = 1.21488268964 0.476771284741 y[1] (closed_form) = 1.21488320711 0.476777214076 absolute error = 5.952e-06 relative error = 0.0004561 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.344 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.966 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2404 0.695 h = 0.003 0.006 y[1] (numeric) = 1.21474369495 0.479552320482 y[1] (closed_form) = 1.21474403559 0.479558157136 absolute error = 5.847e-06 relative error = 0.0004477 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.346 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.933 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = 1.21651114028 0.483873641537 y[1] (closed_form) = 1.21651155652 0.483880350753 absolute error = 6.722e-06 relative error = 0.0005134 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.752 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1530.9MB, alloc=52.3MB, time=18.53 x[1] = 0.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = 1.21631628616 0.48735114628 y[1] (closed_form) = 1.21631674997 0.48735728979 absolute error = 6.161e-06 relative error = 0.0004702 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.352 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.412 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2436 0.709 h = 0.001 0.001 y[1] (numeric) = 1.21622610816 0.48943973281 y[1] (closed_form) = 1.21622678648 0.489445818617 absolute error = 6.123e-06 relative error = 0.0004671 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.353 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.109 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2446 0.71 h = 0.001 0.003 y[1] (numeric) = 1.21686722185 0.49018754481 y[1] (closed_form) = 1.21686799534 0.49019356655 absolute error = 6.071e-06 relative error = 0.0004628 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.354 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.264 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = 1.21740181497 0.492324571332 y[1] (closed_form) = 1.21740238934 0.492330715665 absolute error = 6.171e-06 relative error = 0.0004699 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.356 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.981 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2457 0.717 h = 0.003 0.006 y[1] (numeric) = 1.21725690274 0.495108758065 y[1] (closed_form) = 1.21725730037 0.495114811152 absolute error = 6.066e-06 relative error = 0.0004616 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.357 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.952 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1576.3MB, alloc=52.3MB, time=19.07 x[1] = 0.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = 1.21901762492 0.499439081829 y[1] (closed_form) = 1.21901810322 0.499446003754 absolute error = 6.938e-06 relative error = 0.0005267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.362 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.761 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = 1.21881538461 0.502920501615 y[1] (closed_form) = 1.21881590684 0.502926859659 absolute error = 6.379e-06 relative error = 0.0004838 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.364 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.419 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2489 0.731 h = 0.001 0.001 y[1] (numeric) = 1.21872080875 0.505011503372 y[1] (closed_form) = 1.21872154432 0.505017802616 absolute error = 6.342e-06 relative error = 0.0004807 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.365 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.114 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = 1.21936118817 0.505761561812 y[1] (closed_form) = 1.21936201818 0.505767796646 absolute error = 6.290e-06 relative error = 0.0004765 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.366 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.694 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.25 0.736 h = 0.003 0.006 y[1] (numeric) = 1.21921146238 0.508548334533 y[1] (closed_form) = 1.21921183094 0.508554555481 absolute error = 6.232e-06 relative error = 0.0004717 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.367 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.969 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1621.7MB, alloc=52.3MB, time=19.62 x[1] = 0.253 0.742 h = 0.0001 0.005 y[1] (numeric) = 1.22096635452 0.512886334738 y[1] (closed_form) = 1.2209668081 0.512893421345 absolute error = 7.101e-06 relative error = 0.0005362 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.372 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.768 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = 1.22075775064 0.516371061675 y[1] (closed_form) = 1.22075824503 0.516377585957 absolute error = 6.543e-06 relative error = 0.0004936 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.374 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.425 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2532 0.75 h = 0.001 0.001 y[1] (numeric) = 1.22065938523 0.518464104701 y[1] (closed_form) = 1.22066009199 0.518470569246 absolute error = 6.503e-06 relative error = 0.0004904 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.375 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.119 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2542 0.751 h = 0.001 0.003 y[1] (numeric) = 1.22129911912 0.519216085127 y[1] (closed_form) = 1.22129991966 0.519222484969 absolute error = 6.450e-06 relative error = 0.000486 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.376 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.313 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = 1.22182678625 0.521360064674 y[1] (closed_form) = 1.22182739045 0.521366588516 absolute error = 6.552e-06 relative error = 0.0004932 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.378 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.009 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1667.3MB, alloc=52.3MB, time=20.17 x[1] = 0.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = 1.22167093504 0.524150110008 y[1] (closed_form) = 1.22167136269 0.52415654524 absolute error = 6.449e-06 relative error = 0.0004851 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.379 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.379 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2554 0.762 h = 0.003 0.006 y[1] (numeric) = 1.22151378252 0.526940406258 y[1] (closed_form) = 1.22151421016 0.52694684149 absolute error = 6.449e-06 relative error = 0.0004848 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.381 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.991 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = 1.22326063729 0.531288740367 y[1] (closed_form) = 1.22326115585 0.531296036981 absolute error = 7.315e-06 relative error = 0.0005485 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.385 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.778 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = 1.22304333966 0.534777858944 y[1] (closed_form) = 1.22304389481 0.534784595323 absolute error = 6.759e-06 relative error = 0.0005064 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.387 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.433 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2586 0.776 h = 0.001 0.001 y[1] (numeric) = 1.222939796 0.536873614706 y[1] (closed_form) = 1.22294056218 0.536880290077 absolute error = 6.719e-06 relative error = 0.0005031 % Correct digits = 5 memory used=1712.7MB, alloc=52.3MB, time=20.71 Radius of convergence (given) for eq 1 = 2.388 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.125 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2596 0.777 h = 0.001 0.003 y[1] (numeric) = 1.2235786231 0.53762819511 y[1] (closed_form) = 1.22357948221 0.537634805381 absolute error = 6.666e-06 relative error = 0.0004988 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.389 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.343 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = 1.22410187799 0.53977646534 y[1] (closed_form) = 1.22410254247 0.53978320049 absolute error = 6.768e-06 relative error = 0.0005059 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.391 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.026 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2607 0.784 h = 0.003 0.006 y[1] (numeric) = 1.22393910916 0.542570074913 y[1] (closed_form) = 1.22393959721 0.542576723094 absolute error = 6.666e-06 relative error = 0.0004979 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.393 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.012 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = 1.22567948251 0.546927434447 y[1] (closed_form) = 1.22568006626 0.546934940169 absolute error = 7.528e-06 relative error = 0.0005609 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.398 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.787 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1758.2MB, alloc=52.3MB, time=21.26 x[1] = 0.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = 1.22545495381 0.550420559681 y[1] (closed_form) = 1.22545557069 0.550427507099 absolute error = 6.975e-06 relative error = 0.0005192 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.399 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.44 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2639 0.798 h = 0.001 0.001 y[1] (numeric) = 1.22534710629 0.552518784083 y[1] (closed_form) = 1.22534793302 0.552525669473 absolute error = 6.935e-06 relative error = 0.0005159 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.131 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2649 0.799 h = 0.001 0.003 y[1] (numeric) = 1.22598524863 0.553275598984 y[1] (closed_form) = 1.22598616754 0.553282418973 absolute error = 6.882e-06 relative error = 0.0005116 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.402 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.37 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = 1.22650490047 0.555427651282 y[1] (closed_form) = 1.22650562625 0.555434596826 absolute error = 6.983e-06 relative error = 0.0005187 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.404 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.041 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.266 0.806 h = 0.003 0.006 y[1] (numeric) = 1.22633638015 0.558224507937 y[1] (closed_form) = 1.22633692966 0.558231367891 absolute error = 6.882e-06 relative error = 0.0005108 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.405 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.032 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1803.6MB, alloc=52.3MB, time=21.80 x[1] = 0.269 0.812 h = 0.0001 0.005 y[1] (numeric) = 1.22807035063 0.562590896734 y[1] (closed_form) = 1.22807100053 0.562598610357 absolute error = 7.741e-06 relative error = 0.0005731 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.797 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = 1.22783864239 0.56608805602 y[1] (closed_form) = 1.227839322 0.566095213299 absolute error = 7.189e-06 relative error = 0.0005317 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.412 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.448 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2692 0.82 h = 0.001 0.001 y[1] (numeric) = 1.2277265222 0.568188764981 y[1] (closed_form) = 1.22772741049 0.568195859238 absolute error = 7.150e-06 relative error = 0.0005285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.413 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.137 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2702 0.821 h = 0.001 0.003 y[1] (numeric) = 1.22836399561 0.5689478098 y[1] (closed_form) = 1.22836497534 0.568954838368 absolute error = 7.097e-06 relative error = 0.0005242 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.414 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.398 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = 1.22888008062 0.571103650853 y[1] (closed_form) = 1.2288808687 0.571110805623 absolute error = 7.198e-06 relative error = 0.0005312 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.416 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.057 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1849.0MB, alloc=52.3MB, time=22.35 x[1] = 0.2713 0.828 h = 0.003 0.006 y[1] (numeric) = 1.22870585015 0.573903775943 y[1] (closed_form) = 1.22870646215 0.573910846488 absolute error = 7.097e-06 relative error = 0.0005233 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.418 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.053 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = 1.23043349564 0.578279196729 y[1] (closed_form) = 1.23043421264 0.578287117041 absolute error = 7.953e-06 relative error = 0.0005849 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.422 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.806 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = 1.23019465928 0.581780416508 y[1] (closed_form) = 1.23019540263 0.581787782466 absolute error = 7.403e-06 relative error = 0.000544 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.424 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.455 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2745 0.842 h = 0.001 0.001 y[1] (numeric) = 1.23007829755 0.583883625379 y[1] (closed_form) = 1.23007924839 0.583890927345 absolute error = 7.364e-06 relative error = 0.0005408 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.425 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.143 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2755 0.843 h = 0.001 0.003 y[1] (numeric) = 1.23071511767 0.584644895362 y[1] (closed_form) = 1.23071615921 0.584652131363 absolute error = 7.311e-06 relative error = 0.0005365 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.427 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.426 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1894.4MB, alloc=52.3MB, time=22.89 x[1] = 0.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = 1.23122767183 0.586804531302 y[1] (closed_form) = 1.2312285232 0.586811894127 absolute error = 7.412e-06 relative error = 0.0005434 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.429 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.073 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2766 0.85 h = 0.003 0.006 y[1] (numeric) = 1.23104777247 0.589607945423 y[1] (closed_form) = 1.23104844796 0.589615225373 absolute error = 7.311e-06 relative error = 0.0005356 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.074 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = 1.23276917019 0.59399239984 y[1] (closed_form) = 1.23276995519 0.594000525629 absolute error = 8.164e-06 relative error = 0.0005966 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.435 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.815 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = 1.23252325703 0.59749770562 y[1] (closed_form) = 1.23252406508 0.59750527907 absolute error = 7.616e-06 relative error = 0.0005561 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.437 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.463 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2798 0.864 h = 0.001 0.001 y[1] (numeric) = 1.23240268479 0.599603429189 y[1] (closed_form) = 1.23240369916 0.599610937705 absolute error = 7.577e-06 relative error = 0.0005528 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.438 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.149 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1939.9MB, alloc=52.3MB, time=23.43 x[1] = 0.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = 1.23303886705 0.600366919414 y[1] (closed_form) = 1.23303997138 0.600374361701 absolute error = 7.524e-06 relative error = 0.0005486 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.439 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.902 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2809 0.869 h = 0.003 0.006 y[1] (numeric) = 1.23285435703 0.603173029327 y[1] (closed_form) = 1.23285501017 0.603180474253 absolute error = 7.474e-06 relative error = 0.0005445 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.441 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.092 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = 1.23457033058 0.607565186919 y[1] (closed_form) = 1.23457109708 0.607573474334 absolute error = 8.323e-06 relative error = 0.0006049 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.446 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.823 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.284 0.88 h = 0.0001 0.003 y[1] (numeric) = 1.23431831787 0.611073946045 y[1] (closed_form) = 1.2343191046 0.611081682839 absolute error = 7.777e-06 relative error = 0.0005646 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.448 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.469 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2841 0.883 h = 0.001 0.001 y[1] (numeric) = 1.23419411598 0.613181795952 y[1] (closed_form) = 1.23419510802 0.613189467004 absolute error = 7.735e-06 relative error = 0.0005613 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.449 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.154 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1985.2MB, alloc=52.3MB, time=23.98 x[1] = 0.2851 0.884 h = 0.001 0.003 y[1] (numeric) = 1.23482973501 0.61394718587 y[1] (closed_form) = 1.23483081639 0.613954790468 absolute error = 7.681e-06 relative error = 0.000557 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.479 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = 1.23533576866 0.616113856625 y[1] (closed_form) = 1.2353366626 0.616121589154 absolute error = 7.784e-06 relative error = 0.0005639 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.452 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.103 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2862 0.891 h = 0.003 0.006 y[1] (numeric) = 1.23514539054 0.618923376776 y[1] (closed_form) = 1.23514610899 0.618931028905 absolute error = 7.686e-06 relative error = 0.0005563 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.454 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.114 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = 1.23685525819 0.623324569174 y[1] (closed_form) = 1.23685609434 0.623333059821 absolute error = 8.532e-06 relative error = 0.000616 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.459 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.833 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = 1.23659626355 0.626837459932 y[1] (closed_form) = 1.23659711673 0.626845402021 absolute error = 7.988e-06 relative error = 0.0005762 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.461 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.477 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2030.6MB, alloc=52.3MB, time=24.52 x[1] = 0.2894 0.905 h = 0.001 0.001 y[1] (numeric) = 1.23646790852 0.628947850967 y[1] (closed_form) = 1.23646896583 0.628955726415 absolute error = 7.946e-06 relative error = 0.0005728 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.462 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.16 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2904 0.906 h = 0.001 0.003 y[1] (numeric) = 1.2371029179 0.629715451723 y[1] (closed_form) = 1.23710406382 0.629723260476 absolute error = 7.892e-06 relative error = 0.0005686 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.463 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.508 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = 1.23760552222 0.63188593238 y[1] (closed_form) = 1.23760648215 0.631893869614 absolute error = 7.995e-06 relative error = 0.0005754 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.465 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.119 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2915 0.913 h = 0.003 0.006 y[1] (numeric) = 1.23740959241 0.63469879691 y[1] (closed_form) = 1.2374103771 0.63470665505 absolute error = 7.897e-06 relative error = 0.0005679 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.467 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.135 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = 1.2391134294 0.639109022815 y[1] (closed_form) = 1.23911433603 0.639117715481 absolute error = 8.740e-06 relative error = 0.0006269 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.472 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.843 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2076.1MB, alloc=52.3MB, time=25.07 x[1] = 0.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = 1.23884750372 0.64262606812 y[1] (closed_form) = 1.23884842425 0.642634214313 absolute error = 8.198e-06 relative error = 0.0005874 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.474 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.485 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2947 0.927 h = 0.001 0.001 y[1] (numeric) = 1.23871502635 0.644739013521 y[1] (closed_form) = 1.23871614981 0.644747092198 absolute error = 8.156e-06 relative error = 0.0005841 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.475 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.166 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2957 0.928 h = 0.001 0.003 y[1] (numeric) = 1.23934944091 0.645508819748 y[1] (closed_form) = 1.23935065226 0.645516831501 absolute error = 8.103e-06 relative error = 0.0005799 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.476 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.537 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = 1.23984865088 0.647683114417 y[1] (closed_form) = 1.23984967772 0.647691255176 absolute error = 8.205e-06 relative error = 0.0005866 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.478 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.136 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2968 0.935 h = 0.003 0.006 y[1] (numeric) = 1.23964721019 0.650499341122 y[1] (closed_form) = 1.23964806204 0.650507404079 absolute error = 8.108e-06 relative error = 0.0005791 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.157 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2121.5MB, alloc=52.3MB, time=25.62 x[1] = 0.