|\^/| 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(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )); > end; exact_soln_y := proc(x) return c(1.0)/((c(x) - c(6.0))*(c(x) - c(6.0))) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 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0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_6D0, #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_tmp6, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_6D0, 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_tmp6, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_6D0, #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_tmp6, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_6D0, 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_tmp6, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_6D0, #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_tmp6, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_6D0, 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_tmp6, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_6D0, #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_tmp6, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_6D0, 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_tmp6, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_6D0, #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_tmp6, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > ind_var := array_x[1]; > omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > abserr := float_abs(numeric_val - closed_form_val_y); > if (float_abs(closed_form_val_y) > 0.0) then # if number 3 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 4 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > fi;# end if 4; > else > ; > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 3; > if (glob_good_digits < glob_min_good_digits) then # if number 3 > glob_min_good_digits := glob_good_digits; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,4," "); > omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > #BOTTOM DISPLAY ALOT > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_6D0, 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_tmp6, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ind_var := array_x[1]; omniout_complex(ALWAYS, "x[1] ", 33, ind_var, 20, " "); term_no := 1; numeric_val := array_y[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_complex(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); abserr := float_abs(numeric_val - closed_form_val_y); if 0. < float_abs(closed_form_val_y) then relerr := abserr/float_abs(closed_form_val_y); if 0. < float_abs(c(relerr)) then glob_good_digits := round(-log10(relerr)) else relerr := 0.; glob_good_digits := Digits - 2 end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 4, " "); omniout_float(ALWAYS, "relative error ", 4, relerr*glob__100, 4, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " ") end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_6D0, #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_tmp6, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_6D0, 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_tmp6, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_6D0, #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_tmp6, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > ; > if (true) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_6D0, 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_tmp6, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; display_poles() end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_6D0, #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_tmp6, > array_tmp7, > array_tmp8, > 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 neg ID_CONST $eq_no = 1 > array_tmp1[1] := neg(array_const_2D0[1]); > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_x[1] - array_const_6D0[1]; > #emit pre div CONST - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp1[1] / array_tmp2[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp4[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp3[1] / array_tmp4[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 1 > array_tmp6[1] := array_x[1] - array_const_6D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp5[1] / array_tmp6[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp8[1] := array_const_0D0[1] + array_tmp7[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_tmp8[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 sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_x[2]; > #emit pre div CONST - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := neg(array_tmp3[1])* array_tmp2[2] / array_tmp2[1]; > #emit pre div CONST - LINEAR $eq_no = 1 i = 3 > #emit pre div CONST - LINEAR $eq_no = 1 i = 4 > #emit pre div CONST - LINEAR $eq_no = 1 i = 5 > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp4[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp3[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1]; > #emit pre sub LINEAR - CONST $eq_no = 1 i = 2 > array_tmp6[2] := array_x[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp7[2] := (array_tmp5[2] - array_tmp7[1] * array_tmp6[2]) / array_tmp6[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp8[2] := array_tmp7[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_tmp8[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 > array_tmp3[3] := neg(array_tmp3[2])* array_tmp2[2] / array_tmp2[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp3[3] - array_tmp5[2] * array_tmp4[2]) / array_tmp4[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp7[3] := (array_tmp5[3] - array_tmp7[2] * array_tmp6[2]) / array_tmp6[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp8[3] := array_tmp7[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_tmp8[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 > array_tmp3[4] := neg(array_tmp3[3])* array_tmp2[2] / array_tmp2[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp3[4] - array_tmp5[3] * array_tmp4[2]) / array_tmp4[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp7[4] := (array_tmp5[4] - array_tmp7[3] * array_tmp6[2]) / array_tmp6[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp8[4] := array_tmp7[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_tmp8[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 > array_tmp3[5] := neg(array_tmp3[4])* array_tmp2[2] / array_tmp2[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp3[5] - array_tmp5[4] * array_tmp4[2]) / array_tmp4[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp7[5] := (array_tmp5[5] - array_tmp7[4] * array_tmp6[2]) / array_tmp6[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp8[5] := array_tmp7[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_tmp8[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 div CONST LINEAR (NOP) $eq_no = 1 i = 1 > array_tmp3[kkk] := array_tmp1[1] * array_tmp2[kkk]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp7[kkk] := neg(ats(kkk,array_tmp6,array_tmp7,2)) / array_tmp6[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp8[kkk] := array_tmp7[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_tmp8[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_6D0, 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_tmp6, array_tmp7, array_tmp8, 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] := neg(array_const_2D0[1]); array_tmp2[1] := array_x[1] - array_const_6D0[1]; array_tmp3[1] := array_tmp1[1]/array_tmp2[1]; array_tmp4[1] := array_x[1] - array_const_6D0[1]; array_tmp5[1] := array_tmp3[1]/array_tmp4[1]; array_tmp6[1] := array_x[1] - array_const_6D0[1]; array_tmp7[1] := array_tmp5[1]/array_tmp6[1]; array_tmp8[1] := array_const_0D0[1] + array_tmp7[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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_tmp2[2] := array_x[2]; array_tmp3[2] := neg(array_tmp3[1])*array_tmp2[2]/array_tmp2[1]; array_tmp4[2] := array_x[2]; array_tmp5[2] := (-array_tmp4[2]*array_tmp5[1] + array_tmp3[2])/array_tmp4[1]; array_tmp6[2] := array_x[2]; array_tmp7[2] := (-array_tmp6[2]*array_tmp7[1] + array_tmp5[2])/array_tmp6[1]; array_tmp8[2] := array_tmp7[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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] := neg(array_tmp3[2])*array_tmp2[2]/array_tmp2[1]; array_tmp5[3] := (-array_tmp4[2]*array_tmp5[2] + array_tmp3[3])/array_tmp4[1]; array_tmp7[3] := (-array_tmp6[2]*array_tmp7[2] + array_tmp5[3])/array_tmp6[1]; array_tmp8[3] := array_tmp7[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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] := neg(array_tmp3[3])*array_tmp2[2]/array_tmp2[1]; array_tmp5[4] := (-array_tmp4[2]*array_tmp5[3] + array_tmp3[4])/array_tmp4[1]; array_tmp7[4] := (-array_tmp6[2]*array_tmp7[3] + array_tmp5[4])/array_tmp6[1]; array_tmp8[4] := array_tmp7[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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] := neg(array_tmp3[4])*array_tmp2[2]/array_tmp2[1]; array_tmp5[5] := (-array_tmp4[2]*array_tmp5[4] + array_tmp3[5])/array_tmp4[1]; array_tmp7[5] := (-array_tmp6[2]*array_tmp7[4] + array_tmp5[5])/array_tmp6[1]; array_tmp8[5] := array_tmp7[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp8[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] := array_tmp1[1]*array_tmp2[kkk]; array_tmp5[kkk] := neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp7[kkk] := neg(ats(kkk, array_tmp6, array_tmp7, 2))/array_tmp6[1]; array_tmp8[kkk] := array_tmp7[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_tmp8[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_6D0, > #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_tmp6, > array_tmp7, > array_tmp8, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 20; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=30; > max_terms:=20; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(20),[]); > array_norms:= Array(0..(20),[]); > array_fact_1:= Array(0..(20),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(20),[]); > array_x:= Array(0..(20),[]); > array_tmp0:= Array(0..(20),[]); > array_tmp1:= Array(0..(20),[]); > array_tmp2:= Array(0..(20),[]); > array_tmp3:= Array(0..(20),[]); > array_tmp4:= Array(0..(20),[]); > array_tmp5:= Array(0..(20),[]); > array_tmp6:= Array(0..(20),[]); > array_tmp7:= Array(0..(20),[]); > array_tmp8:= Array(0..(20),[]); > array_m1:= Array(0..(20),[]); > array_y_higher := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..20+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(20) ,(0..20+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 20) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp6[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp7[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp8[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=20) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_tmp6); > zero_ats_ar(array_tmp7); > zero_ats_ar(array_tmp8); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_2D0); > array_const_2D0[1] := c(2.0); > zero_ats_ar(array_const_6D0); > array_const_6D0[1] := c(6.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 20; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sing6postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=30;"); > omniout_str(ALWAYS,"max_terms:=20;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 2.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(6.0);"); > 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(3.0);"); > 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,"return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) ));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 2.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(6.0); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(3.0); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=10000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1 > #left paren 0001C > if (true) then # if number 10 > omniout_str(INFO," "); > fi;# end if 10; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > atomall(); > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10 > display_alot(current_iter); > fi;# end if 10; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (true) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2017-11-26T16:24:49-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing6") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ") > ; > logitem_complex(html_log_file,x_start) > ; > logitem_complex(html_log_file,x_end) > ; > logitem_complex(html_log_file,array_x[1]) > ; > logitem_complex(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > glob_desired_digits_correct := 0.0; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > glob_least_ratio_sing := 0; > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > glob_least_6_sing := 0.0; > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 309 ") > ; > logitem_str(html_log_file,"sing6 diffeq.mxt") > ; > logitem_str(html_log_file,"sing6 maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_6D0, 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_tmp6, array_tmp7, array_tmp8, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 20; Digits := 30; max_terms := 20; glob_html_log := true; array_y_init := Array(0 .. 20, []); array_norms := Array(0 .. 20, []); array_fact_1 := Array(0 .. 20, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 20, []); array_x := Array(0 .. 20, []); array_tmp0 := Array(0 .. 20, []); array_tmp1 := Array(0 .. 20, []); array_tmp2 := Array(0 .. 20, []); array_tmp3 := Array(0 .. 20, []); array_tmp4 := Array(0 .. 20, []); array_tmp5 := Array(0 .. 20, []); array_tmp6 := Array(0 .. 20, []); array_tmp7 := Array(0 .. 20, []); array_tmp8 := Array(0 .. 20, []); array_m1 := Array(0 .. 20, []); array_y_higher := Array(0 .. 2, 0 .. 21, []); array_y_higher_work := Array(0 .. 2, 0 .. 21, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []); array_y_set_initial := Array(0 .. 2, 0 .. 21, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 20, 0 .. 21, []); term := 1; while term <= 20 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 20 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 20 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp6[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp7[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp8[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 20 do term := 1; while term <= 20 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_tmp6); zero_ats_ar(array_tmp7); zero_ats_ar(array_tmp8); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_2D0); array_const_2D0[1] := c(2.0); zero_ats_ar(array_const_6D0); array_const_6D0[1] := c(6.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 20; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sing6postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 2.0 ) / \ ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; \ "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=30;"); omniout_str(ALWAYS, "max_terms:=20;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 2.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(6.0);"); 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(3.0);"); 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, "return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) ));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); 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 + 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0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.000 + 0.000 * I ];"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;"); omniout_str(ALWAYS, "it := x_delta[glob_nxt];"); omniout_str(ALWAYS, "return it;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 2.