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = 1.24134509105 0.654918598263 y[1] (closed_form) = 1.24134606898 0.654927491737 absolute error = 8.947e-06 relative error = 0.0006375 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.485 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.852 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = 1.24107228509 0.658439820155 y[1] (closed_form) = 1.24107327384 0.658448169262 absolute error = 8.407e-06 relative error = 0.0005984 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.487 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.493 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3 0.949 h = 0.001 0.001 y[1] (numeric) = 1.24093571602 0.660555332639 y[1] (closed_form) = 1.24093690652 0.660563613377 absolute error = 8.366e-06 relative error = 0.0005951 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.488 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.172 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.301 0.95 h = 0.001 0.003 y[1] (numeric) = 1.24156955039 0.661327338828 y[1] (closed_form) = 1.24157082806 0.661335552425 absolute error = 8.312e-06 relative error = 0.0005909 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.489 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.566 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.302 0.953 h = 0.0001 0.004 y[1] (numeric) = 1.24206540076 0.663505451126 y[1] (closed_form) = 1.24206649535 0.663513794232 absolute error = 8.415e-06 relative error = 0.0005976 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.491 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.152 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2166.9MB, alloc=52.3MB, time=26.16 x[1] = 0.3021 0.957 h = 0.003 0.006 y[1] (numeric) = 1.24185848984 0.666325057108 y[1] (closed_form) = 1.24185940972 0.666333323688 absolute error = 8.318e-06 relative error = 0.0005902 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.493 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.18 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = 1.24355048836 0.670753342276 y[1] (closed_form) = 1.24355153839 0.670762435346 absolute error = 9.153e-06 relative error = 0.0006478 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.498 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.862 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = 1.24327085266 0.674278761936 y[1] (closed_form) = 1.24327191048 0.674287312766 absolute error = 8.616e-06 relative error = 0.0006092 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.501 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3053 0.971 h = 0.001 0.001 y[1] (numeric) = 1.24313022243 0.676396853707 y[1] (closed_form) = 1.24313148082 0.676405335339 absolute error = 8.574e-06 relative error = 0.0006059 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.501 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.179 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = 1.24376349104 0.677171054212 y[1] (closed_form) = 1.24376483587 0.677179468497 absolute error = 8.521e-06 relative error = 0.0006017 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.503 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.081 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2212.4MB, alloc=52.3MB, time=26.70 x[1] = 0.3064 0.976 h = 0.003 0.006 y[1] (numeric) = 1.2435521313 0.679993427548 y[1] (closed_form) = 1.24355303378 0.680001856481 absolute error = 8.477e-06 relative error = 0.0005981 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.504 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.199 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = 1.24523901757 0.684429411584 y[1] (closed_form) = 1.24524005367 0.684438663579 absolute error = 9.310e-06 relative error = 0.0006552 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.871 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = 1.24495349306 0.687958380322 y[1] (closed_form) = 1.24495453436 0.687967091886 absolute error = 8.774e-06 relative error = 0.0006168 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.512 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.507 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3096 0.99 h = 0.001 0.001 y[1] (numeric) = 1.24480936056 0.690078653761 y[1] (closed_form) = 1.24481060142 0.690087295418 absolute error = 8.730e-06 relative error = 0.0006134 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.513 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.184 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2257.8MB, alloc=52.3MB, time=27.25 x[1] = 0.3106 0.991 h = 0.001 0.003 y[1] (numeric) = 1.24544212751 0.690854731931 y[1] (closed_form) = 1.24544345421 0.690863306064 absolute error = 8.676e-06 relative error = 0.0006092 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.514 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.622 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = 1.24593177234 0.69303991689 y[1] (closed_form) = 1.24593291864 0.693048621422 absolute error = 8.780e-06 relative error = 0.0006158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.516 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.184 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3117 0.998 h = 0.003 0.006 y[1] (numeric) = 1.24571474953 0.695865790091 y[1] (closed_form) = 1.24571572165 0.695874420433 absolute error = 8.685e-06 relative error = 0.0006087 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.518 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.221 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = 1.2473958889 0.700310794631 y[1] (closed_form) = 1.24739699853 0.700320243984 absolute error = 9.514e-06 relative error = 0.0006651 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.523 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.881 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = 1.24710362793 0.70384399892 y[1] (closed_form) = 1.24710473984 0.703852910002 absolute error = 8.980e-06 relative error = 0.0006271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.525 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.516 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2303.2MB, alloc=52.3MB, time=27.79 x[1] = 0.3149 1.012 h = 0.001 0.001 y[1] (numeric) = 1.24695549061 0.705966873384 y[1] (closed_form) = 1.24695680089 0.705975713773 absolute error = 8.937e-06 relative error = 0.0006237 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.526 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.19 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3159 1.013 h = 0.001 0.003 y[1] (numeric) = 1.24758771814 0.706745135192 y[1] (closed_form) = 1.24758911354 0.706753907871 absolute error = 8.883e-06 relative error = 0.0006195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.528 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.652 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = 1.24807410112 0.708934145932 y[1] (closed_form) = 1.24807531757 0.708943049446 absolute error = 8.986e-06 relative error = 0.0006261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.53 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.201 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.317 1.02 h = 0.003 0.006 y[1] (numeric) = 1.24785172327 0.711763444101 y[1] (closed_form) = 1.24785276584 0.711772274658 absolute error = 8.892e-06 relative error = 0.000619 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.532 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.244 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.32 1.026 h = 0.0001 0.005 y[1] (numeric) = 1.24952718743 0.716217463391 y[1] (closed_form) = 1.24952837132 0.716227108898 absolute error = 9.718e-06 relative error = 0.0006747 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.537 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.891 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2348.7MB, alloc=52.3MB, time=28.34 x[1] = 0.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = 1.24922823994 0.719754922046 y[1] (closed_form) = 1.24922942323 0.719764031457 absolute error = 9.186e-06 relative error = 0.0006371 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.539 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.524 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3202 1.034 h = 0.001 0.001 y[1] (numeric) = 1.24907612794 0.721880408327 y[1] (closed_form) = 1.24907750843 0.721889446281 absolute error = 9.143e-06 relative error = 0.0006337 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.197 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3212 1.035 h = 0.001 0.003 y[1] (numeric) = 1.24970782988 0.722660847769 y[1] (closed_form) = 1.24970929479 0.722669817837 absolute error = 9.089e-06 relative error = 0.0006296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.541 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.683 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = 1.25019098465 0.724853686124 y[1] (closed_form) = 1.25019227202 0.724862787443 absolute error = 9.192e-06 relative error = 0.0006361 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.544 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.218 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3223 1.042 h = 0.003 0.006 y[1] (numeric) = 1.24996329174 0.727686423809 y[1] (closed_form) = 1.24996440555 0.727695453387 absolute error = 9.098e-06 relative error = 0.000629 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.545 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.267 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2394.1MB, alloc=52.3MB, time=28.88 x[1] = 0.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = 1.25163315163 0.732149451261 y[1] (closed_form) = 1.25163441048 0.732159291719 absolute error = 9.921e-06 relative error = 0.0006842 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.551 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.901 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = 1.2513275673 0.735691182304 y[1] (closed_form) = 1.25132882275 0.735700488857 absolute error = 9.391e-06 relative error = 0.0006469 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.553 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.532 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3255 1.056 h = 0.001 0.001 y[1] (numeric) = 1.25117151062 0.737819290718 y[1] (closed_form) = 1.25117296208 0.737828525071 absolute error = 9.348e-06 relative error = 0.0006436 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.554 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.203 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3265 1.057 h = 0.001 0.003 y[1] (numeric) = 1.25180270059 0.738601901678 y[1] (closed_form) = 1.25180423577 0.73861106798 absolute error = 9.294e-06 relative error = 0.0006394 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.555 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.714 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = 1.25228266048 0.740798569052 y[1] (closed_form) = 1.25228401953 0.740807866999 absolute error = 9.397e-06 relative error = 0.0006458 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.558 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.236 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2439.6MB, alloc=52.3MB, time=29.43 x[1] = 0.3276 1.064 h = 0.003 0.006 y[1] (numeric) = 1.25204969227 0.743634760171 y[1] (closed_form) = 1.2520508781 0.743643987577 absolute error = 9.303e-06 relative error = 0.0006389 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.559 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.291 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = 1.25371401808 0.748106788391 y[1] (closed_form) = 1.25371535258 0.748116822603 absolute error = 1.012e-05 relative error = 0.0006933 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.564 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.912 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = 1.25340184637 0.751652809064 y[1] (closed_form) = 1.25340317471 0.751662311574 absolute error = 9.595e-06 relative error = 0.0006565 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.567 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3308 1.078 h = 0.001 0.001 y[1] (numeric) = 1.25324187482 0.753783549466 y[1] (closed_form) = 1.25324339799 0.753792979054 absolute error = 9.552e-06 relative error = 0.0006531 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.568 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.21 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = 1.25387256625 0.754568325722 y[1] (closed_form) = 1.25387417244 0.754577687104 absolute error = 9.498e-06 relative error = 0.000649 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.569 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.269 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2485.1MB, alloc=52.3MB, time=29.98 x[1] = 0.3319 1.083 h = 0.003 0.006 y[1] (numeric) = 1.25363530784 0.757407342823 y[1] (closed_form) = 1.25363648084 0.757416729784 absolute error = 9.460e-06 relative error = 0.0006459 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.571 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.311 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = 1.25529481863 0.761887047289 y[1] (closed_form) = 1.25529614341 0.761897237587 absolute error = 1.028e-05 relative error = 0.0006998 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.576 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.921 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.335 1.094 h = 0.0001 0.003 y[1] (numeric) = 1.25497696474 0.765436695887 y[1] (closed_form) = 1.254978281 0.765446356356 absolute error = 9.750e-06 relative error = 0.0006633 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.579 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.548 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3351 1.097 h = 0.001 0.001 y[1] (numeric) = 1.25481361568 0.767569663206 y[1] (closed_form) = 1.25481512576 0.767579250136 absolute error = 9.705e-06 relative error = 0.0006598 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.216 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3361 1.098 h = 0.001 0.003 y[1] (numeric) = 1.25544386287 0.768356292489 y[1] (closed_form) = 1.25544545537 0.768365811079 absolute error = 9.651e-06 relative error = 0.0006557 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.581 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.772 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2530.4MB, alloc=52.3MB, time=30.52 x[1] = 0.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = 1.25591791987 0.770560049951 y[1] (closed_form) = 1.25591933886 0.77056970088 absolute error = 9.755e-06 relative error = 0.000662 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.583 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.269 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3372 1.105 h = 0.003 0.006 y[1] (numeric) = 1.25567519921 0.773402640317 y[1] (closed_form) = 1.25567644561 0.773412222903 absolute error = 9.663e-06 relative error = 0.0006553 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.585 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.334 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = 1.25732930458 0.777891330554 y[1] (closed_form) = 1.25733070625 0.777901712392 absolute error = 1.048e-05 relative error = 0.0007086 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.591 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.931 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = 1.25700495441 0.781445299434 y[1] (closed_form) = 1.25700634489 0.781455153669 absolute error = 9.952e-06 relative error = 0.0006724 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.593 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.556 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3404 1.119 h = 0.001 0.001 y[1] (numeric) = 1.25683774544 0.783580916226 y[1] (closed_form) = 1.25683932857 0.78359069624 absolute error = 9.907e-06 relative error = 0.0006689 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.594 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.222 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2575.9MB, alloc=52.3MB, time=31.07 x[1] = 0.3414 1.12 h = 0.001 0.003 y[1] (numeric) = 1.25746751858 0.784369699113 y[1] (closed_form) = 1.25746918346 0.784379410649 absolute error = 9.853e-06 relative error = 0.0006648 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.595 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.804 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = 1.25793847439 0.786577287722 y[1] (closed_form) = 1.25793996712 0.786587131933 absolute error = 9.957e-06 relative error = 0.0006711 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.598 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.287 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3425 1.127 h = 0.003 0.006 y[1] (numeric) = 1.25769059087 0.789423368448 y[1] (closed_form) = 1.2576919114 0.789433145472 absolute error = 9.866e-06 relative error = 0.0006644 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.6 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.358 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = 1.25933935885 0.793921034891 y[1] (closed_form) = 1.25934083803 0.793931607082 absolute error = 1.068e-05 relative error = 0.0007171 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.605 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.942 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = 1.25900856106 0.797479339159 y[1] (closed_form) = 1.25901002645 0.797489385982 absolute error = 1.015e-05 relative error = 0.0006813 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.607 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.565 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2621.3MB, alloc=52.3MB, time=31.61 x[1] = 0.3457 1.141 h = 0.001 0.001 y[1] (numeric) = 1.25883752152 0.799617614005 y[1] (closed_form) = 1.25883917839 0.799627585945 absolute error = 1.011e-05 relative error = 0.0006778 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.608 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.229 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3467 1.142 h = 0.001 0.003 y[1] (numeric) = 1.25946683346 0.800408543991 y[1] (closed_form) = 1.25946857139 0.800418447326 absolute error = 1.005e-05 relative error = 0.0006738 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.836 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = 1.25993472022 0.802619963597 y[1] (closed_form) = 1.25993628739 0.802629999923 absolute error = 1.016e-05 relative error = 0.00068 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.612 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.305 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3478 1.149 h = 0.003 0.006 y[1] (numeric) = 1.25968171278 0.805469546294 y[1] (closed_form) = 1.25968310811 0.805479516574 absolute error = 1.007e-05 relative error = 0.0006733 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.614 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.382 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = 1.26132521059 0.809976178674 y[1] (closed_form) = 1.2613267679 0.809986940035 absolute error = 1.087e-05 relative error = 0.0007254 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.619 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.953 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2666.8MB, alloc=52.3MB, time=32.16 x[1] = 0.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = 1.26098801356 0.81353883272 y[1] (closed_form) = 1.26098955451 0.813549070957 absolute error = 1.035e-05 relative error = 0.0006899 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.622 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.573 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.351 1.163 h = 0.001 0.001 y[1] (numeric) = 1.26081317261 0.815679773775 y[1] (closed_form) = 1.26081490388 0.815689936486 absolute error = 1.031e-05 relative error = 0.0006865 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.623 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.236 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.352 1.164 h = 0.001 0.003 y[1] (numeric) = 1.26144203599 0.81647284427 y[1] (closed_form) = 1.26144384764 0.816482938259 absolute error = 1.026e-05 relative error = 0.0006825 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.624 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.868 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.353 1.167 h = 0.0001 0.004 y[1] (numeric) = 1.26190688554 0.818688094349 y[1] (closed_form) = 1.2619085278 0.818698321626 absolute error = 1.036e-05 relative error = 0.0006886 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.626 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.323 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3531 1.171 h = 0.003 0.006 y[1] (numeric) = 1.26164879286 0.821541190062 y[1] (closed_form) = 1.26165026367 0.821551352419 absolute error = 1.027e-05 relative error = 0.000682 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.628 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.407 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2712.1MB, alloc=52.3MB, time=32.69 x[1] = 0.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = 1.26328708697 0.826056777428 y[1] (closed_form) = 1.263288723 0.826067726781 absolute error = 1.107e-05 relative error = 0.0007335 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.634 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.963 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = 1.26294353877 0.829623794944 y[1] (closed_form) = 1.26294515593 0.829634223424 absolute error = 1.055e-05 relative error = 0.0006984 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.636 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.582 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3563 1.185 h = 0.001 0.001 y[1] (numeric) = 1.26276492538 0.831767409946 y[1] (closed_form) = 1.2627667317 0.831777762279 absolute error = 1.051e-05 relative error = 0.000695 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.637 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.243 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = 1.26339335264 0.832562614281 y[1] (closed_form) = 1.26339523867 0.832572897781 absolute error = 1.046e-05 relative error = 0.000691 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.639 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.466 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3574 1.19 h = 0.003 0.006 y[1] (numeric) = 1.26313112426 0.83541858291 y[1] (closed_form) = 1.26313258641 0.835428901893 absolute error = 1.042e-05 relative error = 0.0006882 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.641 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.427 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2757.6MB, alloc=52.3MB, time=33.24 x[1] = 0.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = 1.26476488536 0.839941808233 y[1] (closed_form) = 1.26476651551 0.839952910737 absolute error = 1.122e-05 relative error = 0.0007391 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.646 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.973 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = 1.26441585635 0.84351251724 y[1] (closed_form) = 1.26441746549 0.843523100786 absolute error = 1.071e-05 relative error = 0.0007043 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.648 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.59 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3606 1.204 h = 0.001 0.001 y[1] (numeric) = 1.26423398686 0.845658395303 y[1] (closed_form) = 1.26423578416 0.845668902167 absolute error = 1.066e-05 relative error = 0.0007008 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.65 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.248 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3616 1.205 h = 0.001 0.003 y[1] (numeric) = 1.26486202323 0.846455425976 y[1] (closed_form) = 1.26486389966 0.846465863913 absolute error = 1.061e-05 relative error = 0.0006968 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.651 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.928 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = 1.26532125933 0.848677765745 y[1] (closed_form) = 1.26532296889 0.848688337488 absolute error = 1.071e-05 relative error = 0.0007029 % Correct digits = 5 memory used=2803.0MB, alloc=52.3MB, time=33.78 Radius of convergence (given) for eq 1 = 2.654 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.358 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3627 1.212 h = 0.003 0.006 y[1] (numeric) = 1.26505376415 0.85153736638 y[1] (closed_form) = 1.26505530299 0.851547875262 absolute error = 1.062e-05 relative error = 0.0006965 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.655 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.452 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = 1.26668244334 0.856069525351 y[1] (closed_form) = 1.26668415327 0.856080813674 absolute error = 1.142e-05 relative error = 0.0007468 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.661 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.984 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = 1.26632715164 0.859644622065 y[1] (closed_form) = 1.26632883813 0.859655393693 absolute error = 1.090e-05 relative error = 0.0007123 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.663 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.598 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3659 1.226 h = 0.001 0.001 y[1] (numeric) = 1.26614156301 0.861793187744 y[1] (closed_form) = 1.26614343651 0.861803882104 absolute error = 1.086e-05 relative error = 0.0007089 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.665 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.255 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2848.4MB, alloc=52.3MB, time=34.32 x[1] = 0.3669 1.227 h = 0.001 0.003 y[1] (numeric) = 1.26676918597 0.862592339782 y[1] (closed_form) = 1.26677113794 0.862602965121 absolute error = 1.080e-05 relative error = 0.0007049 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.666 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.961 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = 1.26722547424 0.864818506927 y[1] (closed_form) = 1.26722726068 0.864829266318 absolute error = 1.091e-05 relative error = 0.0007109 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.668 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.376 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.368 1.234 h = 0.003 0.006 y[1] (numeric) = 1.26695300298 0.867681649626 y[1] (closed_form) = 1.2669546191 0.867692347237 absolute error = 1.082e-05 relative error = 0.0007045 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.477 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.371 1.24 h = 0.0001 0.005 y[1] (numeric) = 1.26857666452 0.872222729467 y[1] (closed_form) = 1.26857845476 0.872234202445 absolute error = 1.161e-05 relative error = 0.0007543 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.676 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.995 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = 1.2682151573 0.875802225665 y[1] (closed_form) = 1.26821692173 0.875813184218 absolute error = 1.110e-05 relative error = 0.0007202 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.678 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.607 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2894.0MB, alloc=52.3MB, time=34.86 x[1] = 0.3712 1.248 h = 0.001 0.001 y[1] (numeric) = 1.26802587795 0.877953485561 y[1] (closed_form) = 1.26802782825 0.877964366277 absolute error = 1.105e-05 relative error = 0.0007167 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.262 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3722 1.249 h = 0.001 0.003 y[1] (numeric) = 1.26865309938 0.878754752082 y[1] (closed_form) = 1.2686551275 0.878765563692 absolute error = 1.100e-05 relative error = 0.0007128 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.681 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.995 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = 1.26910647046 0.880984744739 y[1] (closed_form) = 1.26910833436 0.880995690628 absolute error = 1.110e-05 relative error = 0.0007187 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.683 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.395 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3733 1.256 h = 0.003 0.006 y[1] (numeric) = 1.2688290608 0.883851438482 y[1] (closed_form) = 1.26883075481 0.883862323659 absolute error = 1.102e-05 relative error = 0.0007124 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.685 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.502 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = 1.2704477682 0.888401425826 y[1] (closed_form) = 1.27044963927 0.888413082302 absolute error = 1.181e-05 relative error = 0.0007615 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.691 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.006 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2939.6MB, alloc=52.3MB, time=35.40 x[1] = 0.