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(6.0); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(3.0); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 10000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius ; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and (glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do omniout_str(INFO, " "); found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); atomall(); if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = neg ( 2.0 ) /\ ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 \ ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2017-11-26T16:24:49-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing6"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\ g ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) \ / ( x - 6.0 ) ; "); logitem_complex(html_log_file, x_start); logitem_complex(html_log_file, x_end); logitem_complex(html_log_file, array_x[1]); logitem_complex(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); glob_desired_digits_correct := 0.; logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then glob_least_ratio_sing := 0; logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then glob_least_6_sing := 0.; logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 309 "); logitem_str(html_log_file, "sing6 diffeq.mxt"); logitem_str(html_log_file, "sing6 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/sing6postcpx.cpx################# diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=30; max_terms:=20; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 2.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(6.0); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(3.0); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=10000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) )); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 2.1 0.1 h = 0.0001 0.005 y[1] (numeric) = 0.0656166845961 0.0033671719727 y[1] (closed_form) = 0.0656166845961 0.0033671719727 absolute error = 0 relative error = 0 % Correct digits = 28 Radius of convergence (given) for eq 1 = 3.901 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.876 Order of pole (three term test) = 1.358e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = 0.0656068449068 0.00353533163166 y[1] (closed_form) = 0.0656067803786 0.00353532609315 absolute error = 6.477e-08 relative error = 9.857e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.901 Order of pole (given) = 3 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) = 1.785e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1002 0.108 h = 0.001 0.001 y[1] (numeric) = 0.0656018572616 0.00363630907876 y[1] (closed_form) = 0.0656018702466 0.00363630952707 absolute error = 1.299e-08 relative error = 1.978e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 3.901 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.838 Order of pole (three term test) = 1.664e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1012 0.109 h = 0.001 0.003 y[1] (numeric) = 0.0656325873365 0.00367270555364 y[1] (closed_form) = 0.0656326392491 0.00367269604465 absolute error = 5.278e-08 relative error = 8.029e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.721 Order of pole (three term test) = 9.436e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = 0.0656576757237 0.00377634486587 y[1] (closed_form) = 0.0656576473737 0.00377635234382 absolute error = 2.932e-08 relative error = 4.458e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.899 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.934 Order of pole (three term test) = 5.814e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1023 0.116 h = 0.003 0.006 y[1] (numeric) = 0.065649263148 0.0039110974409 y[1] (closed_form) = 0.0656491873934 0.00391105358949 absolute error = 8.753e-08 relative error = 0.0001331 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.899 Order of pole (given) = 3 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) = 7.294e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = 0.0657316877679 0.00412182279105 y[1] (closed_form) = 0.0657315323504 0.00412207534135 absolute error = 2.965e-07 relative error = 0.0004503 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.897 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.905 Order of pole (three term test) = 1.494e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = 0.0657187887821 0.00429056740708 y[1] (closed_form) = 0.0657187186765 0.00429063926746 absolute error = 1.004e-07 relative error = 0.0001524 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.897 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.339 Order of pole (three term test) = 3.378e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1055 0.13 h = 0.001 0.001 y[1] (numeric) = 0.0657120570041 0.00439180511158 y[1] (closed_form) = 0.0657120646238 0.00439188475542 absolute error = 8.001e-08 relative error = 0.0001215 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.897 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.836 Order of pole (three term test) = 9.552e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=32.5MB, alloc=40.3MB, time=0.42 x[1] = 2.1065 0.131 h = 0.001 0.003 y[1] (numeric) = 0.0657422693997 0.00442885147022 y[1] (closed_form) = 0.0657423163491 0.00442892200097 absolute error = 8.473e-08 relative error = 0.0001286 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.896 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.711 Order of pole (three term test) = 4.938e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = 0.0657656699995 0.00453327395712 y[1] (closed_form) = 0.0657656359382 0.00453335971752 absolute error = 9.228e-08 relative error = 0.00014 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.895 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.928 Order of pole (three term test) = 1.255e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1076 0.138 h = 0.003 0.006 y[1] (numeric) = 0.0657549220173 0.00466834032541 y[1] (closed_form) = 0.0657548415129 0.00466837344414 absolute error = 8.705e-08 relative error = 0.0001321 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.895 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.53 Order of pole (three term test) = 7.042e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = 0.0658340172749 0.00488118849125 y[1] (closed_form) = 0.0658338499785 0.00488151750464 absolute error = 3.691e-07 relative error = 0.0005591 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.892 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.902 Order of pole (three term test) = 1.839e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = 0.0658181819608 0.00505027710195 y[1] (closed_form) = 0.0658181044865 0.00505042658291 absolute error = 1.684e-07 relative error = 0.0002551 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.892 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.336 Order of pole (three term test) = 8.156e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1108 0.152 h = 0.001 0.001 y[1] (numeric) = 0.0658096923615 0.00515173635473 y[1] (closed_form) = 0.0658096927744 0.0051518954317 absolute error = 1.591e-07 relative error = 0.000241 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.892 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.834 Order of pole (three term test) = 4.613e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1118 0.153 h = 0.001 0.003 y[1] (numeric) = 0.0658393699312 0.00518942364016 y[1] (closed_form) = 0.065839410054 0.00518957446434 absolute error = 1.561e-07 relative error = 0.0002363 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.891 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.701 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = 0.0658610573625 0.00529459417432 y[1] (closed_form) = 0.0658610157727 0.00529475843987 absolute error = 1.694e-07 relative error = 0.0002565 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.922 Order of pole (three term test) = 1.626e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1129 0.16 h = 0.003 0.006 y[1] (numeric) = 0.0658479565094 0.00542992229213 y[1] (closed_form) = 0.0658478694807 0.00543003262412 absolute error = 1.405e-07 relative error = 0.0002127 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.522 Order of pole (three term test) = 1.388e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = 0.0659236592645 0.00564482639619 y[1] (closed_form) = 0.065923478291 0.00564523190892 absolute error = 4.441e-07 relative error = 0.0006711 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.888 Order of pole (given) = 3 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) = 1.559e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.116 0.171 h = 0.0001 0.003 y[1] (numeric) = 0.065904866999 0.0058141932216 y[1] (closed_form) = 0.0659047803484 0.00581442049483 absolute error = 2.432e-07 relative error = 0.0003676 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.888 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.333 Order of pole (three term test) = 5.685e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1161 0.174 h = 0.001 0.001 y[1] (numeric) = 0.0658946069245 0.00591583471297 y[1] (closed_form) = 0.0658945982718 0.00591607340902 absolute error = 2.389e-07 relative error = 0.000361 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.888 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.832 Order of pole (three term test) = 1.601e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1171 0.175 h = 0.001 0.003 y[1] (numeric) = 0.065923732686 0.00595415342906 y[1] (closed_form) = 0.0659237641009 0.0059543847481 absolute error = 2.334e-07 relative error = 0.0003527 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.887 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.691 Order of pole (three term test) = 6.188e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = 0.0659436824375 0.00606003596714 y[1] (closed_form) = 0.0659436314855 0.00606027890967 absolute error = 2.482e-07 relative error = 0.0003748 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.886 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.917 Order of pole (three term test) = 5.646e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1182 0.182 h = 0.003 0.006 y[1] (numeric) = 0.0659282126471 0.00619557301193 y[1] (closed_form) = 0.0659281173027 0.00619576075101 absolute error = 2.106e-07 relative error = 0.000318 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.886 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.515 Order of pole (three term test) = 5.923e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = 0.0660004613407 0.00641246401183 y[1] (closed_form) = 0.0660002648818 0.00641294600871 absolute error = 5.205e-07 relative error = 0.0007849 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.883 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.895 Order of pole (three term test) = 4.769e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = 0.0659786932798 0.00658204233369 y[1] (closed_form) = 0.0659785956309 0.00658234752003 absolute error = 3.204e-07 relative error = 0.0004833 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.883 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.331 Order of pole (three term test) = 1.526e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1214 0.196 h = 0.001 0.001 y[1] (numeric) = 0.0659666511379 0.00668382618526 y[1] (closed_form) = 0.0659666315459 0.00668414463381 absolute error = 3.191e-07 relative error = 0.0004812 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.884 Order of pole (given) = 3 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) = 2.878e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=78.5MB, alloc=44.3MB, time=1.01 x[1] = 2.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = 0.0659952082929 0.00672276629904 y[1] (closed_form) = 0.0659952291027 0.00672307826111 absolute error = 3.127e-07 relative error = 0.0004713 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.883 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.99 Order of pole (three term test) = 4.987e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1225 0.201 h = 0.003 0.006 y[1] (numeric) = 0.0659777900236 0.00685843073627 y[1] (closed_form) = 0.065977663376 0.00685866756483 absolute error = 2.686e-07 relative error = 0.0004049 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.883 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.509 Order of pole (three term test) = 4.489e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = 0.066046995042 0.00707693296849 y[1] (closed_form) = 0.0660467611146 0.00707746300608 absolute error = 5.794e-07 relative error = 0.0008722 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.893 Order of pole (three term test) = 5.006e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = 0.0660226503948 0.00724660351893 y[1] (closed_form) = 0.0660225191059 0.00724695813828 absolute error = 3.781e-07 relative error = 0.0005693 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.329 Order of pole (three term test) = 8.924e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1257 0.215 h = 0.001 0.001 y[1] (numeric) = 0.0660090648165 0.00734845617057 y[1] (closed_form) = 0.066009011571 0.00734882564404 absolute error = 3.733e-07 relative error = 0.000562 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.828 Order of pole (three term test) = 1.465e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1267 0.216 h = 0.001 0.003 y[1] (numeric) = 0.0660371120079 0.00738791567928 y[1] (closed_form) = 0.0660370994218 0.00738827944769 absolute error = 3.640e-07 relative error = 0.0005478 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.879 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.674 Order of pole (three term test) = 1.569e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = 0.0660537588108 0.00749500277926 y[1] (closed_form) = 0.0660536627939 0.00749537470843 absolute error = 3.841e-07 relative error = 0.0005778 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.878 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.907 Order of pole (three term test) = 5.769e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1278 0.223 h = 0.003 0.006 y[1] (numeric) = 0.0660338421849 0.00763075691054 y[1] (closed_form) = 0.0660337038483 0.00763107135097 absolute error = 3.435e-07 relative error = 0.0005168 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.879 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.503 Order of pole (three term test) = 1.019e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = 0.0660994839731 0.00785111126333 y[1] (closed_form) = 0.0660992311771 0.00785171759621 absolute error = 6.569e-07 relative error = 0.0009869 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.876 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.89 Order of pole (three term test) = 1.351e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = 0.066072134167 0.00802086668569 y[1] (closed_form) = 0.0660719884566 0.0080212992828 absolute error = 4.565e-07 relative error = 0.0006858 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.876 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.327 Order of pole (three term test) = 2.143e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.131 0.237 h = 0.001 0.001 y[1] (numeric) = 0.0660567483549 0.00812278598701 y[1] (closed_form) = 0.0660566806481 0.00812323529582 absolute error = 4.544e-07 relative error = 0.0006827 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.876 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.826 Order of pole (three term test) = 4.080e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.132 0.238 h = 0.001 0.003 y[1] (numeric) = 0.0660841963732 0.00816284661265 y[1] (closed_form) = 0.0660841696149 0.00816329113221 absolute error = 4.453e-07 relative error = 0.0006688 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.875 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.665 Order of pole (three term test) = 5.660e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.133 0.241 h = 0.0001 0.004 y[1] (numeric) = 0.0660990409704 0.00827053751655 y[1] (closed_form) = 0.0660989302704 0.00827098830323 absolute error = 4.642e-07 relative error = 0.0006968 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.875 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.902 Order of pole (three term test) = 4.797e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1331 0.245 h = 0.003 0.006 y[1] (numeric) = 0.0660767181336 0.00840634542356 y[1] (closed_form) = 0.0660765662783 0.00840673752383 absolute error = 4.205e-07 relative error = 0.0006313 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.875 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.496 Order of pole (three term test) = 6.025e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = 0.0661387401423 0.00862847692288 y[1] (closed_form) = 0.0661384666518 0.00862915938553 absolute error = 7.352e-07 relative error = 0.001102 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.872 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.887 Order of pole (three term test) = 4.456e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = 0.0661083716645 0.00879824815221 y[1] (closed_form) = 0.066108209679 0.00879875869797 absolute error = 5.356e-07 relative error = 0.0008031 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.872 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.324 Order of pole (three term test) = 2.080e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1363 0.259 h = 0.001 0.001 y[1] (numeric) = 0.0660911772093 0.00890019279902 y[1] (closed_form) = 0.0660910931338 0.00890072192163 absolute error = 5.358e-07 relative error = 0.0008034 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.872 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.824 Order of pole (three term test) = 1.320e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1373 0.26 h = 0.001 0.003 y[1] (numeric) = 0.0661180098972 0.00894084299561 y[1] (closed_form) = 0.066117967034 0.0089413682574 absolute error = 5.270e-07 relative error = 0.0007899 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.871 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.657 Order of pole (three term test) = 1.840e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=124.3MB, alloc=44.3MB, time=1.58 x[1] = 2.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = 0.0661310314853 0.0090490983782 y[1] (closed_form) = 0.066130904222 0.00904962798988 absolute error = 5.447e-07 relative error = 0.000816 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.871 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.898 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1384 0.267 h = 0.003 0.006 y[1] (numeric) = 0.0661062920955 0.0091849046719 y[1] (closed_form) = 0.0661061248813 0.0091853744276 absolute error = 4.986e-07 relative error = 0.0007471 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.871 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.49 Order of pole (three term test) = 5.849e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = 0.0661646396752 0.00940873635869 y[1] (closed_form) = 0.0661643436611 0.00940949473217 absolute error = 8.141e-07 relative error = 0.001218 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.868 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.884 Order of pole (three term test) = 1.273e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = 0.0661312409474 0.00957845361859 y[1] (closed_form) = 0.0661310608252 0.00957904203026 absolute error = 6.154e-07 relative error = 0.0009209 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.869 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.322 Order of pole (three term test) = 2.581e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1416 0.281 h = 0.001 0.001 y[1] (numeric) = 0.0661122305951 0.00968038187326 y[1] (closed_form) = 0.0661121282349 0.00968099073266 absolute error = 6.174e-07 relative error = 0.000924 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.869 Order of pole (given) = 3 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) = 3.846e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1426 0.282 h = 0.001 0.003 y[1] (numeric) = 0.0661384320547 0.00972160957462 y[1] (closed_form) = 0.066138371145 0.00972221551345 absolute error = 6.090e-07 relative error = 0.000911 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.868 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.648 Order of pole (three term test) = 1.788e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = 0.0661496108724 0.00983038932832 y[1] (closed_form) = 0.0661494651576 0.00983099767788 absolute error = 6.256e-07 relative error = 0.0009354 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.867 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.893 Order of pole (three term test) = 1.430e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1437 0.289 h = 0.003 0.006 y[1] (numeric) = 0.0661224461428 0.00996613806758 y[1] (closed_form) = 0.0661222617208 0.00996668542126 absolute error = 5.776e-07 relative error = 0.0008638 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.867 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.483 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = 0.0661770666232 0.010191591053 y[1] (closed_form) = 0.0661767462554 0.0101924250645 absolute error = 8.934e-07 relative error = 0.001334 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.865 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.881 Order of pole (three term test) = 1.304e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = 0.0661406280367 0.010361183919 y[1] (closed_form) = 0.0661404279103 0.0103618500596 absolute error = 6.956e-07 relative error = 0.001039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.865 Order of pole (given) = 3 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) = 6.604e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1469 0.303 h = 0.001 0.001 y[1] (numeric) = 0.0661197957099 0.0104630536483 y[1] (closed_form) = 0.0661196731427 0.0104637421114 absolute error = 6.993e-07 relative error = 0.001045 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.865 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.821 Order of pole (three term test) = 3.739e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = 0.0661453503224 0.0105048462743 y[1] (closed_form) = 0.0661452694177 0.0105055327681 absolute error = 6.912e-07 relative error = 0.001032 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.864 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.93 Order of pole (three term test) = 1.080e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.148 0.308 h = 0.003 0.006 y[1] (numeric) = 0.0661161969199 0.0106405022507 y[1] (closed_form) = 0.0661159752168 0.0106410958463 absolute error = 6.336e-07 relative error = 0.0009462 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.864 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.479 Order of pole (three term test) = 1.112e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.151 0.314 h = 0.0001 0.005 y[1] (numeric) = 0.0661675506294 0.0108672409811 y[1] (closed_form) = 0.0661671868773 0.0108681192902 absolute error = 9.507e-07 relative error = 0.001418 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.862 Order of pole (given) = 3 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = 0.0661284919016 0.0110366336034 y[1] (closed_form) = 0.066128252074 0.0110373460006 absolute error = 7.517e-07 relative error = 0.001121 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.862 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.318 Order of pole (three term test) = 1.293e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1512 0.322 h = 0.001 0.001 y[1] (numeric) = 0.0661060887132 0.0111383971639 y[1] (closed_form) = 0.0661059262035 0.0111391334957 absolute error = 7.541e-07 relative error = 0.001125 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.862 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.82 Order of pole (three term test) = 1.364e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1522 0.323 h = 0.001 0.003 y[1] (numeric) = 0.0661310677455 0.0111806576444 y[1] (closed_form) = 0.0661309470479 0.0111813928359 absolute error = 7.450e-07 relative error = 0.001111 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.861 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.634 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = 0.0661387636217 0.0112902813815 y[1] (closed_form) = 0.0661385575347 0.0112910153199 absolute error = 7.623e-07 relative error = 0.001136 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.861 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.885 Order of pole (three term test) = 4.306e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=170.2MB, alloc=44.3MB, time=2.16 x[1] = 2.1533 0.33 h = 0.003 0.006 y[1] (numeric) = 0.0661070702355 0.0114257433961 y[1] (closed_form) = 0.0661068278696 0.0114264143174 absolute error = 7.134e-07 relative error = 0.001063 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.861 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.473 Order of pole (three term test) = 5.412e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = 0.0661546053611 0.0116539511304 y[1] (closed_form) = 0.066154213858 0.0116549044042 absolute error = 1.031e-06 relative error = 0.001534 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.858 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.876 Order of pole (three term test) = 8.786e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = 0.0661124951018 0.0118230867579 y[1] (closed_form) = 0.0661122317883 0.0118238764609 absolute error = 8.324e-07 relative error = 0.001239 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.859 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.316 Order of pole (three term test) = 2.518e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1565 0.344 h = 0.001 0.001 y[1] (numeric) = 0.06608826234 0.0119247124356 y[1] (closed_form) = 0.0660880760384 0.0119255279494 absolute error = 8.365e-07 relative error = 0.001246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.859 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.818 Order of pole (three term test) = 1.188e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1575 0.345 h = 0.001 0.003 y[1] (numeric) = 0.066112566435 0.0119675129119 y[1] (closed_form) = 0.0661124221073 0.0119683282545 absolute error = 8.280e-07 relative error = 0.001232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.858 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.627 Order of pole (three term test) = 1.154e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = 0.0661183695561 0.0120775420634 y[1] (closed_form) = 0.0661181395925 0.0120783541615 absolute error = 8.440e-07 relative error = 0.001256 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.857 Order of pole (given) = 3 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) = 5.933e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1586 0.352 h = 0.003 0.006 y[1] (numeric) = 0.0660842352038 0.0122127838641 y[1] (closed_form) = 0.066083970312 0.0122135318988 absolute error = 7.936e-07 relative error = 0.001181 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.857 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.467 Order of pole (three term test) = 5.274e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = 0.0661279051786 0.0124423765556 y[1] (closed_form) = 0.066127484102 0.012443404366 absolute error = 1.111e-06 relative error = 0.001651 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.855 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.874 Order of pole (three term test) = 8.563e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = 0.066082739591 0.0126111833007 y[1] (closed_form) = 0.0660824509179 0.012612050015 absolute error = 9.135e-07 relative error = 0.001358 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.855 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.314 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1618 0.366 h = 0.001 0.001 y[1] (numeric) = 0.066056674652 0.0127126280638 y[1] (closed_form) = 0.0660564626288 0.0127135224634 absolute error = 9.192e-07 relative error = 0.001366 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.856 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.817 Order of pole (three term test) = 1.159e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1628 0.367 h = 0.001 0.003 y[1] (numeric) = 0.0660802891013 0.0127559545315 y[1] (closed_form) = 0.066080119186 0.0127568497375 absolute error = 9.112e-07 relative error = 0.001354 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.855 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.619 Order of pole (three term test) = 1.798e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = 0.0660841840327 0.0128663462977 y[1] (closed_form) = 0.0660839282923 0.012867236253 absolute error = 9.260e-07 relative error = 0.001375 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.854 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.876 Order of pole (three term test) = 1.309e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1639 0.374 h = 0.003 0.006 y[1] (numeric) = 0.066047606176 0.0130013103245 y[1] (closed_form) = 0.0660473168938 0.0130021352053 absolute error = 8.741e-07 relative error = 0.001299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.854 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.462 Order of pole (three term test) = 9.706e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = 0.0660873666994 0.0132322022428 y[1] (closed_form) = 0.0660869142331 0.0132333041074 absolute error = 1.191e-06 relative error = 0.001767 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.852 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.872 Order of pole (three term test) = 8.354e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.167 0.385 h = 0.0001 0.003 y[1] (numeric) = 0.0660391440683 0.0134006078314 y[1] (closed_form) = 0.0660388281628 0.0134015512066 absolute error = 9.949e-07 relative error = 0.001476 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.852 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.312 Order of pole (three term test) = 2.678e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1671 0.388 h = 0.001 0.001 y[1] (numeric) = 0.0660112455925 0.0135018284084 y[1] (closed_form) = 0.0660110059191 0.0135028013401 absolute error = 1.002e-06 relative error = 0.001487 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.852 Order of pole (given) = 3 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1681 0.389 h = 0.001 0.003 y[1] (numeric) = 0.0660341560398 0.0135456663815 y[1] (closed_form) = 0.0660339585805 0.0135466411046 absolute error = 9.945e-07 relative error = 0.001475 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.852 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.612 Order of pole (three term test) = 1.569e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = 0.0660361285366 0.0136563773503 y[1] (closed_form) = 0.0660358451205 0.0136573448034 absolute error = 1.008e-06 relative error = 0.001495 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.851 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.873 Order of pole (three term test) = 1.199e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=216.2MB, alloc=44.3MB, time=2.74 x[1] = 2.1692 0.396 h = 0.003 0.006 y[1] (numeric) = 0.0659971063066 0.0137910057525 y[1] (closed_form) = 0.0659967907698 0.013791907157 absolute error = 9.550e-07 relative error = 0.001416 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.851 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.457 Order of pole (three term test) = 