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = 1.27008009231 0.891985332649 y[1] (closed_form) = 1.27008193525 0.891996476972 absolute error = 1.130e-05 relative error = 0.0007278 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.693 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.616 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3765 1.27 h = 0.001 0.001 y[1] (numeric) = 1.26988715045 0.894139292984 y[1] (closed_form) = 1.26988917811 0.894150358921 absolute error = 1.125e-05 relative error = 0.0007244 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.695 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.27 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3775 1.271 h = 0.001 0.003 y[1] (numeric) = 1.27051398205 0.894942667042 y[1] (closed_form) = 1.27051608687 0.894953663795 absolute error = 1.120e-05 relative error = 0.0007205 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.696 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.028 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = 1.27096446623 0.897176483027 y[1] (closed_form) = 1.27096640816 0.89718761427 absolute error = 1.130e-05 relative error = 0.0007263 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.698 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.414 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3786 1.278 h = 0.003 0.006 y[1] (numeric) = 1.27068215561 0.900046736293 y[1] (closed_form) = 1.27068392807 0.900057807876 absolute error = 1.121e-05 relative error = 0.0007201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.527 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2985.1MB, alloc=52.3MB, time=35.95 x[1] = 0.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = 1.27229597161 0.904605617203 y[1] (closed_form) = 1.272297924 0.904617456025 absolute error = 1.200e-05 relative error = 0.0007686 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.706 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.017 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = 1.27192217355 0.90819394517 y[1] (closed_form) = 1.27192409555 0.908205274115 absolute error = 1.149e-05 relative error = 0.0007352 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.708 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.625 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3818 1.292 h = 0.001 0.001 y[1] (numeric) = 1.27172559718 0.910350611798 y[1] (closed_form) = 1.27172770275 0.910361861824 absolute error = 1.145e-05 relative error = 0.0007318 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.277 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = 1.27235205045 0.911156086387 y[1] (closed_form) = 1.27235423254 0.91116726716 absolute error = 1.139e-05 relative error = 0.0007279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.711 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.67 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3829 1.297 h = 0.003 0.006 y[1] (numeric) = 1.27206575382 0.914029249024 y[1] (closed_form) = 1.27206752146 0.914040474219 absolute error = 1.136e-05 relative error = 0.0007255 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.713 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.548 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3030.5MB, alloc=52.3MB, time=36.49 x[1] = 0.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = 1.27367530342 0.91859571638 y[1] (closed_form) = 1.27367725345 0.91860770536 absolute error = 1.215e-05 relative error = 0.0007735 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.719 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.027 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.386 1.308 h = 0.0001 0.003 y[1] (numeric) = 1.27329621977 0.922187785699 y[1] (closed_form) = 1.27329813746 0.922199266736 absolute error = 1.164e-05 relative error = 0.0007404 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.721 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.633 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3861 1.311 h = 0.001 0.001 y[1] (numeric) = 1.27309650486 0.924346743382 y[1] (closed_form) = 1.27309860515 0.924358145042 absolute error = 1.159e-05 relative error = 0.0007369 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.723 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.283 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3871 1.312 h = 0.001 0.003 y[1] (numeric) = 1.27372261663 0.92515401606 y[1] (closed_form) = 1.2737247929 0.925165348407 absolute error = 1.154e-05 relative error = 0.000733 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.724 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.091 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = 1.27416776307 0.927394905944 y[1] (closed_form) = 1.27416977887 0.927406373145 absolute error = 1.164e-05 relative error = 0.0007388 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.726 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.449 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3076.0MB, alloc=52.3MB, time=37.03 x[1] = 0.3882 1.319 h = 0.003 0.006 y[1] (numeric) = 1.27387638896 0.930271746206 y[1] (closed_form) = 1.27387823609 0.93028315567 absolute error = 1.156e-05 relative error = 0.0007327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.728 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.574 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = 1.27548116204 0.934847080487 y[1] (closed_form) = 1.2754831943 0.934859249691 absolute error = 1.234e-05 relative error = 0.0007802 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.734 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.038 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = 1.27509604176 0.938443589463 y[1] (closed_form) = 1.27509803949 0.938455253004 absolute error = 1.183e-05 relative error = 0.0007474 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.736 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.642 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3914 1.333 h = 0.001 0.001 y[1] (numeric) = 1.27489274381 0.940605263707 y[1] (closed_form) = 1.27489492302 0.940616847371 absolute error = 1.179e-05 relative error = 0.000744 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.738 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.29 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3924 1.334 h = 0.001 0.003 y[1] (numeric) = 1.27551849824 0.941414623865 y[1] (closed_form) = 1.27552075278 0.941426138161 absolute error = 1.173e-05 relative error = 0.0007401 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.739 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.125 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3121.5MB, alloc=52.3MB, time=37.58 x[1] = 0.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = 1.27596084275 0.943659329497 y[1] (closed_form) = 1.27596293812 0.943670978812 absolute error = 1.184e-05 relative error = 0.0007458 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.742 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.469 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3935 1.341 h = 0.003 0.006 y[1] (numeric) = 1.27566467315 0.946539751304 y[1] (closed_form) = 1.27566660029 0.946551343892 absolute error = 1.175e-05 relative error = 0.0007398 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.744 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.6 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = 1.27726473027 0.951123937059 y[1] (closed_form) = 1.27726684521 0.951136285354 absolute error = 1.253e-05 relative error = 0.0007867 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.749 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.049 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = 1.27687361889 0.95472489451 y[1] (closed_form) = 1.27687569716 0.954736739422 absolute error = 1.203e-05 relative error = 0.0007543 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.752 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.652 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3967 1.355 h = 0.001 0.001 y[1] (numeric) = 1.2766667653 0.95688929016 y[1] (closed_form) = 1.27666902392 0.956901054712 absolute error = 1.198e-05 relative error = 0.0007508 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.753 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.297 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3167.0MB, alloc=52.3MB, time=38.12 x[1] = 0.3977 1.356 h = 0.001 0.003 y[1] (numeric) = 1.27729217336 0.957700730642 y[1] (closed_form) = 1.27729450668 0.957712425777 absolute error = 1.193e-05 relative error = 0.000747 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.755 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.159 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = 1.27773174501 0.959949248692 y[1] (closed_form) = 1.27773392043 0.959961078997 absolute error = 1.203e-05 relative error = 0.0007527 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.757 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.488 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3988 1.363 h = 0.003 0.006 y[1] (numeric) = 1.27743081627 0.962833258691 y[1] (closed_form) = 1.27743282392 0.962845033264 absolute error = 1.194e-05 relative error = 0.0007467 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.759 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.626 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = 1.27902621724 0.967426279983 y[1] (closed_form) = 1.27902841529 0.967438806241 absolute error = 1.272e-05 relative error = 0.000793 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.765 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.061 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = 1.27862915993 0.971031694164 y[1] (closed_form) = 1.27863131921 0.97104371932 absolute error = 1.222e-05 relative error = 0.0007609 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.767 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.661 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3212.4MB, alloc=52.3MB, time=38.66 x[1] = 0.402 1.377 h = 0.001 0.001 y[1] (numeric) = 1.27841877787 0.973198815729 y[1] (closed_form) = 1.27842111639 0.973210760058 absolute error = 1.217e-05 relative error = 0.0007575 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.769 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.304 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.403 1.378 h = 0.001 0.003 y[1] (numeric) = 1.27904385034 0.974012329333 y[1] (closed_form) = 1.27904626294 0.974024204205 absolute error = 1.212e-05 relative error = 0.0007537 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.77 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.194 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.404 1.381 h = 0.0001 0.004 y[1] (numeric) = 1.27948067789 0.976264656203 y[1] (closed_form) = 1.27948293386 0.976276666378 absolute error = 1.222e-05 relative error = 0.0007593 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.772 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.508 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4041 1.385 h = 0.003 0.006 y[1] (numeric) = 1.27917502609 0.979152260595 y[1] (closed_form) = 1.27917711474 0.979164216019 absolute error = 1.214e-05 relative error = 0.0007534 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.775 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.652 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = 1.28076582995 0.983754101021 y[1] (closed_form) = 1.28076811153 0.983766804121 absolute error = 1.291e-05 relative error = 0.0007992 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.073 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3257.8MB, alloc=52.3MB, time=39.20 x[1] = 0.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = 1.28036287153 0.987363979636 y[1] (closed_form) = 1.2803651123 0.987376183913 absolute error = 1.241e-05 relative error = 0.0007674 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.783 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.67 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4073 1.399 h = 0.001 0.001 y[1] (numeric) = 1.28014898796 0.989533831302 y[1] (closed_form) = 1.28015140685 0.989545954302 absolute error = 1.236e-05 relative error = 0.000764 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.784 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.312 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4083 1.4 h = 0.003 0.006 y[1] (numeric) = 1.28077373545 0.990349410785 y[1] (closed_form) = 1.2807762278 0.990361464294 absolute error = 1.231e-05 relative error = 0.0007602 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.786 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.21 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = 1.28236220995 0.994957054052 y[1] (closed_form) = 1.28236431943 0.994970220462 absolute error = 1.333e-05 relative error = 0.0008215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.791 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.081 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = 1.28195533074 0.998570155208 y[1] (closed_form) = 1.28195739807 0.998582824413 absolute error = 1.284e-05 relative error = 0.00079 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.794 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.677 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3303.2MB, alloc=52.3MB, time=39.75 x[1] = 0.4115 1.414 h = 0.001 0.001 y[1] (numeric) = 1.28173912293 1.00074197454 y[1] (closed_form) = 1.28174136761 1.0007545622 absolute error = 1.279e-05 relative error = 0.0007863 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.795 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.317 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4125 1.415 h = 0.001 0.003 y[1] (numeric) = 1.28236370476 1.00155897877 y[1] (closed_form) = 1.28236602247 1.00157149693 absolute error = 1.273e-05 relative error = 0.0007824 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.797 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.254 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = 1.28279606063 1.00381779317 y[1] (closed_form) = 1.28279822383 1.0038304468 absolute error = 1.284e-05 relative error = 0.0007881 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.799 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.542 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4136 1.422 h = 0.003 0.006 y[1] (numeric) = 1.28248260868 1.00671159438 y[1] (closed_form) = 1.28248460537 1.00672419486 absolute error = 1.276e-05 relative error = 0.0007825 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.801 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.697 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = 1.2840660062 1.01132839467 y[1] (closed_form) = 1.28406819986 1.01134173604 absolute error = 1.352e-05 relative error = 0.0008272 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.807 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.093 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3348.7MB, alloc=52.3MB, time=40.29 x[1] = 0.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = 1.28365330088 1.01494597095 y[1] (closed_form) = 1.28365545041 1.01495881739 absolute error = 1.303e-05 relative error = 0.0007959 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.686 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4168 1.436 h = 0.001 0.001 y[1] (numeric) = 1.28343363664 1.01712052607 y[1] (closed_form) = 1.28343596241 1.01713329053 absolute error = 1.297e-05 relative error = 0.0007923 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.811 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.324 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4178 1.437 h = 0.001 0.003 y[1] (numeric) = 1.28405791079 1.01793958361 y[1] (closed_form) = 1.284060309 1.01795227856 absolute error = 1.292e-05 relative error = 0.0007884 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.813 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.289 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = 1.28448759816 1.02020219518 y[1] (closed_form) = 1.28448984308 1.02021502569 absolute error = 1.303e-05 relative error = 0.0007941 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.815 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.562 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4189 1.444 h = 0.003 0.006 y[1] (numeric) = 1.28416951877 1.02309960445 y[1] (closed_form) = 1.28417159767 1.02311238276 absolute error = 1.295e-05 relative error = 0.0007885 % Correct digits = 5 memory used=3394.2MB, alloc=52.3MB, time=40.83 Radius of convergence (given) for eq 1 = 2.817 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.723 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = 1.28574847376 1.0277251762 y[1] (closed_form) = 1.28575075197 1.02773869142 absolute error = 1.371e-05 relative error = 0.0008327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.823 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.104 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.422 1.455 h = 0.0001 0.003 y[1] (numeric) = 1.28532998615 1.03134723391 y[1] (closed_form) = 1.2853322183 1.03136025647 absolute error = 1.321e-05 relative error = 0.0008017 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.825 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.696 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4221 1.458 h = 0.001 0.001 y[1] (numeric) = 1.28510689182 1.03352452816 y[1] (closed_form) = 1.28510929913 1.03353746835 absolute error = 1.316e-05 relative error = 0.0007981 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.827 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.332 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4231 1.459 h = 0.001 0.003 y[1] (numeric) = 1.28573086844 1.03434563169 y[1] (closed_form) = 1.28573334757 1.03435850234 absolute error = 1.311e-05 relative error = 0.0007943 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.828 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.325 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3439.5MB, alloc=52.3MB, time=41.37 x[1] = 0.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = 1.28615791487 1.03661203591 y[1] (closed_form) = 1.28616024195 1.03662504221 absolute error = 1.321e-05 relative error = 0.0007999 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.831 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.582 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4242 1.466 h = 0.003 0.006 y[1] (numeric) = 1.28583524303 1.03951305791 y[1] (closed_form) = 1.28583740455 1.03952601294 absolute error = 1.313e-05 relative error = 0.0007943 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.833 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.75 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = 1.28740981177 1.04414738317 y[1] (closed_form) = 1.28741217491 1.04416107116 absolute error = 1.389e-05 relative error = 0.000838 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.839 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.116 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = 1.28698558535 1.04777392811 y[1] (closed_form) = 1.28698790053 1.04778712571 absolute error = 1.340e-05 relative error = 0.0008074 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.841 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.705 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4274 1.48 h = 0.001 0.001 y[1] (numeric) = 1.28675908705 1.04995396457 y[1] (closed_form) = 1.2867615763 1.04996707939 absolute error = 1.335e-05 relative error = 0.0008038 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.843 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.339 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3484.9MB, alloc=52.3MB, time=41.91 x[1] = 0.