7.246e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = 0.0660329154131 0.0140231095563 y[1] (closed_form) = 0.0660324297491 0.0140242849381 absolute error = 1.272e-06 relative error = 0.001884 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.869 Order of pole (three term test) = 3.284e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = 0.0659816361274 0.0141910413985 y[1] (closed_form) = 0.0659812911201 0.0141920610285 absolute error = 1.076e-06 relative error = 0.001595 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.31 Order of pole (three term test) = 1.498e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1724 0.41 h = 0.001 0.001 y[1] (numeric) = 0.0659519040133 0.0142919943208 y[1] (closed_form) = 0.0659516347641 0.0142930453728 absolute error = 1.085e-06 relative error = 0.001608 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.814 Order of pole (three term test) = 1.105e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = 0.0659740964735 0.0143363288416 y[1] (closed_form) = 0.065973869516 0.0143373826766 absolute error = 1.078e-06 relative error = 0.001597 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.89 Order of pole (three term test) = 3.831e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1735 0.415 h = 0.003 0.006 y[1] (numeric) = 0.0659330763948 0.014470635829 y[1] (closed_form) = 0.0659327179228 0.0144715797405 absolute error = 1.010e-06 relative error = 0.001496 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.453 Order of pole (three term test) = 9.310e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = 0.0659654394891 0.0147036639628 y[1] (closed_form) = 0.0659649050034 0.0147048790114 absolute error = 1.327e-06 relative error = 0.001964 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.847 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.868 Order of pole (three term test) = 1.202e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = 0.0659115378939 0.0148710933397 y[1] (closed_form) = 0.0659111475033 0.0148721551441 absolute error = 1.131e-06 relative error = 0.001674 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.847 Order of pole (given) = 3 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) = 1.201e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1767 0.429 h = 0.001 0.001 y[1] (numeric) = 0.0658802322292 0.0149717591266 y[1] (closed_form) = 0.0658799171216 0.0149728539461 absolute error = 1.139e-06 relative error = 0.001686 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.847 Order of pole (given) = 3 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) = 1.086e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1777 0.43 h = 0.001 0.003 y[1] (numeric) = 0.0659017901036 0.0150164999575 y[1] (closed_form) = 0.0659015173197 0.0150175984187 absolute error = 1.132e-06 relative error = 0.001675 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.846 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.601 Order of pole (three term test) = 1.623e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = 0.0659001491126 0.0151276641679 y[1] (closed_form) = 0.065899790308 0.0151287515743 absolute error = 1.145e-06 relative error = 0.001694 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.846 Order of pole (given) = 3 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) = 3.837e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1788 0.437 h = 0.003 0.006 y[1] (numeric) = 0.0658565875843 0.0152614842614 y[1] (closed_form) = 0.0658561994018 0.0152625039266 absolute error = 1.091e-06 relative error = 0.001614 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.846 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.448 Order of pole (three term test) = 1.079e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = 0.0658849286969 0.0154955572974 y[1] (closed_form) = 0.065884357685 0.0154968446981 absolute error = 1.408e-06 relative error = 0.002081 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.844 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.866 Order of pole (three term test) = 7.155e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = 0.0658279777068 0.0156623773293 y[1] (closed_form) = 0.0658275547577 0.0156635144615 absolute error = 1.213e-06 relative error = 0.001793 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.844 Order of pole (given) = 3 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) = 2.262e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.182 0.451 h = 0.001 0.001 y[1] (numeric) = 0.0657948421254 0.0157626942357 y[1] (closed_form) = 0.065794493881 0.0157638662321 absolute error = 1.223e-06 relative error = 0.001807 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.845 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.811 Order of pole (three term test) = 1.240e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.183 0.452 h = 0.001 0.003 y[1] (numeric) = 0.0658156572289 0.0158079024096 y[1] (closed_form) = 0.065815351332 0.0158090790488 absolute error = 1.216e-06 relative error = 0.001796 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.844 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.595 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.184 0.455 h = 0.0001 0.004 y[1] (numeric) = 0.0658120603905 0.0159192584841 y[1] (closed_form) = 0.0658116685105 0.015920422024 absolute error = 1.228e-06 relative error = 0.001813 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.843 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.863 Order of pole (three term test) = 8.398e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1841 0.459 h = 0.003 0.006 y[1] (numeric) = 0.0657660620632 0.0160525764264 y[1] (closed_form) = 0.0657656423183 0.0160536713637 absolute error = 1.173e-06 relative error = 0.001732 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.843 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.444 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=262.2MB, alloc=44.3MB, time=3.32 x[1] = 2.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = 0.0657903462826 0.0162876028679 y[1] (closed_form) = 0.065789736971 0.0162889619286 absolute error = 1.489e-06 relative error = 0.002198 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.841 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.864 Order of pole (three term test) = 1.718e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = 0.0657303524068 0.0164537404923 y[1] (closed_form) = 0.0657298950506 0.0164549523859 absolute error = 1.295e-06 relative error = 0.001912 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.842 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.306 Order of pole (three term test) = 1.102e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1873 0.473 h = 0.001 0.001 y[1] (numeric) = 0.0656953904682 0.0165536647425 y[1] (closed_form) = 0.0656950071823 0.0165549133382 absolute error = 1.306e-06 relative error = 0.001928 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.842 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.81 Order of pole (three term test) = 2.083e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1883 0.474 h = 0.001 0.003 y[1] (numeric) = 0.0657154499801 0.0165993240218 y[1] (closed_form) = 0.0657151090364 0.0166005782649 absolute error = 1.300e-06 relative error = 0.001918 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.841 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.589 Order of pole (three term test) = 2.891e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = 0.0657098878831 0.0167108265771 y[1] (closed_form) = 0.065709461054 0.0167120656714 absolute error = 1.311e-06 relative error = 0.001933 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.859 Order of pole (three term test) = 1.562e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1894 0.481 h = 0.003 0.006 y[1] (numeric) = 0.0656614584756 0.0168435839625 y[1] (closed_form) = 0.0656610053244 0.0168447536346 absolute error = 1.254e-06 relative error = 0.00185 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.841 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.439 Order of pole (three term test) = 6.550e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = 0.0656816534656 0.017079471008 y[1] (closed_form) = 0.0656810040962 0.0170809009832 absolute error = 1.571e-06 relative error = 0.002314 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.839 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.862 Order of pole (three term test) = 1.065e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = 0.0656186253768 0.0172448531331 y[1] (closed_form) = 0.0656181317759 0.0172461391657 absolute error = 1.378e-06 relative error = 0.00203 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.839 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.304 Order of pole (three term test) = 1.129e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1926 0.495 h = 0.001 0.001 y[1] (numeric) = 0.0655818419356 0.0173443409253 y[1] (closed_form) = 0.0655814217148 0.0173456654845 absolute error = 1.390e-06 relative error = 0.002048 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.839 Order of pole (given) = 3 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) = 9.193e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1936 0.496 h = 0.001 0.003 y[1] (numeric) = 0.0656011334735 0.0173904346478 y[1] (closed_form) = 0.06560075556 0.017391765862 absolute error = 1.384e-06 relative error = 0.002039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.839 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.583 Order of pole (three term test) = 1.446e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = 0.0655935980106 0.0175020378897 y[1] (closed_form) = 0.0655931343699 0.0175033519025 absolute error = 1.393e-06 relative error = 0.002053 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.838 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.856 Order of pole (three term test) = 1.805e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1947 0.503 h = 0.003 0.006 y[1] (numeric) = 0.0655427449732 0.0176341763088 y[1] (closed_form) = 0.0655422565817 0.0176354201228 absolute error = 1.336e-06 relative error = 0.001969 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.838 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.435 Order of pole (three term test) = 6.427e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = 0.0655588210273 0.0178708299384 y[1] (closed_form) = 0.0655581298596 0.0178723300289 absolute error = 1.652e-06 relative error = 0.002431 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.836 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.86 Order of pole (three term test) = 1.686e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = 0.065492769571 0.0180353835186 y[1] (closed_form) = 0.0654922379005 0.0180367430122 absolute error = 1.460e-06 relative error = 0.002149 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.837 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.303 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1979 0.517 h = 0.001 0.001 y[1] (numeric) = 0.0654541707817 0.0181343910703 y[1] (closed_form) = 0.0654537117457 0.0181357908998 absolute error = 1.473e-06 relative error = 0.002169 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.837 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.808 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = 0.065472682418 0.0181809021637 y[1] (closed_form) = 0.0654722656247 0.0181823096574 absolute error = 1.468e-06 relative error = 0.00216 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.836 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.85 Order of pole (three term test) = 8.695e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.199 0.522 h = 0.003 0.006 y[1] (numeric) = 0.0654198551522 0.0183124872862 y[1] (closed_form) = 0.0654193186502 0.0183137690305 absolute error = 1.389e-06 relative error = 0.002045 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.837 Order of pole (given) = 3 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) = 4.484e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.202 0.528 h = 0.0001 0.005 y[1] (numeric) = 0.065432356435 0.018549675116 y[1] (closed_form) = 0.065431611644 0.0185512094314 absolute error = 1.706e-06 relative error = 0.002508 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.835 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.859 Order of pole (three term test) = 2.089e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = 0.0653637239633 0.0187134213142 y[1] (closed_form) = 0.0653631417663 0.0187148180503 absolute error = 1.513e-06 relative error = 0.002226 % Correct digits = 5 memory used=308.2MB, alloc=44.3MB, time=3.89 Radius of convergence (given) for eq 1 = 3.835 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.302 Order of pole (three term test) = 2.159e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2022 0.536 h = 0.001 0.001 y[1] (numeric) = 0.0653235749358 0.0188119589794 y[1] (closed_form) = 0.065323064666 0.0188133975853 absolute error = 1.526e-06 relative error = 0.002245 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.835 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.807 Order of pole (three term test) = 5.940e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2032 0.537 h = 0.001 0.003 y[1] (numeric) = 0.0653414013787 0.0188588058834 y[1] (closed_form) = 0.0653409332601 0.0188602530214 absolute error = 1.521e-06 relative error = 0.002236 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.835 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.574 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = 0.0653301770132 0.018970449703 y[1] (closed_form) = 0.0653296236482 0.0189718758228 absolute error = 1.530e-06 relative error = 0.002249 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.834 Order of pole (given) = 3 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) = 4.950e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2043 0.544 h = 0.003 0.006 y[1] (numeric) = 0.0652748489592 0.0191012525734 y[1] (closed_form) = 0.065274273846 0.0191026071871 absolute error = 1.472e-06 relative error = 0.002164 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.834 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.429 Order of pole (three term test) = 9.855e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = 0.0652831843533 0.0193390288229 y[1] (closed_form) = 0.0652823945896 0.0193406316064 absolute error = 1.787e-06 relative error = 0.002624 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.832 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.857 Order of pole (three term test) = 1.014e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = 0.0652115553577 0.019501811134 y[1] (closed_form) = 0.0652109317467 0.0195032799008 absolute error = 1.596e-06 relative error = 0.002344 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.833 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.301 Order of pole (three term test) = 2.060e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2075 0.558 h = 0.001 0.001 y[1] (numeric) = 0.0651696064243 0.0195997874087 y[1] (closed_form) = 0.0651690538928 0.01960129982 absolute error = 1.610e-06 relative error = 0.002366 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.833 Order of pole (given) = 3 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2085 0.559 h = 0.001 0.003 y[1] (numeric) = 0.0651866322496 0.0196470187462 y[1] (closed_form) = 0.065186121749 0.0196485406989 absolute error = 1.605e-06 relative error = 0.002358 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.832 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.57 Order of pole (three term test) = 4.056e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = 0.0651734192462 0.0197586303365 y[1] (closed_form) = 0.0651728238317 0.0197601292222 absolute error = 1.613e-06 relative error = 0.002368 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.832 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.849 Order of pole (three term test) = 1.033e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2096 0.566 h = 0.003 0.006 y[1] (numeric) = 0.0651156991691 0.0198886478307 y[1] (closed_form) = 0.0651150836505 0.0198900745631 absolute error = 1.554e-06 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.832 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.425 Order of pole (three term test) = 1.788e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = 0.0651198467756 0.0201269155254 y[1] (closed_form) = 0.0651190103599 0.0201285858285 absolute error = 1.868e-06 relative error = 0.002741 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.856 Order of pole (three term test) = 3.158e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = 0.0650452383311 0.0202886614894 y[1] (closed_form) = 0.0650445715298 0.0202902014513 absolute error = 1.678e-06 relative error = 0.002463 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.831 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.299 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2128 0.58 h = 0.001 0.001 y[1] (numeric) = 0.0650014993764 0.0203860329166 y[1] (closed_form) = 0.0650009027528 0.0203876182768 absolute error = 1.694e-06 relative error = 0.002487 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.831 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.805 Order of pole (three term test) = 9.588e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2138 0.581 h = 0.001 0.003 y[1] (numeric) = 0.0650177140476 0.0204336305311 y[1] (closed_form) = 0.0650171593046 0.0204352264406 absolute error = 1.690e-06 relative error = 0.002479 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.831 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.565 Order of pole (three term test) = 1.331e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = 0.065002509497 0.0205451629543 y[1] (closed_form) = 0.0650018702338 0.0205467337534 absolute error = 1.696e-06 relative error = 0.002488 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.846 Order of pole (three term test) = 3.541e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2149 0.588 h = 0.003 0.006 y[1] (numeric) = 0.0649424115608 0.0206743372456 y[1] (closed_form) = 0.0649417538602 0.0206758352913 absolute error = 1.636e-06 relative error = 0.002401 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.422 Order of pole (three term test) = 6.408e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = 0.0649423522891 0.0209129985486 y[1] (closed_form) = 0.0649414675672 0.0209147353718 absolute error = 1.949e-06 relative error = 0.002857 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.828 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.854 Order of pole (three term test) = 3.111e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.218 0.599 h = 0.0001 0.003 y[1] (numeric) = 0.0648647836453 0.0210736360507 y[1] (closed_form) = 0.0648640718982 0.0210752463181 absolute error = 1.761e-06 relative error = 0.002581 % Correct digits = 5 memory used=354.1MB, alloc=44.3MB, time=4.45 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.298 Order of pole (three term test) = 1.414e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2181 0.602 h = 0.001 0.001 y[1] (numeric) = 0.0648192658565 0.0211703593713 y[1] (closed_form) = 0.0648186233316 0.0211720167678 absolute error = 1.778e-06 relative error = 0.002607 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 3 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) = 9.451e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2191 0.603 h = 0.001 0.003 y[1] (numeric) = 0.0648346593497 0.0212183047571 y[1] (closed_form) = 0.0648340585252 0.0212199737084 absolute error = 1.774e-06 relative error = 0.0026 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.561 Order of pole (three term test) = 1.338e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = 0.0648174617209 0.0213297108894 y[1] (closed_form) = 0.064816776831 0.0213313526942 absolute error = 1.779e-06 relative error = 0.002607 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.828 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.844 Order of pole (three term test) = 6.893e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2202 0.61 h = 0.003 0.006 y[1] (numeric) = 0.0647550018251 0.0214579844475 y[1] (closed_form) = 0.0647543001856 0.0214595529467 absolute error = 1.718e-06 relative error = 0.002519 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.419 Order of pole (three term test) = 5.897e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = 0.0647507194305 0.0216969407563 y[1] (closed_form) = 0.0647497847749 0.0216987430498 absolute error = 2.030e-06 relative error = 0.002973 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.853 Order of pole (three term test) = 9.704e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = 0.0646702120046 0.0218563981053 y[1] (closed_form) = 0.0646694535789 0.0218580777348 absolute error = 1.843e-06 relative error = 0.0027 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 3 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) = 1.085e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2234 0.624 h = 0.001 0.001 y[1] (numeric) = 0.0646229278672 0.0219524303047 y[1] (closed_form) = 0.0646222376554 0.0219541587692 absolute error = 1.861e-06 relative error = 0.002727 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.828 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.803 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = 0.0646374906852 0.022000704624 y[1] (closed_form) = 0.0646368419634 0.0220024456455 absolute error = 1.858e-06 relative error = 0.002721 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.83 Order of pole (three term test) = 8.248e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2245 0.629 h = 0.003 0.006 y[1] (numeric) = 0.0645731137019 0.0221281954313 y[1] (closed_form) = 0.0645723594037 0.0221297965187 absolute error = 1.770e-06 relative error = 0.002593 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.828 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.417 Order of pole (three term test) = 1.252e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = 0.06456518347 0.0223672756867 y[1] (closed_form) = 0.0645641911668 0.0223691060607 absolute error = 2.082e-06 relative error = 0.003047 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.852 Order of pole (three term test) = 3.042e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = 0.0644821804467 0.0225256255518 y[1] (closed_form) = 0.0644813670398 0.0225273367313 absolute error = 1.895e-06 relative error = 0.002774 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 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) = 1.977e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2277 0.643 h = 0.001 0.001 y[1] (numeric) = 0.0644333958052 0.0226210078193 y[1] (closed_form) = 0.0644326496825 0.0226227692678 absolute error = 1.913e-06 relative error = 0.002801 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.803 Order of pole (three term test) = 9.245e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2287 0.644 h = 0.001 0.003 y[1] (numeric) = 0.0644472328046 0.0226695399095 y[1] (closed_form) = 0.0644465279551 0.0226713147712 absolute error = 1.910e-06 relative error = 0.002795 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.555 Order of pole (three term test) = 2.568e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = 0.064426330042 0.0227805614675 y[1] (closed_form) = 0.0644255421593 0.0227823054283 absolute error = 1.914e-06 relative error = 0.0028 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.825 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.84 Order of pole (three term test) = 7.317e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2298 0.651 h = 0.003 0.006 y[1] (numeric) = 0.0643595356523 0.0229069795175 y[1] (closed_form) = 0.0643587342164 0.0229086492965 absolute error = 1.852e-06 relative error = 0.002711 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.414 Order of pole (three term test) = 4.124e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = 0.064347360948 0.0231461694944 y[1] (closed_form) = 0.0643463157736 0.0231480632359 absolute error = 2.163e-06 relative error = 0.003163 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.824 Order of pole (given) = 3 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) = 1.503e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = 0.0642614655649 0.0233032075137 y[1] (closed_form) = 0.0642606023342 0.0233049861399 absolute error = 1.977e-06 relative error = 0.002892 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.825 Order of pole (given) = 3 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) = 1.063e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.233 0.665 h = 0.001 0.001 y[1] (numeric) = 0.0642109417456 0.0233978196153 y[1] (closed_form) = 0.0642101446949 0.0233996501644 absolute error = 1.997e-06 relative error = 0.002921 % Correct digits = 5 memory used=400.0MB, alloc=44.3MB, time=5.04 Radius of convergence (given) for eq 1 = 3.825 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.802 Order of pole (three term test) = 9.185e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.234 0.666 h = 0.001 0.003 y[1] (numeric) = 0.0642239320749 0.0234466446667 y[1] (closed_form) = 0.0642231760314 0.0234484896213 absolute error = 1.994e-06 relative error = 0.002916 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.824 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.552 Order of pole (three term test) = 1.269e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.235 0.669 h = 0.0001 0.004 y[1] (numeric) = 0.0642010401086 0.0235574045693 y[1] (closed_form) = 0.0642002016604 0.0235592166211 absolute error = 1.997e-06 relative error = 0.00292 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.824 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.838 Order of pole (three term test) = 7.235e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2351 0.673 h = 0.003 0.006 y[1] (numeric) = 0.0641319394274 0.023682759755 y[1] (closed_form) = 0.0641310891641 0.0236844972147 absolute error = 1.934e-06 relative error = 0.002829 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.825 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.412 Order of pole (three term test) = 9.119e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = 0.0641155123241 0.0239219592493 y[1] (closed_form) = 0.0641144127379 0.0239239151701 absolute error = 2.244e-06 relative error = 0.003279 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.85 Order of pole (three term test) = 6.649e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = 0.0640267521235 0.0240776153961 y[1] (closed_form) = 0.064025837412 0.0240794603767 absolute error = 2.059e-06 relative error = 0.00301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.295 Order of pole (three term test) = 9.562e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2383 0.687 h = 0.001 0.001 y[1] (numeric) = 0.0639745052832 0.0241714152888 y[1] (closed_form) = 0.063973655597 0.0241733138156 absolute error = 2.080e-06 relative error = 0.003041 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.824 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.802 Order of pole (three term test) = 1.809e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2393 0.688 h = 0.001 0.003 y[1] (numeric) = 0.0639866410226 0.0242205136212 y[1] (closed_form) = 0.063985832048 0.0242224275396 absolute error = 2.078e-06 relative error = 0.003037 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.549 Order of pole (three term test) = 1.256e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = 0.0639617637163 0.0243309645018 y[1] (closed_form) = 0.0639608730254 0.0243328435313 absolute error = 2.079e-06 relative error = 0.003039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.837 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2404 0.695 h = 0.003 0.006 y[1] (numeric) = 0.0638903792529 0.0244552010385 y[1] (closed_form) = 0.0638894784996 0.0244570051165 absolute error = 2.016e-06 relative error = 0.002948 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.41 Order of pole (three term test) = 4.038e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = 0.0638696947759 0.0246943094718 y[1] (closed_form) = 0.0638685392707 0.0246963263371 absolute error = 2.324e-06 relative error = 0.003394 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.849 Order of pole (three term test) = 1.062e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = 0.0637780994092 0.0248485144409 y[1] (closed_form) = 0.0637771315899 0.0248504246331 absolute error = 2.141e-06 relative error = 0.003128 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.294 Order of pole (three term test) = 1.630e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2436 0.709 h = 0.001 0.001 y[1] (numeric) = 0.0637241469693 0.0249414605045 y[1] (closed_form) = 0.0637232429712 0.0249434258342 absolute error = 2.163e-06 relative error = 0.003161 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 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) = 9.651e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2446 0.71 h = 0.001 0.003 y[1] (numeric) = 0.0637354207712 0.0249908121784 y[1] (closed_form) = 0.0637345571595 0.0249927938781 absolute error = 2.162e-06 relative error = 0.003158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.546 Order of pole (three term test) = 1.245e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = 0.063708563395 0.0251009067237 y[1] (closed_form) = 0.063707618815 0.0251028515663 absolute error = 2.162e-06 relative error = 0.003157 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.835 Order of pole (three term test) = 3.173e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2457 0.717 h = 0.003 0.006 y[1] (numeric) = 0.0636349193375 0.0252239694227 y[1] (closed_form) = 0.0636339664605 0.0252258390059 absolute error = 2.098e-06 relative error = 0.003066 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.408 Order of pole (three term test) = 5.659e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = 0.0636099754816 0.0254628859465 y[1] (closed_form) = 0.0636087625856 0.0254649624763 absolute error = 2.405e-06 relative error = 0.00351 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 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) = 4.128e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = 0.0635155766869 0.0256155712301 y[1] (closed_form) = 0.0635145541646 0.0256175454416 absolute error = 2.223e-06 relative error = 0.003246 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.294 Order of pole (three term test) = 9.392e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2489 0.731 h = 0.001 0.001 y[1] (numeric) = 0.0634599373203 0.0257076223131 y[1] (closed_form) = 0.0634589773665 0.0257096532192 absolute error = 2.246e-06 relative error = 0.003281 % Correct digits = 4 memory used=446.1MB, alloc=44.3MB, time=5.61 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 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) = 9.935e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = 0.0634703424187 0.0257572071492 y[1] (closed_form) = 0.063469422497 0.0257592553952 absolute error = 2.245e-06 relative error = 0.003278 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.81 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.25 0.736 h = 0.003 0.006 y[1] (numeric) = 0.0633948715176 0.0258792658745 y[1] (closed_form) = 0.0633938621927 0.0258811620451 absolute error = 2.148e-06 relative error = 0.003137 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.407 Order of pole (three term test) = 5.632e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.253 0.742 h = 