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = 1.28738277609 1.05077710672 y[1] (closed_form) = 1.28738533657 1.050790152 absolute error = 1.329e-05 relative error = 0.0008 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.844 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.048 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4285 1.485 h = 0.003 0.006 y[1] (numeric) = 1.28705636863 1.05368107932 y[1] (closed_form) = 1.28705853122 1.05369418253 absolute error = 1.328e-05 relative error = 0.0007984 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.847 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.772 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = 1.2886271024 1.0583228733 y[1] (closed_form) = 1.28862946858 1.05833670611 absolute error = 1.403e-05 relative error = 0.0008416 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.852 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.126 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = 1.28819791718 1.06195321732 y[1] (closed_form) = 1.28820023377 1.06196656167 absolute error = 1.354e-05 relative error = 0.0008113 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.855 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.714 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4317 1.499 h = 0.001 0.001 y[1] (numeric) = 1.28796847689 1.06413557628 y[1] (closed_form) = 1.28797096663 1.06414883751 absolute error = 1.349e-05 relative error = 0.0008076 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.857 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.346 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3530.4MB, alloc=52.3MB, time=42.45 x[1] = 0.4327 1.5 h = 0.001 0.003 y[1] (numeric) = 1.28859190207 1.06496046403 y[1] (closed_form) = 1.28859446253 1.0649736557 absolute error = 1.344e-05 relative error = 0.0008038 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.858 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.391 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = 1.2890140616 1.06723388201 y[1] (closed_form) = 1.28901647226 1.06724720947 absolute error = 1.354e-05 relative error = 0.0008093 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.86 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.619 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4338 1.507 h = 0.003 0.006 y[1] (numeric) = 1.2886828932 1.07014158381 y[1] (closed_form) = 1.28868513918 1.07015486169 absolute error = 1.347e-05 relative error = 0.0008039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.863 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.799 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = 1.29024934377 1.07479209757 y[1] (closed_form) = 1.29025179553 1.07480610113 absolute error = 1.422e-05 relative error = 0.0008466 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.868 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.138 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = 1.28981449957 1.07842693886 y[1] (closed_form) = 1.28981689992 1.07844045622 absolute error = 1.373e-05 relative error = 0.0008166 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.871 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.723 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3575.9MB, alloc=52.3MB, time=43.00 x[1] = 0.437 1.521 h = 0.001 0.001 y[1] (numeric) = 1.28958170328 1.08061204526 y[1] (closed_form) = 1.28958427571 1.08062547913 absolute error = 1.368e-05 relative error = 0.000813 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.873 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.353 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.438 1.522 h = 0.001 0.003 y[1] (numeric) = 1.29020485905 1.081438958 y[1] (closed_form) = 1.29020750161 1.08145232231 absolute error = 1.362e-05 relative error = 0.0008092 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.874 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.427 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.439 1.525 h = 0.0001 0.004 y[1] (numeric) = 1.29062445485 1.08371615479 y[1] (closed_form) = 1.29062694879 1.08372965494 absolute error = 1.373e-05 relative error = 0.0008146 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.877 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.64 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4391 1.529 h = 0.003 0.006 y[1] (numeric) = 1.29028879236 1.08662748095 y[1] (closed_form) = 1.29029112213 1.08664093242 absolute error = 1.365e-05 relative error = 0.0008093 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.879 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.826 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = 1.29185101396 1.09128669549 y[1] (closed_form) = 1.29185355163 1.09130086873 absolute error = 1.440e-05 relative error = 0.0008514 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.884 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.15 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3621.4MB, alloc=52.3MB, time=43.54 x[1] = 0.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = 1.29141055318 1.0949260385 y[1] (closed_form) = 1.29141303766 1.0949397278 absolute error = 1.391e-05 relative error = 0.0008217 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.887 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.733 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4423 1.543 h = 0.001 0.001 y[1] (numeric) = 1.29117442638 1.09711389461 y[1] (closed_form) = 1.29117708185 1.09712750006 absolute error = 1.386e-05 relative error = 0.0008181 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.889 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.361 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4433 1.544 h = 0.001 0.003 y[1] (numeric) = 1.29179732221 1.0979428249 y[1] (closed_form) = 1.29180004724 1.0979563608 absolute error = 1.381e-05 relative error = 0.0008144 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.89 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.463 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = 1.29221438064 1.10022379515 y[1] (closed_form) = 1.29221695824 1.10023746693 absolute error = 1.391e-05 relative error = 0.0008198 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.893 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.66 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4444 1.551 h = 0.003 0.006 y[1] (numeric) = 1.2918742579 1.10313874888 y[1] (closed_form) = 1.29187667182 1.10315237285 absolute error = 1.384e-05 relative error = 0.0008145 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.895 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.853 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3666.8MB, alloc=52.3MB, time=44.08 x[1] = 0.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = 1.29343230404 1.10780664489 y[1] (closed_form) = 1.29343492792 1.10782098673 absolute error = 1.458e-05 relative error = 0.0008561 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.901 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.162 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = 1.29298626871 1.11145049361 y[1] (closed_form) = 1.29298883766 1.11146435377 absolute error = 1.410e-05 relative error = 0.0008267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.903 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.743 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4476 1.565 h = 0.001 0.001 y[1] (numeric) = 1.29274683663 1.11364110142 y[1] (closed_form) = 1.29274957552 1.1136548774 absolute error = 1.405e-05 relative error = 0.0008232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.905 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.369 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4486 1.566 h = 0.001 0.003 y[1] (numeric) = 1.29336948184 1.11447204182 y[1] (closed_form) = 1.29337228971 1.11448574826 absolute error = 1.399e-05 relative error = 0.0008195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.907 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.499 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = 1.29378402895 1.11675677998 y[1] (closed_form) = 1.29378669056 1.11677062232 absolute error = 1.410e-05 relative error = 0.0008248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.909 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.681 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3712.1MB, alloc=52.3MB, time=44.63 x[1] = 0.4497 1.573 h = 0.003 0.006 y[1] (numeric) = 1.29343947949 1.11967536413 y[1] (closed_form) = 1.29344197791 1.11968915952 absolute error = 1.402e-05 relative error = 0.0008195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.911 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.881 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = 1.29499340297 1.12435192196 y[1] (closed_form) = 1.29499611336 1.12436643136 absolute error = 1.476e-05 relative error = 0.0008607 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.917 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.175 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = 1.29454183475 1.12800027997 y[1] (closed_form) = 1.29454448851 1.12801430994 absolute error = 1.428e-05 relative error = 0.0008316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.92 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.753 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4529 1.587 h = 0.001 0.001 y[1] (numeric) = 1.2942991224 1.13019364122 y[1] (closed_form) = 1.29430194505 1.13020758668 absolute error = 1.423e-05 relative error = 0.000828 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.922 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.376 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = 1.29492152615 1.13102658428 y[1] (closed_form) = 1.29492441721 1.13104046021 absolute error = 1.417e-05 relative error = 0.0008244 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.923 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.27 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3757.7MB, alloc=52.3MB, time=45.17 x[1] = 0.454 1.592 h = 0.003 0.006 y[1] (numeric) = 1.29457337549 1.13394813244 y[1] (closed_form) = 1.29457587792 1.13396207293 absolute error = 1.416e-05 relative error = 0.000823 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.925 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.904 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.457 1.598 h = 0.0001 0.005 y[1] (numeric) = 1.29612368922 1.13863208185 y[1] (closed_form) = 1.29612640535 1.13864673305 absolute error = 1.490e-05 relative error = 0.0008637 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.931 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.185 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = 1.29566733777 1.1422842586 y[1] (closed_form) = 1.29566999581 1.14229843228 absolute error = 1.442e-05 relative error = 0.0008349 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.934 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.761 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4572 1.606 h = 0.001 0.001 y[1] (numeric) = 1.29542178892 1.14447995245 y[1] (closed_form) = 1.29542461495 1.14449404133 absolute error = 1.437e-05 relative error = 0.0008313 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.935 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.383 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4582 1.607 h = 0.001 0.003 y[1] (numeric) = 1.29604396829 1.14531461061 y[1] (closed_form) = 1.29604686225 1.14532862999 absolute error = 1.431e-05 relative error = 0.0008276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.937 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.567 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3803.2MB, alloc=52.3MB, time=45.71 x[1] = 0.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = 1.296453866 1.14760631534 y[1] (closed_form) = 1.29645661584 1.14762047064 absolute error = 1.442e-05 relative error = 0.0008328 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.939 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.719 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4593 1.614 h = 0.003 0.006 y[1] (numeric) = 1.29610112431 1.15053160948 y[1] (closed_form) = 1.29610371188 1.15054571941 absolute error = 1.435e-05 relative error = 0.0008277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.942 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.932 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = 1.29764741201 1.15522418398 y[1] (closed_form) = 1.29765021519 1.1552390008 absolute error = 1.508e-05 relative error = 0.000868 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.947 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.197 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = 1.29718560416 1.15888087603 y[1] (closed_form) = 1.29718834761 1.15889521756 absolute error = 1.460e-05 relative error = 0.0008394 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.771 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4625 1.628 h = 0.001 0.001 y[1] (numeric) = 1.29693682096 1.16107932618 y[1] (closed_form) = 1.29693973137 1.16109358261 absolute error = 1.455e-05 relative error = 0.0008359 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.952 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.391 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3848.7MB, alloc=52.3MB, time=46.26 x[1] = 0.4635 1.629 h = 0.001 0.003 y[1] (numeric) = 1.29755877556 1.1619159732 y[1] (closed_form) = 1.29756175334 1.16193016015 absolute error = 1.450e-05 relative error = 0.0008323 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.953 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.604 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = 1.29796623487 1.16421142921 y[1] (closed_form) = 1.29796906967 1.16422575208 absolute error = 1.460e-05 relative error = 0.0008374 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.956 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.74 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4646 1.636 h = 0.003 0.006 y[1] (numeric) = 1.29760916066 1.16714036047 y[1] (closed_form) = 1.2976118337 1.16715463879 absolute error = 1.453e-05 relative error = 0.0008323 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.958 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.959 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = 1.29915147315 1.1718415396 y[1] (closed_form) = 1.29915436364 1.17185652099 absolute error = 1.526e-05 relative error = 0.0008721 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.964 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.21 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = 1.29868424948 1.17550274932 y[1] (closed_form) = 1.29868707865 1.17551725765 absolute error = 1.478e-05 relative error = 0.0008438 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.967 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.781 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3894.2MB, alloc=52.3MB, time=46.80 x[1] = 0.4678 1.65 h = 0.001 0.001 y[1] (numeric) = 1.2984322563 1.17770395682 y[1] (closed_form) = 1.29843525139 1.17771837977 absolute error = 1.473e-05 relative error = 0.0008403 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.969 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.399 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4688 1.651 h = 0.001 0.003 y[1] (numeric) = 1.29905399484 1.17854258521 y[1] (closed_form) = 1.29905705674 1.1785569387 absolute error = 1.468e-05 relative error = 0.0008367 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.641 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = 1.29945904061 1.18084178625 y[1] (closed_form) = 1.29946196067 1.18085627564 absolute error = 1.478e-05 relative error = 0.0008418 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.972 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.761 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4699 1.658 h = 0.003 0.006 y[1] (numeric) = 1.29909766625 1.18377435621 y[1] (closed_form) = 1.29910042506 1.18378880187 absolute error = 1.471e-05 relative error = 0.0008368 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.975 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.987 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = 1.30063605365 1.18848411923 y[1] (closed_form) = 1.30063903172 1.18849926417 absolute error = 1.543e-05 relative error = 0.0008761 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.981 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.222 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=3939.7MB, alloc=52.3MB, time=47.34 x[1] = 0.473 1.669 h = 0.0001 0.003 y[1] (numeric) = 1.30016345437 1.19214984862 y[1] (closed_form) = 1.30016636955 1.19216452272 absolute error = 1.496e-05 relative error = 0.0008481 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.984 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.791 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4731 1.672 h = 0.001 0.001 y[1] (numeric) = 1.29990827535 1.19435381428 y[1] (closed_form) = 1.29991135542 1.19436840271 absolute error = 1.491e-05 relative error = 0.0008446 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.985 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.406 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4741 1.673 h = 0.001 0.003 y[1] (numeric) = 1.30052980637 1.19519441654 y[1] (closed_form) = 1.3005329527 1.19520893556 absolute error = 1.486e-05 relative error = 0.0008411 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.987 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.678 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = 1.30093246319 1.1974973562 y[1] (closed_form) = 1.3009354688 1.1975120111 absolute error = 1.496e-05 relative error = 0.0008461 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.989 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.782 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4752 1.68 h = 0.003 0.006 y[1] (numeric) = 1.30056682074 1.20043356614 y[1] (closed_form) = 1.3005696656 1.2004481781 absolute error = 1.489e-05 relative error = 0.0008411 % Correct digits = 5 memory used=3985.3MB, alloc=52.3MB, time=47.88 Radius of convergence (given) for eq 1 = 2.991 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.015 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = 1.3021013325 1.20515189207 y[1] (closed_form) = 1.30210439837 1.20516719954 absolute error = 1.561e-05 relative error = 0.0008799 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.997 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.235 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = 1.30162339745 1.20882214275 y[1] (closed_form) = 1.3016263989 1.20883698159 absolute error = 1.514e-05 relative error = 0.0008523 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.801 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4784 1.694 h = 0.001 0.001 y[1] (numeric) = 1.30136505648 1.21102886715 y[1] (closed_form) = 1.30136822181 1.21104362006 absolute error = 1.509e-05 relative error = 0.0008488 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.002 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.414 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = 1.30198638838 1.21187143579 y[1] (closed_form) = 1.30198961944 1.21188611932 absolute error = 1.503e-05 relative error = 0.0008453 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.003 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.498 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4030.7MB, alloc=52.3MB, time=48.42 x[1] = 0.4795 1.699 h = 0.003 0.006 y[1] (numeric) = 1.30161727336 1.21481061666 y[1] (closed_form) = 1.3016201249 1.21482537065 absolute error = 1.503e-05 relative error = 0.000844 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.006 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.039 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = 1.30314838653 1.21953625091 y[1] (closed_form) = 1.30315146059 1.2195516972 absolute error = 1.575e-05 relative error = 0.0008824 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.012 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.245 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = 1.30266583636 1.22321033145 y[1] (closed_form) = 1.30266884468 1.223225311 absolute error = 1.528e-05 relative error = 0.000855 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.015 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.809 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4827 1.713 h = 0.001 0.001 y[1] (numeric) = 1.30240475979 1.22541939351 y[1] (closed_form) = 1.30240793113 1.22543428689 absolute error = 1.523e-05 relative error = 0.0008515 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.016 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.421 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4837 1.714 h = 0.001 0.003 y[1] (numeric) = 1.30302590361 1.22626364651 y[1] (closed_form) = 1.30302914021 1.22627847054 absolute error = 1.517e-05 relative error = 0.000848 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.018 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.748 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4076.2MB, alloc=52.3MB, time=48.97 x[1] = 0.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = 1.30342413521 1.22857349748 y[1] (closed_form) = 1.30342723313 1.22858845733 absolute error = 1.528e-05 relative error = 0.0008529 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.822 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4848 1.721 h = 0.003 0.006 y[1] (numeric) = 1.30305059173 1.23151643299 y[1] (closed_form) = 1.30305352985 1.23153135138 absolute error = 1.520e-05 relative error = 0.000848 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.023 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.067 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = 1.30457791977 1.23625059109 y[1] (closed_form) = 1.30458108206 1.23626619803 absolute error = 1.592e-05 relative error = 0.000886 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.028 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.258 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = 1.30409010693 1.23992919542 y[1] (closed_form) = 1.30409320203 1.23994433781 absolute error = 1.546e-05 relative error = 0.0008589 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.031 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.819 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.488 1.735 h = 0.001 0.001 y[1] (numeric) = 1.30382591229 1.24214101701 y[1] (closed_form) = 1.30382916939 1.242156073 absolute error = 1.540e-05 relative error = 0.0008554 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.033 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.429 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4121.7MB, alloc=52.3MB, time=49.51 x[1] = 0.489 1.736 h = 0.001 0.003 y[1] (numeric) = 1.30444687232 1.24298722255 y[1] (closed_form) = 1.30445019415 1.24300220924 absolute error = 1.535e-05 relative error = 0.0008519 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.035 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.786 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.49 1.739 h = 0.0001 0.004 y[1] (numeric) = 1.30484278373 1.24530079323 y[1] (closed_form) = 1.30484596797 1.24531591568 absolute error = 1.545e-05 relative error = 0.0008568 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.037 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.843 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4901 1.743 h = 0.003 0.006 y[1] (numeric) = 1.30446506218 1.24824737112 y[1] (closed_form) = 1.30446808714 1.24826245287 absolute error = 1.538e-05 relative error = 0.000852 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.04 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.096 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = 1.30598865264 1.25299003144 y[1] (closed_form) = 1.30599190338 1.25300579805 absolute error = 1.610e-05 relative error = 0.0008895 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.045 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.27 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = 1.30549561592 1.25667316014 y[1] (closed_form) = 1.30549879803 1.25668846439 absolute error = 1.563e-05 relative error = 0.0008626 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.048 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.83 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4167.2MB, alloc=52.3MB, time=50.05 x[1] = 0.4933 1.757 h = 0.001 0.001 y[1] (numeric) = 1.30522832644 1.25888774127 y[1] (closed_form) = 1.30523166957 1.25890295887 absolute error = 1.558e-05 relative error = 0.0008592 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.05 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.437 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4943 1.758 h = 0.001 0.003 y[1] (numeric) = 1.30584911066 1.25973589185 y[1] (closed_form) = 1.305852518 1.2597510402 absolute error = 1.553e-05 relative error = 0.0008557 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.052 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.824 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = 1.30624272533 1.26205317524 y[1] (closed_form) = 1.30624599614 1.2620684593 absolute error = 1.563e-05 relative error = 0.0008605 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.054 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.864 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4954 1.765 h = 0.003 0.006 y[1] (numeric) = 1.30586085662 1.2650033957 y[1] (closed_form) = 1.30586396866 1.26501863981 absolute error = 1.556e-05 relative error = 0.0008557 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.057 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.124 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = 1.3073807564 1.26975453643 y[1] (closed_form) = 1.30738409578 1.2697704617 absolute error = 1.627e-05 relative error = 0.0008928 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.062 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.283 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4212.6MB, alloc=52.3MB, time=50.60 x[1] = 0.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = 1.30688253419 1.27344218975 y[1] (closed_form) = 1.30688580354 1.27345765485 absolute error = 1.581e-05 relative error = 0.0008663 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.065 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.84 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4986 1.779 h = 0.001 0.001 y[1] (numeric) = 1.30661217291 1.27565953018 y[1] (closed_form) = 1.30661560229 1.27567490842 absolute error = 1.576e-05 relative error = 0.0008628 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.067 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.445 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4996 1.78 h = 0.001 0.003 y[1] (numeric) = 1.30723278917 1.27650961832 y[1] (closed_form) = 1.30723628224 1.27652492736 absolute error = 1.570e-05 relative error = 0.0008594 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.069 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.862 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = 1.30762413024 1.27883060732 y[1] (closed_form) = 1.30762748785 1.27884605199 absolute error = 1.581e-05 relative error = 0.0008641 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.071 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.886 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5007 1.787 h = 0.003 0.006 y[1] (numeric) = 1.30723814496 1.28178447024 y[1] (closed_form) = 1.30724134432 1.2817998757 absolute error = 1.573e-05 relative error = 0.0008594 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.074 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.153 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4258.1MB, alloc=52.3MB, time=51.14 x[1] = 0.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = 1.30875440033 1.28654406938 y[1] (closed_form) = 1.30875782855 1.28656015235 absolute error = 1.644e-05 relative error = 0.000896 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.08 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.296 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = 1.30825103065 1.29023624725 y[1] (closed_form) = 1.30825438747 1.29025187221 absolute error = 1.598e-05 relative error = 0.0008698 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.083 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5039 1.801 h = 0.001 0.001 y[1] (numeric) = 1.30797762037 1.29245634658 y[1] (closed_form) = 1.30798113624 1.29247188447 absolute error = 1.593e-05 relative error = 0.0008663 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.084 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.453 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = 1.30859807636 1.2933083648 y[1] (closed_form) = 1.3086016554 1.29332383354 absolute error = 1.588e-05 relative error = 0.000863 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.086 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.73 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.505 1.806 h = 0.003 0.006 y[1] (numeric) = 1.30820874136 1.29626519993 y[1] (closed_form) = 1.3082119498 1.29628074439 absolute error = 1.587e-05 relative error = 0.0008618 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.088 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.177 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4303.6MB, alloc=52.3MB, time=51.68 x[1] = 0.508 1.812 h = 0.0001 0.005 y[1] (numeric) = 1.3097217959 1.30103201936 y[1] (closed_form) = 1.30972523451 1.30104823821 absolute error = 1.658e-05 relative error = 0.0008981 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.094 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.307 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = 1.30921397172 1.3047280308 y[1] (closed_form) = 1.30921733777 1.30474379349 absolute error = 1.612e-05 relative error = 0.000872 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.097 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.859 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5082 1.82 h = 0.001 0.001 y[1] (numeric) = 1.3089379222 1.30695046849 y[1] (closed_form) = 1.30894144645 1.30696614391 absolute error = 1.607e-05 relative error = 0.0008686 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.099 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.46 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5092 1.821 h = 0.001 0.003 y[1] (numeric) = 1.30955822343 1.30780414027 y[1] (closed_form) = 1.30956181041 1.3078197466 absolute error = 1.601e-05 relative error = 0.0008652 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.933 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = 1.30994535059 1.31013197871 y[1] (closed_form) = 1.30994880407 1.31014772054 absolute error = 1.612e-05 relative error = 0.0008699 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.926 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4349.1MB, alloc=52.3MB, time=52.23 x[1] = 0.5103 1.828 h = 0.003 0.006 y[1] (numeric) = 1.30955174239 1.31309257011 y[1] (closed_form) = 1.30955503857 1.31310827408 absolute error = 1.605e-05 relative error = 0.0008653 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.105 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.206 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = 1.31106123719 1.3178678071 y[1] (closed_form) = 1.31106476497 1.31788418183 absolute error = 1.675e-05 relative error = 0.0009011 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.111 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.319 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = 1.31054833532 1.32156834254 y[1] (closed_form) = 1.31055178923 1.32158426327 absolute error = 1.629e-05 relative error = 0.0008753 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.114 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.869 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5135 1.842 h = 0.001 0.001 y[1] (numeric) = 1.31026927863 1.32379353814 y[1] (closed_form) = 1.31027288978 1.32380937141 absolute error = 1.624e-05 relative error = 0.0008719 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.116 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.468 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5145 1.843 h = 0.001 0.003 y[1] (numeric) = 1.31088943365 1.3246491262 y[1] (closed_form) = 1.31089310703 1.32466489045 absolute error = 1.619e-05 relative error = 0.0008685 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.118 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.971 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4394.5MB, alloc=52.3MB, time=52.77 x[1] = 0.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = 1.31127435198 1.32698064947 y[1] (closed_form) = 1.31127789289 1.32699654911 absolute error = 1.629e-05 relative error = 0.0008731 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.948 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5156 1.85 h = 0.003 0.006 y[1] (numeric) = 1.31087671311 1.32994488203 y[1] (closed_form) = 1.31088009724 1.32996074453 absolute error = 1.622e-05 relative error = 0.0008686 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.123 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.235 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = 1.31238269264 1.3347285141 y[1] (closed_form) = 1.31238630975 1.33474504377 absolute error = 1.692e-05 relative error = 0.000904 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.129 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.332 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = 1.31186475006 1.33843357259 y[1] (closed_form) = 1.31186829201 1.33844965039 absolute error = 1.646e-05 relative error = 0.0008784 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.88 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5188 1.864 h = 0.001 0.001 y[1] (numeric) = 1.31158270835 1.34066152518 y[1] (closed_form) = 1.3115864066 1.34067751534 absolute error = 1.641e-05 relative error = 0.0008751 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.134 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.476 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4440.1MB, alloc=52.3MB, time=53.32 x[1] = 0.5198 1.865 h = 0.001 0.003 y[1] (numeric) = 1.31220272448 1.34151902205 y[1] (closed_form) = 1.31220648445 1.34153494326 absolute error = 1.636e-05 relative error = 0.0008717 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.135 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.01 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = 1.31258545606 1.34385422258 y[1] (closed_form) = 1.31258908458 1.34387027908 absolute error = 1.646e-05 relative error = 0.0008763 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.137 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.97 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5209 1.872 h = 0.003 0.006 y[1] (numeric) = 1.31218381597 1.34682209526 y[1] (closed_form) = 1.31218728823 1.34683811532 absolute error = 1.639e-05 relative error = 0.0008717 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.264 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = 1.31368632409 1.35161409978 y[1] (closed_form) = 1.31369003068 1.35163078343 absolute error = 1.709e-05 relative error = 0.0009067 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.146 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.345 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.524 1.883 h = 0.0001 0.003 y[1] (numeric) = 1.31316337739 1.35532368006 y[1] (closed_form) = 1.31316700758 1.35533991398 absolute error = 1.663e-05 relative error = 0.0008815 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.149 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.89 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4485.5MB, alloc=52.3MB, time=53.86 x[1] = 0.5241 1.886 h = 0.001 0.001 y[1] (numeric) = 1.31287837262 1.35755438855 y[1] (closed_form) = 1.31288215815 1.35757053465 absolute error = 1.658e-05 relative error = 0.0008781 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.485 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5251 1.887 h = 0.001 0.003 y[1] (numeric) = 1.31349825702 1.35841378679 y[1] (closed_form) = 1.31350210379 1.35842986401 absolute error = 1.653e-05 relative error = 0.0008748 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.152 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.049 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = 1.31387882364 1.36075265689 y[1] (closed_form) = 1.31388253997 1.3607688693 absolute error = 1.663e-05 relative error = 0.0008793 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.155 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.992 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5262 1.894 h = 0.003 0.006 y[1] (numeric) = 1.3134732115 1.36372416842 y[1] (closed_form) = 1.31347677209 1.36374034508 absolute error = 1.656e-05 relative error = 0.0008748 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.157 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.293 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = 1.31497229145 1.36852452265 y[1] (closed_form) = 1.31497608767 1.36854135934 absolute error = 1.726e-05 relative error = 0.0009094 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.163 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.358 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4531.1MB, alloc=52.3MB, time=54.41 x[1] = 0.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = 1.31444437688 1.37223862319 y[1] (closed_form) = 1.31444809548 1.37225501227 absolute error = 1.681e-05 relative error = 0.0008844 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.166 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.901 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5294 1.908 h = 0.001 0.001 y[1] (numeric) = 1.31415643076 1.37447208631 y[1] (closed_form) = 1.31416030376 1.3744883874 absolute error = 1.675e-05 relative error = 0.0008811 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.168 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.493 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = 1.31477619051 1.3753333785 y[1] (closed_form) = 1.31478012425 1.3753496108 absolute error = 1.670e-05 relative error = 0.0008778 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.968 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5305 1.913 h = 0.003 0.006 y[1] (numeric) = 1.31436734576 1.37830785867 y[1] (closed_form) = 1.31437091761 1.37832417133 absolute error = 1.670e-05 relative error = 0.0008768 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.172 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.318 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = 1.31586340995 1.38311534158 y[1] (closed_form) = 1.31586721855 1.38313231126 absolute error = 1.739e-05 relative error = 0.000911 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.369 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4576.6MB, alloc=52.3MB, time=54.95 x[1] = 0.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = 1.31533119414 1.38683327297 y[1] (closed_form) = 1.31533492407 1.38684979685 absolute error = 1.694e-05 relative error = 0.0008862 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.181 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.909 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5337 1.927 h = 0.001 0.001 y[1] (numeric) = 1.31504070063 1.38906907136 y[1] (closed_form) = 1.31504458416 1.3890855071 absolute error = 1.689e-05 relative error = 0.0008829 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.183 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5347 1.928 h = 0.001 0.003 y[1] (numeric) = 1.31566033619 1.38993198649 y[1] (closed_form) = 1.31566428005 1.3899483535 absolute error = 1.684e-05 relative error = 0.0008797 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.185 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.121 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = 1.31603688791 1.39227763884 y[1] (closed_form) = 1.31604070318 1.39229414082 absolute error = 1.694e-05 relative error = 0.0008841 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.187 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.033 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5358 1.935 h = 0.003 0.006 y[1] (numeric) = 1.31562391801 1.39525587079 y[1] (closed_form) = 1.31562757851 1.39527233827 absolute error = 1.687e-05 relative error = 0.0008797 % Correct digits = 5 memory used=4622.1MB, alloc=52.3MB, time=55.50 Radius of convergence (given) for eq 1 = 3.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.348 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = 1.3171166332 1.40007166124 y[1] (closed_form) = 1.31712053168 1.40008878224 absolute error = 1.756e-05 relative error = 0.0009135 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.196 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.382 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = 1.31657951603 1.40379410974 y[1] (closed_form) = 1.31658333467 1.40381078703 absolute error = 1.711e-05 relative error = 0.000889 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.199 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.92 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.539 1.949 h = 0.001 0.001 y[1] (numeric) = 1.31628612102 1.40603266023 y[1] (closed_form) = 1.31629009233 1.40604924924 absolute error = 1.706e-05 relative error = 0.0008856 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.201 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.508 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.54 1.95 h = 0.001 0.003 y[1] (numeric) = 1.31690564479 1.40689745563 y[1] (closed_form) = 1.31690967596 1.40691397598 absolute error = 1.701e-05 relative error = 0.0008824 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.202 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.16 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4667.7MB, alloc=52.3MB, time=56.04 x[1] = 0.541 1.953 h = 0.0001 0.004 y[1] (numeric) = 1.31728009251 1.40924675528 y[1] (closed_form) = 1.31728399606 1.40926341049 absolute error = 1.711e-05 relative error = 0.0008868 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.205 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.055 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5411 1.957 h = 0.003 0.006 y[1] (numeric) = 1.31686323239 1.41222862159 y[1] (closed_form) = 1.3168669817 1.41224524296 absolute error = 1.704e-05 relative error = 0.0008824 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.207 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.377 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = 1.31835264013 1.41705269649 y[1] (closed_form) = 1.31835662861 1.41706996788 absolute error = 1.773e-05 relative error = 0.0009158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.396 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = 1.31781065682 1.4207796598 y[1] (closed_form) = 1.31781456432 1.42079648958 absolute error = 1.728e-05 relative error = 0.0008916 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.217 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.931 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5443 1.971 h = 0.001 0.001 y[1] (numeric) = 1.3175143814 1.4230209607 y[1] (closed_form) = 1.31751844065 1.42303770205 absolute error = 1.723e-05 relative error = 0.0008883 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.218 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.516 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4713.1MB, alloc=52.3MB, time=56.59 x[1] = 0.5453 1.972 h = 0.001 0.003 y[1] (numeric) = 1.31813380008 1.42388762897 y[1] (closed_form) = 1.31813791872 1.42390430176 absolute error = 1.717e-05 relative error = 0.0008851 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.2 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = 1.31850616456 1.4262405679 y[1] (closed_form) = 1.31851015655 1.42625737539 absolute error = 1.728e-05 relative error = 0.0008894 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.222 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.077 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5464 1.979 h = 0.003 0.006 y[1] (numeric) = 1.31808544228 1.42922606648 y[1] (closed_form) = 1.31808928055 1.42924284079 absolute error = 1.721e-05 relative error = 0.0008851 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.225 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.407 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = 1.31957158355 1.43405840264 y[1] (closed_form) = 1.31957566214 1.43407582351 absolute error = 1.789e-05 relative error = 0.0009181 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.231 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.409 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = 1.31902476895 1.43778987822 y[1] (closed_form) = 1.31902876546 1.43780685955 absolute error = 1.745e-05 relative error = 0.0008941 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.234 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.941 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4758.5MB, alloc=52.3MB, time=57.14 x[1] = 0.5496 1.993 h = 0.001 0.001 y[1] (numeric) = 1.318725634 1.44003392766 y[1] (closed_form) = 1.31872978134 1.44005082044 absolute error = 1.739e-05 relative error = 0.0008908 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.236 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.525 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5506 1.994 h = 0.001 0.003 y[1] (numeric) = 1.31934495418 1.44090246146 y[1] (closed_form) = 1.31934916044 1.44091928576 absolute error = 1.734e-05 relative error = 0.0008877 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.238 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.239 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = 1.31971525592 1.44325903152 y[1] (closed_form) = 1.31971933649 1.4432759904 absolute error = 1.744e-05 relative error = 0.0008919 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.1 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5517 2.001 h = 0.003 0.006 y[1] (numeric) = 1.31929069923 1.44624816011 y[1] (closed_form) = 1.3192946266 1.44626508642 absolute error = 1.738e-05 relative error = 0.0008876 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.243 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.436 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = 1.32077361445 1.45108873423 y[1] (closed_form) = 1.32077778326 1.45110630369 absolute error = 1.806e-05 relative error = 0.0009203 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.249 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.422 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4804.0MB, alloc=52.3MB, time=57.68 x[1] = 0.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = 1.32022200308 1.45482471929 y[1] (closed_form) = 1.32022608871 1.45484185128 absolute error = 1.761e-05 relative error = 0.0008965 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.252 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.952 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5549 2.015 h = 0.001 0.001 y[1] (numeric) = 1.31992002927 1.4570715153 y[1] (closed_form) = 1.31992426482 1.4570885586 absolute error = 1.756e-05 relative error = 0.0008933 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.254 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.533 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = 1.3205392574 1.45794190727 y[1] (closed_form) = 1.32054355141 1.45795888219 absolute error = 1.751e-05 relative error = 0.0008901 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.255 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.21 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.556 2.02 h = 0.003 0.006 y[1] (numeric) = 1.32011157966 1.46093399673 y[1] (closed_form) = 1.32011552025 1.46095105614 absolute error = 1.751e-05 relative error = 0.0008892 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.258 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.462 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.559 2.026 h = 0.0001 0.005 y[1] (numeric) = 1.32159165218 1.46578160534 y[1] (closed_form) = 1.32159583518 1.46579930497 absolute error = 1.819e-05 relative error = 0.0009215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.264 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.433 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4849.5MB, alloc=52.3MB, time=58.23 x[1] = 0.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = 1.32103588561 1.46952141302 y[1] (closed_form) = 1.32103998449 1.46953867693 absolute error = 1.774e-05 relative error = 0.000898 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.267 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.961 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5592 2.034 h = 0.001 0.001 y[1] (numeric) = 1.3207314519 1.47177053798 y[1] (closed_form) = 1.32073569993 1.4717877131 absolute error = 1.769e-05 relative error = 0.0008947 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.269 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5602 2.035 h = 0.001 0.003 y[1] (numeric) = 1.32135058386 1.47264252257 y[1] (closed_form) = 1.32135488995 1.47265962937 absolute error = 1.764e-05 relative error = 0.0008916 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.313 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = 1.32171705798 1.47500580345 y[1] (closed_form) = 1.32172124015 1.47502304456 absolute error = 1.774e-05 relative error = 0.0008958 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.273 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.141 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5613 2.042 h = 0.003 0.006 y[1] (numeric) = 1.32128539611 1.47800163499 y[1] (closed_form) = 1.32128942604 1.47801884471 absolute error = 1.768e-05 relative error = 0.0008916 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.276 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.492 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4895.0MB, alloc=52.3MB, time=58.78 x[1] = 0.