0.0001 0.005 y[1] (numeric) = 0.0633662659253 0.0261178856092 y[1] (closed_form) = 0.0633649922541 0.0261199835092 absolute error = 2.454e-06 relative error = 0.003581 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 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) = 2.906e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = 0.063269500219 0.0262691757618 y[1] (closed_form) = 0.0632684190806 0.0262711751891 absolute error = 2.273e-06 relative error = 0.003318 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.293 Order of pole (three term test) = 1.322e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2532 0.75 h = 0.001 0.001 y[1] (numeric) = 0.0632124360174 0.0263604041443 y[1] (closed_form) = 0.0632114163136 0.0263624615623 absolute error = 2.296e-06 relative error = 0.003353 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 3.540e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2542 0.751 h = 0.001 0.003 y[1] (numeric) = 0.0632220859516 0.0264101629051 y[1] (closed_form) = 0.0632211059402 0.0264122384855 absolute error = 2.295e-06 relative error = 0.00335 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.543 Order of pole (three term test) = 4.916e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = 0.0631915685391 0.0265194454856 y[1] (closed_form) = 0.0631905091308 0.0265214806125 absolute error = 2.294e-06 relative error = 0.003348 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.833 Order of pole (three term test) = 9.914e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = 0.0631138054553 0.0266401531936 y[1] (closed_form) = 0.0631127410646 0.026642112648 absolute error = 2.230e-06 relative error = 0.003255 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.821 Order of pole (three term test) = 1.111e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2554 0.762 h = 0.003 0.006 y[1] (numeric) = 0.0630357071959 0.0267604783043 y[1] (closed_form) = 0.0630346428051 0.0267624377587 absolute error = 2.230e-06 relative error = 0.003256 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.407 Order of pole (three term test) = 1.193e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = 0.0630021294106 0.0269984846449 y[1] (closed_form) = 0.0630007951192 0.0270006384392 absolute error = 2.534e-06 relative error = 0.003696 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 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) = 1.298e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = 0.062902218604 0.0271477388545 y[1] (closed_form) = 0.0629010795353 0.0271497995553 absolute error = 2.355e-06 relative error = 0.003437 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.293 Order of pole (three term test) = 9.342e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2586 0.776 h = 0.001 0.001 y[1] (numeric) = 0.0628432601675 0.0272377650501 y[1] (closed_form) = 0.0628421809043 0.0272398854332 absolute error = 2.379e-06 relative error = 0.003474 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 1.250e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2596 0.777 h = 0.001 0.003 y[1] (numeric) = 0.0628518713489 0.0272877176568 y[1] (closed_form) = 0.0628508312615 0.0272898573003 absolute error = 2.379e-06 relative error = 0.003472 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.542 Order of pole (three term test) = 1.228e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = 0.0628190794012 0.0273963475153 y[1] (closed_form) = 0.0628179610657 0.0273984445098 absolute error = 2.377e-06 relative error = 0.003468 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.833 Order of pole (three term test) = 4.894e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2607 0.784 h = 0.003 0.006 y[1] (numeric) = 0.0627388122347 0.0275154127332 y[1] (closed_form) = 0.0627376910223 0.0275174339418 absolute error = 2.311e-06 relative error = 0.003374 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.405 Order of pole (three term test) = 4.825e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = 0.0627009922141 0.0277529210758 y[1] (closed_form) = 0.0626995963687 0.0277551303207 absolute error = 2.613e-06 relative error = 0.003811 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.847 Order of pole (three term test) = 1.633e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = 0.0625983899345 0.0279004553206 y[1] (closed_form) = 0.0625971916026 0.0279025760599 absolute error = 2.436e-06 relative error = 0.003554 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.293 Order of pole (three term test) = 9.293e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2639 0.798 h = 0.001 0.001 y[1] (numeric) = 0.0625378106252 0.0279894661464 y[1] (closed_form) = 0.062536670709 0.0279916480095 absolute error = 2.462e-06 relative error = 0.003593 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 1.244e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=492.1MB, alloc=44.3MB, time=6.19 x[1] = 2.2649 0.799 h = 0.001 0.003 y[1] (numeric) = 0.0625455372495 0.0280395892164 y[1] (closed_form) = 0.0625444360682 0.0280417912758 absolute error = 2.462e-06 relative error = 0.003592 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.541 Order of pole (three term test) = 2.519e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = 0.0625108030109 0.0281476740269 y[1] (closed_form) = 0.0625096245619 0.028149831566 absolute error = 2.458e-06 relative error = 0.003586 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.833 Order of pole (three term test) = 3.255e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.266 0.806 h = 0.003 0.006 y[1] (numeric) = 0.0624283929703 0.0282653516129 y[1] (closed_form) = 0.0624272134397 0.0282674332703 absolute error = 2.393e-06 relative error = 0.003491 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.404 Order of pole (three term test) = 9.605e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.269 0.812 h = 0.0001 0.005 y[1] (numeric) = 0.062386340767 0.0285022612396 y[1] (closed_form) = 0.0623848820556 0.0285045244869 absolute error = 2.693e-06 relative error = 0.003926 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.847 Order of pole (three term test) = 2.931e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = 0.0622810868189 0.0286480110751 y[1] (closed_form) = 0.0622798277768 0.0286501904743 absolute error = 2.517e-06 relative error = 0.003671 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.292 Order of pole (three term test) = 9.254e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2692 0.82 h = 0.001 0.001 y[1] (numeric) = 0.0622189101511 0.0287359677771 y[1] (closed_form) = 0.0622177080916 0.0287382097007 absolute error = 2.544e-06 relative error = 0.003712 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 1.239e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2702 0.821 h = 0.001 0.003 y[1] (numeric) = 0.0622257478909 0.0287862404057 y[1] (closed_form) = 0.0622245840976 0.0287885034489 absolute error = 2.545e-06 relative error = 0.003712 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.54 Order of pole (three term test) = 1.241e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = 0.0621890836524 0.0288937339505 y[1] (closed_form) = 0.0621878436277 0.0288959506306 absolute error = 2.540e-06 relative error = 0.003704 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 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) = 1.889e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2713 0.828 h = 0.003 0.006 y[1] (numeric) = 0.0621045629931 0.029009972693 y[1] (closed_form) = 0.0621033236853 0.0290121134489 absolute error = 2.474e-06 relative error = 0.003609 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.404 Order of pole (three term test) = 3.920e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = 0.0620582916465 0.0292461831495 y[1] (closed_form) = 0.0620567688 0.0292484989126 absolute error = 2.772e-06 relative error = 0.00404 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.846 Order of pole (three term test) = 6.404e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = 0.061950427756 0.0293900852932 y[1] (closed_form) = 0.061949106597 0.0293923219304 absolute error = 2.598e-06 relative error = 0.003788 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.292 Order of pole (three term test) = 9.631e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2745 0.842 h = 0.001 0.001 y[1] (numeric) = 0.0618866783976 0.0294769498044 y[1] (closed_form) = 0.0618854127464 0.0294792503245 absolute error = 2.626e-06 relative error = 0.00383 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2755 0.843 h = 0.001 0.003 y[1] (numeric) = 0.0618926235439 0.0295273509539 y[1] (closed_form) = 0.0618913956627 0.029529673503 absolute error = 2.627e-06 relative error = 0.003831 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.539 Order of pole (three term test) = 1.307e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = 0.0618540429691 0.029634207369 y[1] (closed_form) = 0.0618527399476 0.0296364817428 absolute error = 2.621e-06 relative error = 0.003822 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.831 Order of pole (three term test) = 6.925e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2766 0.85 h = 0.003 0.006 y[1] (numeric) = 0.0617674454704 0.0297489570023 y[1] (closed_form) = 0.0617661449658 0.0297511554624 absolute error = 2.554e-06 relative error = 0.003726 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.403 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = 0.0617169709979 0.0299843682042 y[1] (closed_form) = 0.0617153827916 0.0299867349594 absolute error = 2.850e-06 relative error = 0.004154 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.846 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = 0.0616065407716 0.0301263606042 y[1] (closed_form) = 0.0616051561308 0.0301286530155 absolute error = 2.678e-06 relative error = 0.003905 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.292 Order of pole (three term test) = 9.337e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2798 0.864 h = 0.001 0.001 y[1] (numeric) = 0.0615412445202 0.0302120955855 y[1] (closed_form) = 0.0615399138723 0.0302144531946 absolute error = 2.707e-06 relative error = 0.003949 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.799 Order of pole (three term test) = 1.743e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=538.1MB, alloc=44.3MB, time=6.76 x[1] = 2.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = 0.0615462939869 0.0302626041072 y[1] (closed_form) = 0.0615450005859 0.0302649846399 absolute error = 2.709e-06 relative error = 0.00395 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.8 Order of pole (three term test) = 7.565e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2809 0.869 h = 0.003 0.006 y[1] (numeric) = 0.0614580265882 0.0303760961359 y[1] (closed_form) = 0.0614566662009 0.0303783130041 absolute error = 2.601e-06 relative error = 0.003794 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.403 Order of pole (three term test) = 7.824e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = 0.0614039604297 0.0306106898291 y[1] (closed_form) = 0.0614023089987 0.0306130690699 absolute error = 2.896e-06 relative error = 0.004221 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.846 Order of pole (three term test) = 6.395e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.284 0.88 h = 0.0001 0.003 y[1] (numeric) = 0.0612913812395 0.0307509598555 y[1] (closed_form) = 0.0612899348192 0.0307532689328 absolute error = 2.725e-06 relative error = 0.003973 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.292 Order of pole (three term test) = 9.216e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2841 0.883 h = 0.001 0.001 y[1] (numeric) = 0.0612247890215 0.030835675273 y[1] (closed_form) = 0.061223395244 0.0308380506251 absolute error = 2.754e-06 relative error = 0.004018 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.799 Order of pole (three term test) = 9.400e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2851 0.884 h = 0.001 0.003 y[1] (numeric) = 0.0612290645898 0.0308862485055 y[1] (closed_form) = 0.0612277075775 0.0308886475322 absolute error = 2.756e-06 relative error = 0.004019 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.539 Order of pole (three term test) = 4.851e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = 0.0611869680335 0.0309917763367 y[1] (closed_form) = 0.0611855380734 0.0309941239178 absolute error = 2.749e-06 relative error = 0.004008 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.831 Order of pole (three term test) = 9.287e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2862 0.891 h = 0.003 0.006 y[1] (numeric) = 0.0610966201087 0.0311036010445 y[1] (closed_form) = 0.0610951960107 0.0311058728953 absolute error = 2.681e-06 relative error = 0.003911 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.403 Order of pole (three term test) = 8.742e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = 0.0610383896839 0.0313372108698 y[1] (closed_form) = 0.0610366707548 0.0313396381609 absolute error = 2.974e-06 relative error = 0.004335 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.846 Order of pole (three term test) = 9.040e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = 0.0609233308529 0.0314754597607 y[1] (closed_form) = 0.0609218185462 0.0314778217669 absolute error = 2.805e-06 relative error = 0.00409 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.292 Order of pole (three term test) = 9.260e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2894 0.905 h = 0.001 0.001 y[1] (numeric) = 0.060855243084 0.0315589785818 y[1] (closed_form) = 0.060853781835 0.031561408092 absolute error = 2.835e-06 relative error = 0.004136 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.799 Order of pole (three term test) = 9.112e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2904 0.906 h = 0.001 0.003 y[1] (numeric) = 0.0608586191551 0.0316096195947 y[1] (closed_form) = 0.0608571940998 0.031612073644 absolute error = 2.838e-06 relative error = 0.004138 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.539 Order of pole (three term test) = 4.851e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = 0.0608146533378 0.0317143816943 y[1] (closed_form) = 0.0608131565757 0.0317167825841 absolute error = 2.829e-06 relative error = 0.004125 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.831 Order of pole (three term test) = 6.924e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2915 0.913 h = 0.003 0.006 y[1] (numeric) = 0.060722333871 0.0318245796567 y[1] (closed_form) = 0.060720844764 0.0318269049792 absolute error = 2.761e-06 relative error = 0.004028 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.403 Order of pole (three term test) = 5.531e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = 0.0606599636205 0.0320571072049 y[1] (closed_form) = 0.0606581761021 0.0320595809264 absolute error = 3.052e-06 relative error = 0.004448 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.846 Order of pole (three term test) = 4.046e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = 0.0605424738652 0.0321932768116 y[1] (closed_form) = 0.0605408944356 0.0321956901719 absolute error = 2.884e-06 relative error = 0.004206 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.292 Order of pole (three term test) = 9.222e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2947 0.927 h = 0.001 0.001 y[1] (numeric) = 0.060472919415 0.0322755640103 y[1] (closed_form) = 0.0604713894225 0.0322780460562 absolute error = 2.916e-06 relative error = 0.004254 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 8.910e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2957 0.928 h = 0.001 0.003 y[1] (numeric) = 0.0604753947039 0.0323262514675 y[1] (closed_form) = 0.0604739003081 0.0323287588997 absolute error = 2.919e-06 relative error = 0.004257 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.539 Order of pole (three term test) = 3.642e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=584.1MB, alloc=44.3MB, time=7.34 x[1] = 2.