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = 1.32276231656 1.48285743851 y[1] (closed_form) = 1.32276658995 1.48287528506 absolute error = 1.835e-05 relative error = 0.0009235 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.282 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.447 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = 1.32220181654 1.48660175028 y[1] (closed_form) = 1.32220600477 1.48661916316 absolute error = 1.791e-05 relative error = 0.0009002 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.285 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.972 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5645 2.056 h = 0.001 0.001 y[1] (numeric) = 1.32189458187 1.48885361797 y[1] (closed_form) = 1.32189891838 1.48887094195 absolute error = 1.786e-05 relative error = 0.000897 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.287 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.549 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5655 2.057 h = 0.001 0.003 y[1] (numeric) = 1.32251363358 1.48972744722 y[1] (closed_form) = 1.32251802769 1.48974470298 absolute error = 1.781e-05 relative error = 0.0008939 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.288 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.353 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = 1.3228781023 1.49209433582 y[1] (closed_form) = 1.32288237341 1.49211172573 absolute error = 1.791e-05 relative error = 0.000898 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.291 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.164 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4940.6MB, alloc=52.3MB, time=59.33 x[1] = 0.5666 2.064 h = 0.003 0.006 y[1] (numeric) = 1.32244268392 1.49509379013 y[1] (closed_form) = 1.32244680332 1.49511114926 absolute error = 1.784e-05 relative error = 0.0008938 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.294 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.522 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = 1.32391649113 1.49995776507 y[1] (closed_form) = 1.32392085499 1.49997575766 absolute error = 1.851e-05 relative error = 0.0009254 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.46 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = 1.32335129117 1.50370657749 y[1] (closed_form) = 1.32335556887 1.50372413845 absolute error = 1.807e-05 relative error = 0.0009023 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.303 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.982 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5698 2.078 h = 0.001 0.001 y[1] (numeric) = 1.32304127562 1.50596118553 y[1] (closed_form) = 1.3230457007 1.50597865748 absolute error = 1.802e-05 relative error = 0.0008991 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.305 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.557 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5708 2.079 h = 0.001 0.003 y[1] (numeric) = 1.32366025319 1.50683685217 y[1] (closed_form) = 1.32366473543 1.506854256 absolute error = 1.797e-05 relative error = 0.000896 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.306 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.393 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=4986.0MB, alloc=52.3MB, time=59.87 x[1] = 0.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = 1.32402273603 1.50920734008 y[1] (closed_form) = 1.3240270962 1.50922487791 absolute error = 1.807e-05 relative error = 0.0009001 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.309 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.187 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5719 2.086 h = 0.003 0.006 y[1] (numeric) = 1.32358358783 1.5122104142 y[1] (closed_form) = 1.32358779681 1.51222792184 absolute error = 1.801e-05 relative error = 0.000896 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.312 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.552 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = 1.32505432008 1.51708253698 y[1] (closed_form) = 1.32505877449 1.51710067474 absolute error = 1.868e-05 relative error = 0.0009272 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.318 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.473 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.575 2.097 h = 0.0001 0.003 y[1] (numeric) = 1.32448445336 1.52083584642 y[1] (closed_form) = 1.32448882061 1.52085355456 absolute error = 1.824e-05 relative error = 0.0009044 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.321 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.993 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5751 2.1 h = 0.001 0.001 y[1] (numeric) = 1.32417167677 1.52309319231 y[1] (closed_form) = 1.32417619054 1.52311081136 absolute error = 1.819e-05 relative error = 0.0009012 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.323 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.566 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5031.5MB, alloc=52.3MB, time=60.42 x[1] = 0.5761 2.101 h = 0.001 0.003 y[1] (numeric) = 1.32479058624 1.52397068909 y[1] (closed_form) = 1.32479515672 1.52398824012 absolute error = 1.814e-05 relative error = 0.0008981 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.324 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.433 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = 1.32515110248 1.52634476785 y[1] (closed_form) = 1.3251555518 1.5263624527 absolute error = 1.824e-05 relative error = 0.0009022 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.327 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.21 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5772 2.108 h = 0.003 0.006 y[1] (numeric) = 1.32470825086 1.52935145862 y[1] (closed_form) = 1.32471254951 1.52936911388 absolute error = 1.817e-05 relative error = 0.0008981 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.582 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = 1.32617594589 1.53423170564 y[1] (closed_form) = 1.32618049092 1.53424998771 absolute error = 1.884e-05 relative error = 0.0009289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.336 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.487 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = 1.32560144524 1.53798950824 y[1] (closed_form) = 1.32560590215 1.5380073627 absolute error = 1.840e-05 relative error = 0.0009063 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.339 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.004 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5076.9MB, alloc=52.3MB, time=60.96 x[1] = 0.5804 2.122 h = 0.001 0.001 y[1] (numeric) = 1.32528592727 1.54024958937 y[1] (closed_form) = 1.32529052983 1.54026735465 absolute error = 1.835e-05 relative error = 0.0009032 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.341 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.574 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = 1.32590477454 1.54112890906 y[1] (closed_form) = 1.32590943337 1.54114660642 absolute error = 1.830e-05 relative error = 0.0009002 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.342 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.456 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5815 2.127 h = 0.003 0.006 y[1] (numeric) = 1.32545890803 1.54413854939 y[1] (closed_form) = 1.32546322166 1.54415633488 absolute error = 1.830e-05 relative error = 0.0008993 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.345 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.608 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = 1.32692392216 1.54902573496 y[1] (closed_form) = 1.326928483 1.54904414443 absolute error = 1.897e-05 relative error = 0.0009299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.351 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.498 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = 1.32634540535 1.5527873472 y[1] (closed_form) = 1.32634987724 1.55280533079 absolute error = 1.853e-05 relative error = 0.0009074 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.354 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.013 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5122.4MB, alloc=52.3MB, time=61.50 x[1] = 0.5847 2.141 h = 0.001 0.001 y[1] (numeric) = 1.32602751073 1.55504974822 y[1] (closed_form) = 1.32603212752 1.55506764254 absolute error = 1.848e-05 relative error = 0.0009043 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.356 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.581 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5857 2.142 h = 0.001 0.003 y[1] (numeric) = 1.32664628751 1.5559306306 y[1] (closed_form) = 1.3266509602 1.55594845709 absolute error = 1.843e-05 relative error = 0.0009013 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.358 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.508 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = 1.32700315231 1.55831134547 y[1] (closed_form) = 1.3270077055 1.55832930547 absolute error = 1.853e-05 relative error = 0.0009052 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.252 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5868 2.149 h = 0.003 0.006 y[1] (numeric) = 1.32655343587 1.56132471372 y[1] (closed_form) = 1.32655783936 1.5613426452 absolute error = 1.846e-05 relative error = 0.0009012 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.363 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.638 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = 1.32801548191 1.5662199799 y[1] (closed_form) = 1.32802013349 1.56623853209 absolute error = 1.913e-05 relative error = 0.0009314 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.369 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.512 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5168.0MB, alloc=52.3MB, time=62.05 x[1] = 0.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = 1.32743239142 1.569986078 y[1] (closed_form) = 1.32743695312 1.57000420629 absolute error = 1.869e-05 relative error = 0.0009092 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.372 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.024 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.59 2.163 h = 0.001 0.001 y[1] (numeric) = 1.32711179148 1.57225120931 y[1] (closed_form) = 1.32711649723 1.57226924827 absolute error = 1.864e-05 relative error = 0.0009061 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.374 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.59 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.591 2.164 h = 0.001 0.003 y[1] (numeric) = 1.32773051685 1.57313390131 y[1] (closed_form) = 1.32773527807 1.57315187254 absolute error = 1.859e-05 relative error = 0.0009031 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.376 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.549 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.592 2.167 h = 0.0001 0.004 y[1] (numeric) = 1.32808546896 1.57551818272 y[1] (closed_form) = 1.32809011157 1.57553628727 absolute error = 1.869e-05 relative error = 0.000907 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.379 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.275 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5921 2.171 h = 0.003 0.006 y[1] (numeric) = 1.3276321232 1.57853515808 y[1] (closed_form) = 1.32763661662 1.57855323468 absolute error = 1.863e-05 relative error = 0.0009031 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.381 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.669 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5213.6MB, alloc=52.3MB, time=62.59 x[1] = 0.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = 1.32909123742 1.58343848114 y[1] (closed_form) = 1.32909597978 1.58345717521 absolute error = 1.929e-05 relative error = 0.0009329 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.387 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.525 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = 1.32850360512 1.5872090607 y[1] (closed_form) = 1.32850825671 1.58722733284 absolute error = 1.885e-05 relative error = 0.0009109 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.391 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.035 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5953 2.185 h = 0.001 0.001 y[1] (numeric) = 1.32818031892 1.58947691937 y[1] (closed_form) = 1.32818511371 1.58949510211 absolute error = 1.880e-05 relative error = 0.0009078 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.393 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.598 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5963 2.186 h = 0.001 0.003 y[1] (numeric) = 1.32879899849 1.59036141384 y[1] (closed_form) = 1.32880384833 1.59037952895 absolute error = 1.875e-05 relative error = 0.0009049 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.394 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.589 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = 1.32915205627 1.59274925311 y[1] (closed_form) = 1.32915678837 1.59276750136 absolute error = 1.885e-05 relative error = 0.0009087 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.397 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.298 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5259.1MB, alloc=52.3MB, time=63.14 x[1] = 0.5974 2.193 h = 0.003 0.006 y[1] (numeric) = 1.32869510656 1.59576983185 y[1] (closed_form) = 1.32869968999 1.59578805271 absolute error = 1.879e-05 relative error = 0.0009048 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.399 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.699 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = 1.33015132472 1.60068118802 y[1] (closed_form) = 1.33015615791 1.60070002313 absolute error = 1.945e-05 relative error = 0.0009343 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.406 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.539 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = 1.32955918215 1.60445624446 y[1] (closed_form) = 1.32956392369 1.6044746596 absolute error = 1.902e-05 relative error = 0.0009126 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.409 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.046 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6006 2.207 h = 0.001 0.001 y[1] (numeric) = 1.32923322856 1.60672682745 y[1] (closed_form) = 1.32923811247 1.60674515313 absolute error = 1.897e-05 relative error = 0.0009095 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.411 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.607 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6016 2.208 h = 0.001 0.003 y[1] (numeric) = 1.32985186785 1.60761311726 y[1] (closed_form) = 1.32985680638 1.60763137543 absolute error = 1.891e-05 relative error = 0.0009066 % Correct digits = 5 memory used=5304.7MB, alloc=52.3MB, time=63.69 Radius of convergence (given) for eq 1 = 3.412 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.63 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = 1.33020304942 1.61000450567 y[1] (closed_form) = 1.33020787108 1.6100228968 absolute error = 1.901e-05 relative error = 0.0009104 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.415 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.321 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6027 2.215 h = 0.003 0.006 y[1] (numeric) = 1.32974252087 1.61302868393 y[1] (closed_form) = 1.32974719437 1.6130470482 absolute error = 1.895e-05 relative error = 0.0009065 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.418 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.73 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = 1.33119587821 1.61794804944 y[1] (closed_form) = 1.33120080227 1.61796702476 absolute error = 1.960e-05 relative error = 0.0009356 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.424 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.552 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = 1.33059925661 1.62172757799 y[1] (closed_form) = 1.33060408816 1.6217461353 absolute error = 1.918e-05 relative error = 0.0009141 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.427 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.057 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5350.1MB, alloc=52.3MB, time=64.23 x[1] = 0.6059 2.229 h = 0.001 0.001 y[1] (numeric) = 1.3302706543 1.62400088216 y[1] (closed_form) = 1.33027562739 1.62401934995 absolute error = 1.913e-05 relative error = 0.000911 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.429 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.616 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = 1.3308892587 1.62488896023 y[1] (closed_form) = 1.33089428599 1.62490736062 absolute error = 1.907e-05 relative error = 0.0009082 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.431 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.706 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.607 2.234 h = 0.003 0.006 y[1] (numeric) = 1.33042581619 1.62791607368 y[1] (closed_form) = 1.33043050627 1.6279345654 absolute error = 1.908e-05 relative error = 0.0009074 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.433 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.756 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.61 2.24 h = 0.0001 0.005 y[1] (numeric) = 1.33187664389 1.63284228077 y[1] (closed_form) = 1.33188158522 1.63286138082 absolute error = 1.973e-05 relative error = 0.0009363 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.439 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.564 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = 1.33127613843 1.63662560199 y[1] (closed_form) = 1.3312809865 1.63664428569 absolute error = 1.930e-05 relative error = 0.0009149 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.443 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.066 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5395.5MB, alloc=52.3MB, time=64.78 x[1] = 0.6102 2.248 h = 0.001 0.001 y[1] (numeric) = 1.33094523864 1.63890121463 y[1] (closed_form) = 1.33095022754 1.63891980875 absolute error = 1.925e-05 relative error = 0.0009119 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.445 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.623 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6112 2.249 h = 0.001 0.003 y[1] (numeric) = 1.33156379607 1.63979082598 y[1] (closed_form) = 1.33156883883 1.63980935279 absolute error = 1.920e-05 relative error = 0.000909 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.446 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.706 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = 1.33191149189 1.64218877332 y[1] (closed_form) = 1.33191641936 1.64220743274 absolute error = 1.930e-05 relative error = 0.0009127 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.449 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.364 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6123 2.256 h = 0.003 0.006 y[1] (numeric) = 1.33144432711 1.64521959674 y[1] (closed_form) = 1.33144910737 1.6452382303 absolute error = 1.924e-05 relative error = 0.0009089 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.452 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.787 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = 1.33289235859 1.65015376927 y[1] (closed_form) = 1.33289739084 1.65017300801 absolute error = 1.989e-05 relative error = 0.0009375 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.458 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.578 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5441.0MB, alloc=52.3MB, time=65.32 x[1] = 0.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = 1.33228743138 1.65394155369 y[1] (closed_form) = 1.33229236957 1.653960378 absolute error = 1.946e-05 relative error = 0.0009163 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.461 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.077 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6155 2.27 h = 0.001 0.001 y[1] (numeric) = 1.33195391715 1.65621988162 y[1] (closed_form) = 1.33195899534 1.65623861632 absolute error = 1.941e-05 relative error = 0.0009133 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.463 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.632 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6165 2.271 h = 0.001 0.003 y[1] (numeric) = 1.33257244957 1.65711126818 y[1] (closed_form) = 1.33257758121 1.65712993568 absolute error = 1.936e-05 relative error = 0.0009104 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.465 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.747 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = 1.33291831987 1.65951273971 y[1] (closed_form) = 1.33292333706 1.65953153961 absolute error = 1.946e-05 relative error = 0.0009141 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.467 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.387 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6176 2.278 h = 0.003 0.006 y[1] (numeric) = 1.33244764669 1.66254715113 y[1] (closed_form) = 1.33245251719 1.6625659257 absolute error = 1.940e-05 relative error = 0.0009103 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.818 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5486.5MB, alloc=52.3MB, time=65.86 x[1] = 0.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = 1.33389291582 1.66748926527 y[1] (closed_form) = 1.33389803903 1.6675086419 absolute error = 2.004e-05 relative error = 0.0009386 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.476 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.592 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = 1.33328359717 1.67128150767 y[1] (closed_form) = 1.33328862551 1.67130047178 absolute error = 1.962e-05 relative error = 0.0009177 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.088 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6208 2.292 h = 0.001 0.001 y[1] (numeric) = 1.3329474866 1.67356254749 y[1] (closed_form) = 1.33295265414 1.67358142195 absolute error = 1.957e-05 relative error = 0.0009146 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.482 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.64 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6218 2.293 h = 0.001 0.003 y[1] (numeric) = 1.33356599914 1.67445570224 y[1] (closed_form) = 1.33357121973 1.67447450963 absolute error = 1.952e-05 relative error = 0.0009118 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.483 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.788 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = 1.33391006119 1.67686068909 y[1] (closed_form) = 1.33391516816 1.67687962867 absolute error = 1.962e-05 relative error = 0.0009155 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.486 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.411 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5532.0MB, alloc=52.3MB, time=66.41 x[1] = 0.6229 2.3 h = 0.003 0.006 y[1] (numeric) = 1.33343590372 1.67989868415 y[1] (closed_form) = 1.33344086451 1.67991759891 absolute error = 1.955e-05 relative error = 0.0009117 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.488 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.849 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = 1.33487844391 1.68484871608 y[1] (closed_form) = 1.33488365808 1.68486822979 absolute error = 2.020e-05 relative error = 0.0009396 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.495 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.605 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.626 2.311 h = 0.0001 0.003 y[1] (numeric) = 1.33426476379 1.68864541109 y[1] (closed_form) = 1.33426988232 1.68866451419 absolute error = 1.978e-05 relative error = 0.0009189 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.498 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6261 2.314 h = 0.001 0.001 y[1] (numeric) = 1.33392607483 1.6909291593 y[1] (closed_form) = 1.33393133176 1.69094817272 absolute error = 1.973e-05 relative error = 0.0009159 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.649 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6271 2.315 h = 0.001 0.003 y[1] (numeric) = 1.33454457253 1.69182407528 y[1] (closed_form) = 1.3345498821 1.69184302174 absolute error = 1.968e-05 relative error = 0.0009131 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.502 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.83 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5577.5MB, alloc=52.3MB, time=66.96 x[1] = 0.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = 1.33488684336 1.69423256855 y[1] (closed_form) = 1.33489204013 1.694251647 absolute error = 1.977e-05 relative error = 0.0009167 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.504 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.434 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6282 2.322 h = 0.003 0.006 y[1] (numeric) = 1.33440922546 1.69727414276 y[1] (closed_form) = 1.33441427656 1.6972931969 absolute error = 1.971e-05 relative error = 0.000913 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.507 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.88 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = 1.33584906963 1.70223206865 y[1] (closed_form) = 1.33585437478 1.70225171866 absolute error = 2.035e-05 relative error = 0.0009406 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.513 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.619 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = 1.33523105773 1.70603321076 y[1] (closed_form) = 1.33523626648 1.70605245205 absolute error = 1.993e-05 relative error = 0.0009201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.517 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.111 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6314 2.336 h = 0.001 0.001 y[1] (numeric) = 1.33488980811 1.70831966378 y[1] (closed_form) = 1.33489515446 1.70833881536 absolute error = 1.988e-05 relative error = 0.0009171 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.519 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.658 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5623.0MB, alloc=52.3MB, time=67.50 x[1] = 0.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = 1.33550829591 1.70921633405 y[1] (closed_form) = 1.33551369451 1.70923541879 absolute error = 1.983e-05 relative error = 0.0009144 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.52 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.959 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6325 2.341 h = 0.003 0.006 y[1] (numeric) = 1.33502786001 1.71226082655 y[1] (closed_form) = 1.33503292911 1.71228000543 absolute error = 1.984e-05 relative error = 0.0009137 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.523 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.906 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = 1.33646531593 1.71722549664 y[1] (closed_form) = 1.33647063966 1.71724526877 absolute error = 2.048e-05 relative error = 0.000941 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.529 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.631 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = 1.33584354601 1.72103041102 y[1] (closed_form) = 1.33584877268 1.72104977603 absolute error = 2.006e-05 relative error = 0.0009207 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.532 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.12 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6357 2.355 h = 0.001 0.001 y[1] (numeric) = 1.33550007417 1.7233191591 y[1] (closed_form) = 1.33550543776 1.72333843437 absolute error = 2.001e-05 relative error = 0.0009177 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.535 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.665 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5668.4MB, alloc=52.3MB, time=68.04 x[1] = 0.6367 2.356 h = 0.001 0.003 y[1] (numeric) = 1.33611853655 1.72421733383 y[1] (closed_form) = 1.33612395206 1.72423654236 absolute error = 1.996e-05 relative error = 0.0009149 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.536 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.907 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = 1.33645747743 1.72663230708 y[1] (closed_form) = 1.33646278164 1.72665164722 absolute error = 2.005e-05 relative error = 0.0009185 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.539 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.478 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6378 2.363 h = 0.003 0.006 y[1] (numeric) = 1.33597344063 1.72968048838 y[1] (closed_form) = 1.33597860011 1.72969980513 absolute error = 1.999e-05 relative error = 0.0009148 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.541 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.937 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = 1.33740826089 1.73465300851 y[1] (closed_form) = 1.33741367561 1.73467291548 absolute error = 2.063e-05 relative error = 0.0009419 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.548 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.645 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = 1.33678221366 1.7384623597 y[1] (closed_form) = 1.33678753059 1.73848186142 absolute error = 2.021e-05 relative error = 0.0009217 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.551 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.131 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5713.9MB, alloc=52.3MB, time=68.59 x[1] = 0.641 2.377 h = 0.001 0.001 y[1] (numeric) = 1.33643621372 1.74075380592 y[1] (closed_form) = 1.3364416668 1.74077321789 absolute error = 2.016e-05 relative error = 0.0009188 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.553 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.674 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.642 2.378 h = 0.001 0.003 y[1] (numeric) = 1.33705467523 1.74165372216 y[1] (closed_form) = 1.33706017984 1.74167306752 absolute error = 2.011e-05 relative error = 0.000916 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.555 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.948 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.643 2.381 h = 0.0001 0.004 y[1] (numeric) = 1.33739187256 1.74407217643 y[1] (closed_form) = 1.33739726667 1.74409165317 absolute error = 2.021e-05 relative error = 0.0009195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.557 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.501 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6431 2.385 h = 0.003 0.006 y[1] (numeric) = 1.33690444228 1.74712392373 y[1] (closed_form) = 1.33690969217 1.74714337756 absolute error = 2.015e-05 relative error = 0.0009159 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.969 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = 1.33833665854 1.75210427009 y[1] (closed_form) = 1.33834216424 1.75212431114 absolute error = 2.078e-05 relative error = 0.0009427 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.566 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.659 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5759.3MB, alloc=52.3MB, time=69.13 x[1] = 0.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = 1.33770636278 1.7559180522 y[1] (closed_form) = 1.33771177 1.75593768985 absolute error = 2.037e-05 relative error = 0.0009227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.57 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.143 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6463 2.399 h = 0.001 0.001 y[1] (numeric) = 1.33735785196 1.75821219276 y[1] (closed_form) = 1.33736339455 1.75823174064 absolute error = 2.032e-05 relative error = 0.0009198 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.572 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.683 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6473 2.4 h = 0.001 0.003 y[1] (numeric) = 1.3379763173 1.75911384366 y[1] (closed_form) = 1.33798191104 1.75913332505 absolute error = 2.027e-05 relative error = 0.0009171 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.573 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.99 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = 1.3383117873 1.76153576994 y[1] (closed_form) = 1.33831727132 1.7615553825 absolute error = 2.036e-05 relative error = 0.0009205 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.576 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.525 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6484 2.407 h = 0.003 0.006 y[1] (numeric) = 1.33782098645 1.76459107834 y[1] (closed_form) = 1.33782632676 1.76461066846 absolute error = 2.030e-05 relative error = 0.0009169 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.579 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5804.9MB, alloc=52.3MB, time=69.68 x[1] = 0.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = 1.3392506299 1.76957922717 y[1] (closed_form) = 1.33925622659 1.76959940153 absolute error = 2.094e-05 relative error = 0.0009434 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.585 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.673 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = 1.33861611413 1.77339743416 y[1] (closed_form) = 1.33862161164 1.77341720696 absolute error = 2.052e-05 relative error = 0.0009237 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.588 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.154 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6516 2.421 h = 0.001 0.001 y[1] (numeric) = 1.33826510946 1.77569426517 y[1] (closed_form) = 1.33827074157 1.77571394819 absolute error = 2.047e-05 relative error = 0.0009207 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.591 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.692 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6526 2.422 h = 0.001 0.003 y[1] (numeric) = 1.33888358323 1.77659764393 y[1] (closed_form) = 1.33888926612 1.77661726058 absolute error = 2.042e-05 relative error = 0.000918 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.592 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.032 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = 1.33921734192 1.77902303321 y[1] (closed_form) = 1.33922291586 1.77904278082 absolute error = 2.052e-05 relative error = 0.0009215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.595 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.548 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5850.6MB, alloc=52.3MB, time=70.22 x[1] = 0.6537 2.429 h = 0.003 0.006 y[1] (numeric) = 1.33872319317 1.78208189771 y[1] (closed_form) = 1.33872862391 1.78210162334 absolute error = 2.046e-05 relative error = 0.0009179 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.598 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.031 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = 1.34015029459 1.78707782526 y[1] (closed_form) = 1.34015598224 1.78709813217 absolute error = 2.109e-05 relative error = 0.0009441 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.604 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.687 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = 1.339511587 1.79090045097 y[1] (closed_form) = 1.33951717481 1.79092035816 absolute error = 2.068e-05 relative error = 0.0009245 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.607 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.165 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6569 2.443 h = 0.001 0.001 y[1] (numeric) = 1.33915810533 1.7931999685 y[1] (closed_form) = 1.33916382697 1.7932197859 absolute error = 2.063e-05 relative error = 0.0009216 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.609 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.701 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = 1.33977659205 1.79410506832 y[1] (closed_form) = 1.3397823641 1.79412481949 absolute error = 2.058e-05 relative error = 0.000919 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.611 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.22 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5896.1MB, alloc=52.3MB, time=70.77 x[1] = 0.658 2.448 h = 0.003 0.006 y[1] (numeric) = 1.33927971651 1.79716683205 y[1] (closed_form) = 1.33928516651 1.7971866798 absolute error = 2.058e-05 relative error = 0.0009183 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.614 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.058 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.661 2.454 h = 0.0001 0.005 y[1] (numeric) = 1.34070456186 1.80216940649 y[1] (closed_form) = 1.34071026927 1.80218983297 absolute error = 2.121e-05 relative error = 0.0009442 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.699 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = 1.34006221593 1.8059957812 y[1] (closed_form) = 1.34006782291 1.80601580952 absolute error = 2.080e-05 relative error = 0.0009248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.623 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.175 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6612 2.462 h = 0.001 0.001 y[1] (numeric) = 1.33970658356 1.80829757873 y[1] (closed_form) = 1.33971232372 1.80831751727 absolute error = 2.075e-05 relative error = 0.0009219 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.625 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.708 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6622 2.463 h = 0.001 0.003 y[1] (numeric) = 1.34032506459 1.80920415482 y[1] (closed_form) = 1.34033085485 1.80922402722 absolute error = 2.070e-05 relative error = 0.0009193 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.627 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.11 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=5941.7MB, alloc=52.3MB, time=71.31 x[1] = 0.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = 1.34065563988 1.81163594396 y[1] (closed_form) = 1.34066132261 1.8116559469 absolute error = 2.079e-05 relative error = 0.0009227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.593 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6633 2.47 h = 0.003 0.006 y[1] (numeric) = 1.3401552788 1.81470137266 y[1] (closed_form) = 1.34016081925 1.81472135448 absolute error = 2.074e-05 relative error = 0.0009192 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.632 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.09 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = 1.34157763853 1.81971168205 y[1] (closed_form) = 1.34158343688 1.8197322397 absolute error = 2.136e-05 relative error = 0.0009448 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.639 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.713 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = 1.34093115256 1.82354246407 y[1] (closed_form) = 1.34093684984 1.82356262536 absolute error = 2.095e-05 relative error = 0.0009256 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.642 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.186 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6665 2.484 h = 0.001 0.001 y[1] (numeric) = 1.34057307413 1.82584694079 y[1] (closed_form) = 1.34057890385 1.82586701229 absolute error = 2.090e-05 relative error = 0.0009227 % Correct digits = 5 memory used=5987.3MB, alloc=52.3MB, time=71.85 Radius of convergence (given) for eq 1 = 3.644 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.717 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6675 2.485 h = 0.001 0.003 y[1] (numeric) = 1.34119157638 1.82675522547 y[1] (closed_form) = 1.34119745582 1.82677523097 absolute error = 2.085e-05 relative error = 0.0009201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.646 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.152 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = 1.34152048518 1.82919045193 y[1] (closed_form) = 1.34152625786 1.82921058774 absolute error = 2.095e-05 relative error = 0.0009234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.648 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.616 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6686 2.492 h = 0.003 0.006 y[1] (numeric) = 1.34101683983 1.83225942219 y[1] (closed_form) = 1.34102247073 1.83227953733 absolute error = 2.089e-05 relative error = 0.00092 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.651 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.121 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = 1.34243674352 1.83727744287 y[1] (closed_form) = 1.34244263277 1.83729813095 absolute error = 2.151e-05 relative error = 0.0009453 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.658 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.727 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6032.8MB, alloc=52.3MB, time=72.40 x[1] = 0.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = 1.34178614487 1.84111262573 y[1] (closed_form) = 1.34179193245 1.84113291924 absolute error = 2.110e-05 relative error = 0.0009263 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.661 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.197 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6718 2.506 h = 0.001 0.001 y[1] (numeric) = 1.34142563672 1.8434197775 y[1] (closed_form) = 1.341431556 1.84343998123 absolute error = 2.105e-05 relative error = 0.0009234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.663 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.726 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6728 2.507 h = 0.001 0.003 y[1] (numeric) = 1.34204416449 1.84432976409 y[1] (closed_form) = 1.34205013313 1.84434990195 absolute error = 2.100e-05 relative error = 0.0009208 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.665 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.194 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = 1.34237142206 1.84676841881 y[1] (closed_form) = 1.34237728468 1.84678868674 absolute error = 2.110e-05 relative error = 0.0009241 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.667 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.64 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6739 2.514 h = 0.003 0.006 y[1] (numeric) = 1.34186451421 1.84984092529 y[1] (closed_form) = 1.34187023554 1.84986117299 absolute error = 2.104e-05 relative error = 0.0009207 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.153 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6078.3MB, alloc=52.3MB, time=72.94 x[1] = 0.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = 1.34328199101 1.85486663364 y[1] (closed_form) = 1.34328797115 1.85488745141 absolute error = 2.166e-05 relative error = 0.0009458 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.676 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.741 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.677 2.525 h = 0.0001 0.003 y[1] (numeric) = 1.34262730678 1.85870621075 y[1] (closed_form) = 1.34263318463 1.85872663573 absolute error = 2.125e-05 relative error = 0.0009269 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.209 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6771 2.528 h = 0.001 0.001 y[1] (numeric) = 1.34226438509 1.86101603337 y[1] (closed_form) = 1.34227039391 1.8610363686 absolute error = 2.120e-05 relative error = 0.0009241 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.682 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.735 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6781 2.529 h = 0.001 0.003 y[1] (numeric) = 1.34288294258 1.86192771523 y[1] (closed_form) = 1.3428890004 1.86194798471 absolute error = 2.116e-05 relative error = 0.0009215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.683 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.237 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = 1.34320856399 1.86436978913 y[1] (closed_form) = 1.34321451652 1.86439018844 absolute error = 2.125e-05 relative error = 0.0009248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.686 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.664 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6123.8MB, alloc=52.3MB, time=73.48 x[1] = 0.6792 2.536 h = 0.003 0.006 y[1] (numeric) = 1.34269841518 1.86744582641 y[1] (closed_form) = 1.34270422692 1.86746620593 absolute error = 2.119e-05 relative error = 0.0009214 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.689 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.185 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = 1.34411349384 1.87247919884 y[1] (closed_form) = 1.34411956484 1.87250014558 absolute error = 2.181e-05 relative error = 0.0009462 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.695 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.755 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = 1.34345475083 1.87632316353 y[1] (closed_form) = 1.34346071895 1.87634371925 absolute error = 2.140e-05 relative error = 0.0009275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.699 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.22 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6824 2.55 h = 0.001 0.001 y[1] (numeric) = 1.34308943162 1.87863565276 y[1] (closed_form) = 1.34309552997 1.87865611875 absolute error = 2.136e-05 relative error = 0.0009247 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.701 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.744 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = 1.34370802296 1.87954902327 y[1] (closed_form) = 1.34371416997 1.87956942364 absolute error = 2.131e-05 relative error = 0.0009222 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.702 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.48 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6169.2MB, alloc=52.3MB, time=74.02 x[1] = 0.6835 2.555 h = 0.003 0.006 y[1] (numeric) = 1.34319523402 1.88262793895 y[1] (closed_form) = 1.34320106619 1.88264843803 absolute error = 2.131e-05 relative error = 0.0009215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.705 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.212 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = 1.34460818027 1.88766786142 y[1] (closed_form) = 1.34461427207 1.88768892529 absolute error = 2.193e-05 relative error = 0.0009461 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.712 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.767 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = 1.34394591269 1.89151554945 y[1] (closed_form) = 1.3439519011 1.89153622381 absolute error = 2.152e-05 relative error = 0.0009276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.715 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.23 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6867 2.569 h = 0.001 0.001 y[1] (numeric) = 1.34357851076 1.89383030226 y[1] (closed_form) = 1.34358462879 1.89385088689 absolute error = 2.147e-05 relative error = 0.0009248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.717 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.751 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6877 2.57 h = 0.001 0.003 y[1] (numeric) = 1.34419711448 1.8947451215 y[1] (closed_form) = 1.34420328086 1.89476564063 absolute error = 2.143e-05 relative error = 0.0009223 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.719 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.315 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6214.7MB, alloc=52.3MB, time=74.56 x[1] = 0.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = 1.34451969034 1.89719351445 y[1] (closed_form) = 1.34452575279 1.89721416297 absolute error = 2.152e-05 relative error = 0.0009255 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.721 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.709 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6888 2.577 h = 0.003 0.006 y[1] (numeric) = 1.34400352554 1.90027606902 y[1] (closed_form) = 1.3440094481 1.90029669854 absolute error = 2.146e-05 relative error = 0.0009221 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.724 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.244 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = 1.3454141264 1.90532361213 y[1] (closed_form) = 1.34542030899 1.90534480364 absolute error = 2.207e-05 relative error = 0.0009464 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.731 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.781 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = 1.34474784925 1.90917567538 y[1] (closed_form) = 1.3447539279 1.90919647912 absolute error = 2.167e-05 relative error = 0.0009281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.734 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.241 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.692 2.591 h = 0.001 0.001 y[1] (numeric) = 1.34437807919 1.91149308693 y[1] (closed_form) = 1.34438428673 1.91151380097 absolute error = 2.162e-05 relative error = 0.0009253 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.736 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.76 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6260.0MB, alloc=52.3MB, time=75.11 x[1] = 0.693 2.592 h = 0.001 0.003 y[1] (numeric) = 1.34499672433 1.91240958266 y[1] (closed_form) = 1.34500297988 1.91243023133 absolute error = 2.158e-05 relative error = 0.0009228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.738 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.358 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.694 2.595 h = 0.0001 0.004 y[1] (numeric) = 1.3453177062 1.91486136897 y[1] (closed_form) = 1.34532385852 1.91488214679 absolute error = 2.167e-05 relative error = 0.000926 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.741 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.733 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6941 2.599 h = 0.003 0.006 y[1] (numeric) = 1.3447983609 1.91794743865 y[1] (closed_form) = 1.34480437383 1.9179681979 absolute error = 2.161e-05 relative error = 0.0009226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.743 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.276 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = 1.34620664402 1.92300257897 y[1] (closed_form) = 1.34621291736 1.92302389741 absolute error = 2.222e-05 relative error = 0.0009467 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.795 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = 1.34553638332 1.92685901048 y[1] (closed_form) = 1.34554255216 1.92687994289 absolute error = 2.182e-05 relative error = 0.0009285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.753 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.253 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6305.5MB, alloc=52.3MB, time=75.65 x[1] = 0.6973 2.613 h = 0.001 0.001 y[1] (numeric) = 1.34516426066 1.92917907637 y[1] (closed_form) = 1.34517055768 1.92919991911 absolute error = 2.177e-05 relative error = 0.0009258 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.755 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.769 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6983 2.614 h = 0.001 0.003 y[1] (numeric) = 1.34578295114 1.93009724208 y[1] (closed_form) = 1.34578929583 1.93011801958 absolute error = 2.172e-05 relative error = 0.0009233 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.757 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.401 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = 1.34610235336 1.93255241265 y[1] (closed_form) = 1.34610859554 1.93257331907 absolute error = 2.182e-05 relative error = 0.0009264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.757 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6994 2.621 h = 0.003 0.006 y[1] (numeric) = 1.34557984825 1.93564199176 y[1] (closed_form) = 1.34558595152 1.93566288 absolute error = 2.176e-05 relative error = 0.0009231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.762 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.308 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = 1.3469858409 1.94070470587 y[1] (closed_form) = 1.34699220493 1.94072615055 absolute error = 2.237e-05 relative error = 0.0009469 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.769 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.81 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6351.0MB, alloc=52.3MB, time=76.21 x[1] = 0.