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = 0.0604295784461 0.0324302038055 y[1] (closed_form) = 0.0604280136345 0.0324326564018 absolute error = 2.909e-06 relative error = 0.004242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 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) = 9.804e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2968 0.935 h = 0.003 0.006 y[1] (numeric) = 0.0603353267516 0.0325387289202 y[1] (closed_form) = 0.0603337713824 0.0325411061655 absolute error = 2.841e-06 relative error = 0.004144 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.403 Order of pole (three term test) = 1.751e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = 0.0602688440178 0.0327700765566 y[1] (closed_form) = 0.0602669868676 0.0327725950577 absolute error = 3.129e-06 relative error = 0.004561 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.846 Order of pole (three term test) = 4.053e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = 0.0601489737499 0.0329041102072 y[1] (closed_form) = 0.0601473260079 0.032906573311 absolute error = 2.963e-06 relative error = 0.004322 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.292 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3 0.949 h = 0.001 0.001 y[1] (numeric) = 0.0600779825078 0.0329851316336 y[1] (closed_form) = 0.0600763825485 0.032987664556 absolute error = 2.996e-06 relative error = 0.004371 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 8.755e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.301 0.95 h = 0.001 0.003 y[1] (numeric) = 0.0600795563618 0.0330358441743 y[1] (closed_form) = 0.0600779913778 0.0330384033117 absolute error = 3.000e-06 relative error = 0.004375 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.54 Order of pole (three term test) = 6.083e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.302 0.953 h = 0.0001 0.004 y[1] (numeric) = 0.0600319097766 0.0331389433057 y[1] (closed_form) = 0.0600302757164 0.0331414459703 absolute error = 2.989e-06 relative error = 0.004359 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 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) = 4.394e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3021 0.957 h = 0.003 0.006 y[1] (numeric) = 0.0599357665084 0.0332457506652 y[1] (closed_form) = 0.05993414367 0.0332481782477 absolute error = 2.920e-06 relative error = 0.00426 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.404 Order of pole (three term test) = 1.963e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = 0.0598652015056 0.0334758216318 y[1] (closed_form) = 0.0598632737309 0.033478383233 absolute error = 3.206e-06 relative error = 0.004674 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.847 Order of pole (three term test) = 1.285e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = 0.0597430027778 0.0336076641906 y[1] (closed_form) = 0.0597412855827 0.0336101753933 absolute error = 3.042e-06 relative error = 0.004438 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.293 Order of pole (three term test) = 9.268e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3053 0.971 h = 0.001 0.001 y[1] (numeric) = 0.0596706056209 0.0336873866065 y[1] (closed_form) = 0.0596689345218 0.0336899687106 absolute error = 3.076e-06 relative error = 0.004489 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 1.242e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = 0.0596712780205 0.0337381028674 y[1] (closed_form) = 0.0596696412512 0.0337407119962 absolute error = 3.080e-06 relative error = 0.004493 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.81 Order of pole (three term test) = 7.775e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3064 0.976 h = 0.003 0.006 y[1] (numeric) = 0.0595736216791 0.0338434700847 y[1] (closed_form) = 0.0595719372331 0.0338459091181 absolute error = 2.964e-06 relative error = 0.004326 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.405 Order of pole (three term test) = 1.186e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = 0.0594995859155 0.0340723173143 y[1] (closed_form) = 0.0594975940786 0.0340748840332 absolute error = 3.249e-06 relative error = 0.004738 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.847 Order of pole (three term test) = 1.556e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = 0.0593754527852 0.0342022040543 y[1] (closed_form) = 0.0593736723567 0.034204724713 absolute error = 3.086e-06 relative error = 0.004504 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.293 Order of pole (three term test) = 9.319e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3096 0.99 h = 0.001 0.001 y[1] (numeric) = 0.0593018869135 0.0342807662012 y[1] (closed_form) = 0.0593001510928 0.034283358632 absolute error = 3.120e-06 relative error = 0.004555 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 8.832e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3106 0.991 h = 0.001 0.003 y[1] (numeric) = 0.0593017841396 0.0343314578454 y[1] (closed_form) = 0.0593000820652 0.0343340779739 absolute error = 3.124e-06 relative error = 0.00456 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.542 Order of pole (three term test) = 1.228e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = 0.0592508009617 0.0344328347412 y[1] (closed_form) = 0.0592490324471 0.0344353954791 absolute error = 3.112e-06 relative error = 0.004541 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.833 Order of pole (three term test) = 9.537e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=630.0MB, alloc=44.3MB, time=7.91 x[1] = 2.3117 0.998 h = 0.003 0.006 y[1] (numeric) = 0.0591512721895 0.0345363091904 y[1] (closed_form) = 0.0591495181761 0.0345387955066 absolute error = 3.043e-06 relative error = 0.004442 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.406 Order of pole (three term test) = 4.622e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = 0.0590732190258 0.0347637028241 y[1] (closed_form) = 0.0590711548734 0.0347663094367 absolute error = 3.325e-06 relative error = 0.004851 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 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) = 8.727e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = 0.0589468590774 0.0348913008213 y[1] (closed_form) = 0.0589450072263 0.0348938664215 absolute error = 3.164e-06 relative error = 0.004619 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.293 Order of pole (three term test) = 1.199e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3149 1.012 h = 0.001 0.001 y[1] (numeric) = 0.0588719476276 0.0349685050447 y[1] (closed_form) = 0.0588701386435 0.0349711434039 absolute error = 3.199e-06 relative error = 0.004672 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3159 1.013 h = 0.001 0.003 y[1] (numeric) = 0.0588709452976 0.0350191607455 y[1] (closed_form) = 0.0588691693717 0.035021827574 absolute error = 3.204e-06 relative error = 0.004678 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.544 Order of pole (three term test) = 9.871e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = 0.0588181967535 0.0351195640702 y[1] (closed_form) = 0.0588163558577 0.0351221699936 absolute error = 3.191e-06 relative error = 0.004657 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.834 Order of pole (three term test) = 1.576e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.317 1.02 h = 0.003 0.006 y[1] (numeric) = 0.0587169001915 0.0352211998333 y[1] (closed_form) = 0.0587150755435 0.0352237317526 absolute error = 3.121e-06 relative error = 0.004558 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.407 Order of pole (three term test) = 7.970e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.32 1.026 h = 0.0001 0.005 y[1] (numeric) = 0.0586348678408 0.0354470462069 y[1] (closed_form) = 0.0586327305278 0.0354496909618 absolute error = 3.400e-06 relative error = 0.004963 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = 0.0585063374823 0.0355723050413 y[1] (closed_form) = 0.0585044132129 0.0355749138512 absolute error = 3.242e-06 relative error = 0.004734 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.294 Order of pole (three term test) = 1.150e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3202 1.034 h = 0.001 0.001 y[1] (numeric) = 0.0584301139552 0.035648120904 y[1] (closed_form) = 0.0584282307851 0.0356508034069 absolute error = 3.278e-06 relative error = 0.004788 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 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) = 9.986e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3212 1.035 h = 0.001 0.003 y[1] (numeric) = 0.0584282138521 0.0356987194229 y[1] (closed_form) = 0.0584263630304 0.0357014311454 absolute error = 3.283e-06 relative error = 0.004795 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.545 Order of pole (three term test) = 6.208e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = 0.0583737248122 0.0357981084206 y[1] (closed_form) = 0.0583718105337 0.0358007577692 absolute error = 3.269e-06 relative error = 0.004773 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.835 Order of pole (three term test) = 3.173e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3223 1.042 h = 0.003 0.006 y[1] (numeric) = 0.0582707058434 0.0358978656346 y[1] (closed_form) = 0.0582688095443 0.0359004414477 absolute error = 3.199e-06 relative error = 0.004673 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.408 Order of pole (three term test) = 5.673e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = 0.0581847352354 0.0361220723414 y[1] (closed_form) = 0.0581825239695 0.0361247534654 absolute error = 3.475e-06 relative error = 0.005075 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.849 Order of pole (three term test) = 2.940e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = 0.0580540922852 0.0362449433329 y[1] (closed_form) = 0.0580520946544 0.0362475935937 absolute error = 3.319e-06 relative error = 0.004849 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.294 Order of pole (three term test) = 1.518e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3255 1.056 h = 0.001 0.001 y[1] (numeric) = 0.0579765910323 0.0363193414322 y[1] (closed_form) = 0.0579746327083 0.0363220662663 absolute error = 3.356e-06 relative error = 0.004905 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 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) = 1.098e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3265 1.057 h = 0.001 0.003 y[1] (numeric) = 0.0579737955641 0.0363698616147 y[1] (closed_form) = 0.0579718688576 0.0363726163964 absolute error = 3.362e-06 relative error = 0.004912 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.547 Order of pole (three term test) = 5.002e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = 0.0579175920671 0.0364681963247 y[1] (closed_form) = 0.0579156034579 0.0364708873107 absolute error = 3.346e-06 relative error = 0.004889 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.837 Order of pole (three term test) = 9.588e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=676.0MB, alloc=44.3MB, time=8.48 x[1] = 2.3276 1.064 h = 0.003 0.006 y[1] (numeric) = 0.0578128971841 0.0365660365279 y[1] (closed_form) = 0.0578109282692 0.0365686544975 absolute error = 3.276e-06 relative error = 0.004789 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.41 Order of pole (three term test) = 5.716e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = 0.0577230319154 0.0367885125123 y[1] (closed_form) = 0.057720745958 0.0367912282126 absolute error = 3.550e-06 relative error = 0.005186 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.849 Order of pole (three term test) = 6.625e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = 0.0575903355383 0.0369089487677 y[1] (closed_form) = 0.0575882636562 0.0369116386953 absolute error = 3.395e-06 relative error = 0.004964 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.824 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.295 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3308 1.078 h = 0.001 0.001 y[1] (numeric) = 0.0575115917233 0.0369819007632 y[1] (closed_form) = 0.0575095573328 0.03698466609 absolute error = 3.433e-06 relative error = 0.005021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.824 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.802 Order of pole (three term test) = 1.058e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = 0.0575079039188 0.0370323215607 y[1] (closed_form) = 0.0575059003947 0.0370351175404 absolute error = 3.440e-06 relative error = 0.005029 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.824 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.82 Order of pole (three term test) = 1.114e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3319 1.083 h = 0.003 0.006 y[1] (numeric) = 0.0574018767977 0.0371285639419 y[1] (closed_form) = 0.0573998455607 0.0371311862427 absolute error = 3.317e-06 relative error = 0.004852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.825 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.412 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = 0.0573087181081 0.0373494327249 y[1] (closed_form) = 0.057306368315 0.0373521461722 absolute error = 3.589e-06 relative error = 0.005247 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.823 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.85 Order of pole (three term test) = 6.690e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.335 1.094 h = 0.0001 0.003 y[1] (numeric) = 0.0571743322945 0.037467713609 y[1] (closed_form) = 0.057172196774 0.0374704056712 absolute error = 3.436e-06 relative error = 0.005027 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.825 Order of pole (given) = 3 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) = 6.763e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3351 1.097 h = 0.001 0.001 y[1] (numeric) = 0.0570945653382 0.0375393847662 y[1] (closed_form) = 0.0570924657208 0.0375421528725 absolute error = 3.474e-06 relative error = 0.005085 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.802 Order of pole (three term test) = 9.566e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3361 1.098 h = 0.001 0.003 y[1] (numeric) = 0.0570901138584 0.0375896926891 y[1] (closed_form) = 0.0570880444374 0.0375924920273 absolute error = 3.481e-06 relative error = 0.005093 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.825 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.553 Order of pole (three term test) = 1.274e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = 0.0570308069746 0.0376859425097 y[1] (closed_form) = 0.0570286786613 0.0376886755558 absolute error = 3.464e-06 relative error = 0.005067 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.825 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.84 Order of pole (three term test) = 3.256e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3372 1.105 h = 0.003 0.006 y[1] (numeric) = 0.0569231447817 0.0377800995786 y[1] (closed_form) = 0.0569210392961 0.0377827607256 absolute error = 3.393e-06 relative error = 0.004967 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.414 Order of pole (three term test) = 9.211e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = 0.0568261805094 0.0379990727066 y[1] (closed_form) = 0.0568237548167 0.0380018173406 absolute error = 3.663e-06 relative error = 0.005358 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.825 Order of pole (given) = 3 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = 0.056689855222 0.0381148372407 y[1] (closed_form) = 0.0566876439613 0.0381175655806 absolute error = 3.512e-06 relative error = 0.005141 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 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) = 2.928e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3404 1.119 h = 0.001 0.001 y[1] (numeric) = 0.0566089134686 0.0381850129165 y[1] (closed_form) = 0.0566067362589 0.0381878180231 absolute error = 3.551e-06 relative error = 0.0052 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.803 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3414 1.12 h = 0.001 0.003 y[1] (numeric) = 0.0566035771689 0.0382351826972 y[1] (closed_form) = 0.0566014293694 0.0382380196965 absolute error = 3.558e-06 relative error = 0.005209 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.556 Order of pole (three term test) = 2.574e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = 0.0565426369299 0.0383302690084 y[1] (closed_form) = 0.0565404318991 0.038333038436 absolute error = 3.540e-06 relative error = 0.005182 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.841 Order of pole (three term test) = 7.357e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3425 1.127 h = 0.003 0.006 y[1] (numeric) = 0.0564334378852 0.0384224076865 y[1] (closed_form) = 0.0564312573396 0.0384251058738 absolute error = 3.469e-06 relative error = 0.005081 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.416 Order of pole (three term test) = 8.326e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=721.8MB, alloc=44.3MB, time=9.05 x[1] = 2.