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = 1.34631162239 1.94456549862 y[1] (closed_form) = 1.34631788139 1.94458655899 absolute error = 2.197e-05 relative error = 0.0009289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.772 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.264 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7026 2.635 h = 0.001 0.001 y[1] (numeric) = 1.34593716249 1.9468882144 y[1] (closed_form) = 1.34594354898 1.94690918513 absolute error = 2.192e-05 relative error = 0.0009262 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.775 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.778 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7036 2.636 h = 0.001 0.003 y[1] (numeric) = 1.34655590217 1.94780804361 y[1] (closed_form) = 1.34656233598 1.94782894923 absolute error = 2.187e-05 relative error = 0.0009237 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.776 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.443 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = 1.34687373891 1.95026658936 y[1] (closed_form) = 1.34688007091 1.95028762366 absolute error = 2.197e-05 relative error = 0.0009268 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.779 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.781 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7047 2.643 h = 0.003 0.006 y[1] (numeric) = 1.34634809447 1.95335967212 y[1] (closed_form) = 1.34635428804 1.95338068864 absolute error = 2.191e-05 relative error = 0.0009235 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.782 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.34 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6396.5MB, alloc=52.3MB, time=76.75 x[1] = 0.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = 1.34775182353 1.95842993668 y[1] (closed_form) = 1.3477582782 1.95845150691 absolute error = 2.252e-05 relative error = 0.0009471 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.788 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.824 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = 1.34707367268 1.96229508355 y[1] (closed_form) = 1.34708002182 1.96231627118 absolute error = 2.212e-05 relative error = 0.0009293 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.792 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.276 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7079 2.657 h = 0.001 0.001 y[1] (numeric) = 1.34669689076 1.96462044472 y[1] (closed_form) = 1.34670336668 1.96464154275 absolute error = 2.207e-05 relative error = 0.0009266 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.794 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.787 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = 1.3473156834 1.96554193099 y[1] (closed_form) = 1.34732220632 1.96556296405 absolute error = 2.202e-05 relative error = 0.0009241 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.795 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.74 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.709 2.662 h = 0.003 0.006 y[1] (numeric) = 1.34678748119 1.96863786986 y[1] (closed_form) = 1.34679369622 1.96865900347 absolute error = 2.203e-05 relative error = 0.0009235 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.798 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.367 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6442.1MB, alloc=52.3MB, time=77.30 x[1] = 0.712 2.668 h = 0.0001 0.005 y[1] (numeric) = 1.34818919352 1.97371458841 y[1] (closed_form) = 1.34819566995 1.97373627339 absolute error = 2.263e-05 relative error = 0.0009468 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.804 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.836 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = 1.34750762629 1.97758343098 y[1] (closed_form) = 1.34751399674 1.97760473481 absolute error = 2.224e-05 relative error = 0.0009292 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.808 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.286 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7122 2.676 h = 0.001 0.001 y[1] (numeric) = 1.34712882627 1.97991103817 y[1] (closed_form) = 1.3471353229 1.97993225243 absolute error = 2.219e-05 relative error = 0.0009265 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.795 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7132 2.677 h = 0.001 0.003 y[1] (numeric) = 1.34774764785 1.98083394635 y[1] (closed_form) = 1.34775419118 1.98085509574 absolute error = 2.214e-05 relative error = 0.000924 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.812 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.523 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = 1.34806256877 1.98329873006 y[1] (closed_form) = 1.34806901158 1.98332000768 absolute error = 2.223e-05 relative error = 0.0009271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.814 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.826 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6487.5MB, alloc=52.3MB, time=77.84 x[1] = 0.7143 2.684 h = 0.003 0.006 y[1] (numeric) = 1.34753109495 1.9863982799 y[1] (closed_form) = 1.34753740022 1.98641954048 absolute error = 2.218e-05 relative error = 0.0009239 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.817 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.4 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = 1.34893059303 1.99148250592 y[1] (closed_form) = 1.34893716001 1.99150431518 absolute error = 2.278e-05 relative error = 0.0009469 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.824 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.851 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = 1.34824514026 1.99535568948 y[1] (closed_form) = 1.34825160076 1.99537711927 absolute error = 2.238e-05 relative error = 0.0009294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.297 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7175 2.698 h = 0.001 0.001 y[1] (numeric) = 1.34786404615 1.99768593376 y[1] (closed_form) = 1.34787063215 1.99770727402 absolute error = 2.233e-05 relative error = 0.0009267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.804 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7185 2.699 h = 0.001 0.003 y[1] (numeric) = 1.34848292761 1.99861048715 y[1] (closed_form) = 1.34848956 1.99863176269 absolute error = 2.229e-05 relative error = 0.0009243 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.831 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.566 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6533.1MB, alloc=52.3MB, time=78.38 x[1] = 0.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = 1.34879632275 2.00107862021 y[1] (closed_form) = 1.34880285528 2.00110002372 absolute error = 2.238e-05 relative error = 0.0009273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.834 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.851 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7196 2.706 h = 0.003 0.006 y[1] (numeric) = 1.34826176706 2.00418165709 y[1] (closed_form) = 1.34826816254 2.00420304395 absolute error = 2.232e-05 relative error = 0.0009241 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.836 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.432 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = 1.34965907675 2.00927336741 y[1] (closed_form) = 1.34966573422 2.00929530027 absolute error = 2.292e-05 relative error = 0.0009469 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.843 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.865 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = 1.34896976315 2.01315088463 y[1] (closed_form) = 1.34897631367 2.0131724397 absolute error = 2.253e-05 relative error = 0.0009296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.846 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.309 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7228 2.72 h = 0.001 0.001 y[1] (numeric) = 1.3485863897 2.01548376137 y[1] (closed_form) = 1.34859306504 2.01550522696 absolute error = 2.248e-05 relative error = 0.000927 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.813 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6578.5MB, alloc=52.3MB, time=78.92 x[1] = 0.7238 2.721 h = 0.001 0.003 y[1] (numeric) = 1.34920533465 2.01640995364 y[1] (closed_form) = 1.34921205605 2.01643135464 absolute error = 2.243e-05 relative error = 0.0009246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.609 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = 1.3495172175 2.01888142697 y[1] (closed_form) = 1.34952383971 2.01890295568 absolute error = 2.252e-05 relative error = 0.0009275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.853 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.875 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7249 2.728 h = 0.003 0.006 y[1] (numeric) = 1.3489795996 2.02198794489 y[1] (closed_form) = 1.34898608524 2.02200945734 absolute error = 2.247e-05 relative error = 0.0009244 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.856 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.464 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = 1.3503747464 2.02708711639 y[1] (closed_form) = 1.3503814943 2.02710917218 absolute error = 2.306e-05 relative error = 0.0009469 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.862 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.879 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.728 2.739 h = 0.0001 0.003 y[1] (numeric) = 1.34968159646 2.03096895987 y[1] (closed_form) = 1.34968823694 2.03099063954 absolute error = 2.267e-05 relative error = 0.0009298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.866 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.32 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6624.1MB, alloc=52.3MB, time=79.47 x[1] = 0.7281 2.742 h = 0.001 0.001 y[1] (numeric) = 1.34929595828 2.03330446443 y[1] (closed_form) = 1.34930272291 2.03332605467 absolute error = 2.263e-05 relative error = 0.0009271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.868 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.822 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7291 2.743 h = 0.001 0.003 y[1] (numeric) = 1.34991497022 2.03423228927 y[1] (closed_form) = 1.34992178059 2.03425381506 absolute error = 2.258e-05 relative error = 0.0009248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.869 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.652 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = 1.35022535412 2.03670709379 y[1] (closed_form) = 1.35023206597 2.03672874704 absolute error = 2.267e-05 relative error = 0.0009277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.872 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.9 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7302 2.75 h = 0.003 0.006 y[1] (numeric) = 1.34968469347 2.03981708671 y[1] (closed_form) = 1.34969126922 2.03983872406 absolute error = 2.261e-05 relative error = 0.0009246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.875 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.497 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = 1.35107770253 2.04492369635 y[1] (closed_form) = 1.35108454079 2.04494587441 absolute error = 2.321e-05 memory used=6669.5MB, alloc=52.3MB, time=80.01 relative error = 0.0009469 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.881 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.894 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = 1.35038074046 2.04880985863 y[1] (closed_form) = 1.35038747085 2.04883166222 absolute error = 2.282e-05 relative error = 0.0009299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.885 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.332 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7334 2.764 h = 0.001 0.001 y[1] (numeric) = 1.349992852 2.0511479863 y[1] (closed_form) = 1.34999970588 2.05116970052 absolute error = 2.277e-05 relative error = 0.0009273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.887 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.831 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = 1.3506119344 2.05207743746 y[1] (closed_form) = 1.35061883369 2.05209908736 absolute error = 2.272e-05 relative error = 0.0009249 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.889 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7345 2.769 h = 0.003 0.006 y[1] (numeric) = 1.35006879427 2.05519026301 y[1] (closed_form) = 1.35007539238 2.05521201504 absolute error = 2.273e-05 relative error = 0.0009244 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.892 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.524 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6714.9MB, alloc=52.3MB, time=80.56 x[1] = 0.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = 1.35145989489 2.06030323167 y[1] (closed_form) = 1.35146675575 2.06032552218 absolute error = 2.332e-05 relative error = 0.0009465 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.898 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.906 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = 1.35075961934 2.06419306039 y[1] (closed_form) = 1.35076637193 2.06421497782 absolute error = 2.293e-05 relative error = 0.0009297 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.902 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.342 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7377 2.783 h = 0.001 0.001 y[1] (numeric) = 1.3503697742 2.06653341559 y[1] (closed_form) = 1.35037664971 2.0665552437 absolute error = 2.289e-05 relative error = 0.000927 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.904 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.839 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7387 2.784 h = 0.001 0.003 y[1] (numeric) = 1.35098890069 2.06746426253 y[1] (closed_form) = 1.35099582135 2.06748602644 absolute error = 2.284e-05 relative error = 0.0009247 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.905 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.732 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = 1.3512964909 2.06994522402 y[1] (closed_form) = 1.35130331426 2.06996711493 absolute error = 2.293e-05 relative error = 0.0009276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.908 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.945 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6760.2MB, alloc=52.3MB, time=81.10 x[1] = 0.7398 2.791 h = 0.003 0.006 y[1] (numeric) = 1.35075017829 2.07306163111 y[1] (closed_form) = 1.35075686642 2.0730835068 absolute error = 2.288e-05 relative error = 0.0009245 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.911 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.557 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = 1.35213918735 2.07818199549 y[1] (closed_form) = 1.35214613845 2.07820440706 absolute error = 2.346e-05 relative error = 0.0009464 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.917 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.92 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = 1.35143514416 2.08207612924 y[1] (closed_form) = 1.35144198656 2.08209816937 absolute error = 2.308e-05 relative error = 0.0009297 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.921 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.353 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.743 2.805 h = 0.001 0.001 y[1] (numeric) = 1.35104307529 2.08441909891 y[1] (closed_form) = 1.35105003995 2.08444104976 absolute error = 2.303e-05 relative error = 0.0009271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.923 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.848 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.744 2.806 h = 0.001 0.003 y[1] (numeric) = 1.35166227856 2.08535156064 y[1] (closed_form) = 1.35166928807 2.08537344744 absolute error = 2.298e-05 relative error = 0.0009248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.925 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.776 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6805.7MB, alloc=52.3MB, time=81.64 x[1] = 0.745 2.809 h = 0.0001 0.004 y[1] (numeric) = 1.35196840719 2.08783582757 y[1] (closed_form) = 1.35197532004 2.08785784111 absolute error = 2.307e-05 relative error = 0.0009276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.928 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.97 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7451 2.813 h = 0.003 0.006 y[1] (numeric) = 1.35141910646 2.09095569231 y[1] (closed_form) = 1.35142588455 2.09097769098 absolute error = 2.302e-05 relative error = 0.0009246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.59 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = 1.35280604815 2.09608342955 y[1] (closed_form) = 1.35281308942 2.09610596154 absolute error = 2.361e-05 relative error = 0.0009463 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.937 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.935 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = 1.35209826083 2.0999818607 y[1] (closed_form) = 1.35210519299 2.10000402286 absolute error = 2.322e-05 relative error = 0.0009297 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.941 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.365 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7483 2.827 h = 0.001 0.001 y[1] (numeric) = 1.35170398226 2.10232744003 y[1] (closed_form) = 1.35171103603 2.10234951298 absolute error = 2.317e-05 relative error = 0.0009271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.943 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.858 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6851.1MB, alloc=52.3MB, time=82.18 x[1] = 0.7493 2.828 h = 0.001 0.003 y[1] (numeric) = 1.3523232656 2.1032615104 y[1] (closed_form) = 1.3523303639 2.10328351943 absolute error = 2.313e-05 relative error = 0.0009248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.944 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.819 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = 1.35262794536 2.10574907374 y[1] (closed_form) = 1.35263494764 2.10577120925 absolute error = 2.322e-05 relative error = 0.0009276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.947 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.994 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7504 2.835 h = 0.003 0.006 y[1] (numeric) = 1.3520756752 2.10887238988 y[1] (closed_form) = 1.35208254319 2.10889451087 absolute error = 2.316e-05 relative error = 0.0009246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.622 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = 1.35346057339 2.11400747721 y[1] (closed_form) = 1.35346770475 2.11403012898 absolute error = 2.375e-05 relative error = 0.0009461 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.956 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.949 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = 1.35274906521 2.11791019807 y[1] (closed_form) = 1.35275608705 2.11793248161 absolute error = 2.336e-05 relative error = 0.0009297 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.377 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6896.6MB, alloc=52.3MB, time=82.73 x[1] = 0.7536 2.849 h = 0.001 0.001 y[1] (numeric) = 1.35235259081 2.12025838225 y[1] (closed_form) = 1.35235973362 2.12028057664 absolute error = 2.332e-05 relative error = 0.0009271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.962 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.867 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7546 2.85 h = 0.001 0.003 y[1] (numeric) = 1.35297195744 2.12119405512 y[1] (closed_form) = 1.35297914448 2.12121618574 absolute error = 2.327e-05 relative error = 0.0009248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.964 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.863 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = 1.35327520089 2.12368490585 y[1] (closed_form) = 1.35328229253 2.12370716269 absolute error = 2.336e-05 relative error = 0.0009276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.966 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.019 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7557 2.857 h = 0.003 0.006 y[1] (numeric) = 1.35271997981 2.12681166712 y[1] (closed_form) = 1.35272693762 2.12683390979 absolute error = 2.331e-05 relative error = 0.0009246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.969 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.655 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = 1.35410285804 2.13195408184 y[1] (closed_form) = 1.3541100794 2.13197685275 absolute error = 2.389e-05 relative error = 0.0009458 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.976 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.964 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=6942.1MB, alloc=52.3MB, time=83.28 x[1] = 0.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = 1.35338765202 2.13586108467 y[1] (closed_form) = 1.35339476348 2.13588348895 absolute error = 2.351e-05 relative error = 0.0009296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.979 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.389 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7589 2.871 h = 0.001 0.001 y[1] (numeric) = 1.35298899553 2.13821186884 y[1] (closed_form) = 1.35299622733 2.13823418404 absolute error = 2.346e-05 relative error = 0.0009271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.982 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.876 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7599 2.872 h = 0.001 0.003 y[1] (numeric) = 1.35360844861 2.13914913814 y[1] (closed_form) = 1.35361572433 2.13917138969 absolute error = 2.341e-05 relative error = 0.0009248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.983 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.907 Order of pole (three term test) = 1.25 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 754 Total Elapsed Time = 1 Minutes 23 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 1 Minutes 23 Seconds > quit memory used=6975.0MB, alloc=52.3MB, time=83.65