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = 0.0563327189295 0.0386393984968 y[1] (closed_form) = 0.0563302167549 0.0386421724793 absolute error = 3.736e-06 relative error = 0.005469 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.852 Order of pole (three term test) = 1.366e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = 0.0561945167902 0.0387526051453 y[1] (closed_form) = 0.0561922290566 0.0387553679183 absolute error = 3.587e-06 relative error = 0.005255 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 3 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) = 9.868e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3457 1.141 h = 0.001 0.001 y[1] (numeric) = 0.0561124374933 0.0388212601872 y[1] (closed_form) = 0.0561101819413 0.0388241003934 absolute error = 3.627e-06 relative error = 0.005315 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.828 Order of pole (given) = 3 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) = 9.360e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3467 1.142 h = 0.001 0.003 y[1] (numeric) = 0.0561062211449 0.0388712712062 y[1] (closed_form) = 0.0561039941992 0.0388741439413 absolute error = 3.635e-06 relative error = 0.005325 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.828 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.559 Order of pole (three term test) = 7.809e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = 0.0560436777874 0.0389651574912 y[1] (closed_form) = 0.0560413953055 0.0389679614266 absolute error = 3.615e-06 relative error = 0.005297 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.828 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.843 Order of pole (three term test) = 4.707e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3478 1.149 h = 0.003 0.006 y[1] (numeric) = 0.0559329921511 0.0390552450597 y[1] (closed_form) = 0.0559307357885 0.0390579784612 absolute error = 3.544e-06 relative error = 0.005196 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.419 Order of pole (three term test) = 9.417e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = 0.0558285718514 0.0392701685805 y[1] (closed_form) = 0.0558259926677 0.0392729700611 absolute error = 3.808e-06 relative error = 0.005579 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.828 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.854 Order of pole (three term test) = 4.371e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = 0.0556885565639 0.0393807777471 y[1] (closed_form) = 0.0556861916805 0.0393835730912 absolute error = 3.662e-06 relative error = 0.005368 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.298 Order of pole (three term test) = 9.988e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.351 1.163 h = 0.001 0.001 y[1] (numeric) = 0.0556053776319 0.0394478881573 y[1] (closed_form) = 0.0556030430457 0.0394507615444 absolute error = 3.702e-06 relative error = 0.00543 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 3 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) = 9.476e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.352 1.164 h = 0.001 0.003 y[1] (numeric) = 0.0555982866018 0.0394977199835 y[1] (closed_form) = 0.0555959798012 0.0395006265105 absolute error = 3.711e-06 relative error = 0.005441 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.562 Order of pole (three term test) = 1.318e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.353 1.167 h = 0.0001 0.004 y[1] (numeric) = 0.0555341713678 0.0395903707002 y[1] (closed_form) = 0.055531810758 0.0395932072525 absolute error = 3.690e-06 relative error = 0.005411 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.845 Order of pole (three term test) = 4.316e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3531 1.171 h = 0.003 0.006 y[1] (numeric) = 0.0554220502454 0.0396783759973 y[1] (closed_form) = 0.0554197173643 0.0396811427682 absolute error = 3.619e-06 relative error = 0.00531 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.422 Order of pole (three term test) = 9.354e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = 0.0553139843147 0.0398911490281 y[1] (closed_form) = 0.0553113276504 0.0398939761464 absolute error = 3.879e-06 relative error = 0.005689 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.855 Order of pole (three term test) = 9.394e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = 0.0551722205927 0.0399991230889 y[1] (closed_form) = 0.055169777939 0.0400019491264 absolute error = 3.735e-06 relative error = 0.005481 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.831 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.299 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3563 1.185 h = 0.001 0.001 y[1] (numeric) = 0.0550879805462 0.0400646660439 y[1] (closed_form) = 0.0550855662922 0.0400675706773 absolute error = 3.777e-06 relative error = 0.005545 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.832 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.805 Order of pole (three term test) = 1.358e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = 0.0550800207891 0.0401142984546 y[1] (closed_form) = 0.0550776334842 0.0401172368132 absolute error = 3.786e-06 relative error = 0.005556 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.831 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.84 Order of pole (three term test) = 1.668e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3574 1.19 h = 0.003 0.006 y[1] (numeric) = 0.0549667675321 0.0402005766843 y[1] (closed_form) = 0.054964372633 0.040203340679 absolute error = 3.657e-06 relative error = 0.00537 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.832 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.425 Order of pole (three term test) = 1.038e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = 0.0548556368687 0.0404113909506 y[1] (closed_form) = 0.0548529176344 0.0404142086231 absolute error = 3.916e-06 relative error = 0.005747 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.831 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.856 Order of pole (three term test) = 9.548e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=767.9MB, alloc=44.3MB, time=9.62 x[1] = 2.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = 0.054712452653 0.0405170484382 y[1] (closed_form) = 0.0547099470017 0.0405198693584 absolute error = 3.773e-06 relative error = 0.005542 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.833 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.3 Order of pole (three term test) = 1.047e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3606 1.204 h = 0.001 0.001 y[1] (numeric) = 0.0546273495355 0.0405812128084 y[1] (closed_form) = 0.0546248706361 0.0405841127319 absolute error = 3.815e-06 relative error = 0.005606 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.833 Order of pole (given) = 3 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) = 9.742e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3616 1.205 h = 0.001 0.003 y[1] (numeric) = 0.0546186499162 0.0406306473083 y[1] (closed_form) = 0.0546161972273 0.0406335814297 absolute error = 3.824e-06 relative error = 0.005618 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.833 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.57 Order of pole (three term test) = 1.355e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = 0.0545517118949 0.0407208899972 y[1] (closed_form) = 0.0545492087013 0.0407237521228 absolute error = 3.802e-06 relative error = 0.005586 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.833 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.85 Order of pole (three term test) = 1.550e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3627 1.212 h = 0.003 0.006 y[1] (numeric) = 0.054437083948 0.0408049275423 y[1] (closed_form) = 0.0544346113965 0.040807721425 absolute error = 3.731e-06 relative error = 0.005484 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.834 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.428 Order of pole (three term test) = 6.205e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = 0.0543224183364 0.0410134422111 y[1] (closed_form) = 0.0543196209147 0.0410162820345 absolute error = 3.986e-06 relative error = 0.005856 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.833 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.857 Order of pole (three term test) = 5.035e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = 0.0541776089329 0.0411164007261 y[1] (closed_form) = 0.0541750245309 0.0411192488059 absolute error = 3.846e-06 relative error = 0.005655 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.834 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.301 Order of pole (three term test) = 1.047e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3659 1.226 h = 0.001 0.001 y[1] (numeric) = 0.0540915180977 0.0411789588314 y[1] (closed_form) = 0.0540889585317 0.0411818863606 absolute error = 3.889e-06 relative error = 0.00572 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.835 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.807 Order of pole (three term test) = 1.033e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3669 1.227 h = 0.001 0.003 y[1] (numeric) = 0.0540819625972 0.0412281569967 y[1] (closed_form) = 0.0540794283786 0.0412311192599 absolute error = 3.898e-06 relative error = 0.005733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.835 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.575 Order of pole (three term test) = 2.751e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = 0.0540135476686 0.0413170685181 y[1] (closed_form) = 0.0540109647525 0.041319957767 absolute error = 3.875e-06 relative error = 0.005699 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.835 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.852 Order of pole (three term test) = 1.113e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.368 1.234 h = 0.003 0.006 y[1] (numeric) = 0.0538976348933 0.0413989440932 y[1] (closed_form) = 0.053895084149 0.0414017659782 absolute error = 3.804e-06 relative error = 0.005597 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.836 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.431 Order of pole (three term test) = 9.966e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.371 1.24 h = 0.0001 0.005 y[1] (numeric) = 0.0537794964173 0.04160508148 y[1] (closed_form) = 0.0537766204962 0.0416079415758 absolute error = 4.056e-06 relative error = 0.005965 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.835 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.859 Order of pole (three term test) = 6.550e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = 0.0536331289999 0.0417053092007 y[1] (closed_form) = 0.05363046539 0.0417081825301 absolute error = 3.918e-06 relative error = 0.005767 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.837 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.303 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3712 1.248 h = 0.001 0.001 y[1] (numeric) = 0.0535460904631 0.0417662416749 y[1] (closed_form) = 0.0535434497662 0.0417691948423 absolute error = 3.962e-06 relative error = 0.005834 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.837 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.808 Order of pole (three term test) = 1.124e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3722 1.249 h = 0.001 0.003 y[1] (numeric) = 0.05353568666 0.0418151839956 y[1] (closed_form) = 0.0535330704343 0.0418181724062 absolute error = 3.972e-06 relative error = 0.005847 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.837 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.579 Order of pole (three term test) = 1.405e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = 0.0534658295725 0.0419027328724 y[1] (closed_form) = 0.0534631664807 0.0419056473062 absolute error = 3.948e-06 relative error = 0.005812 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.837 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.855 Order of pole (three term test) = 3.578e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3733 1.256 h = 0.003 0.006 y[1] (numeric) = 0.0533486857719 0.041982421546 y[1] (closed_form) = 0.053346056351 0.0419852695371 absolute error = 3.876e-06 relative error = 0.00571 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.838 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.435 Order of pole (three term test) = 6.408e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = 0.053227138603 0.0421861060215 y[1] (closed_form) = 0.0532241839259 0.0421889845088 absolute error = 4.125e-06 relative error = 0.006074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.837 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.861 Order of pole (three term test) = 7.448e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=813.9MB, alloc=44.3MB, time=10.20 x[1] = 2.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = 0.0530792810695 0.0422835731939 y[1] (closed_form) = 0.0530765378518 0.0422864698552 absolute error = 3.989e-06 relative error = 0.005879 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.839 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.304 Order of pole (three term test) = 1.083e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3765 1.27 h = 0.001 0.001 y[1] (numeric) = 0.0529913352894 0.0423428619034 y[1] (closed_form) = 0.0529886130564 0.0423458387339 absolute error = 4.034e-06 relative error = 0.005947 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 3 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) = 3.068e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3775 1.271 h = 0.001 0.003 y[1] (numeric) = 0.0529800913095 0.0423915291525 y[1] (closed_form) = 0.0529773926595 0.0423945417081 absolute error = 4.045e-06 relative error = 0.005961 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.839 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.584 Order of pole (three term test) = 1.597e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = 0.0529088276242 0.0424776850245 y[1] (closed_form) = 0.0529060839618 0.0424806226976 absolute error = 4.020e-06 relative error = 0.005924 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.839 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.858 Order of pole (three term test) = 8.141e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3786 1.278 h = 0.003 0.006 y[1] (numeric) = 0.0527905071602 0.0425551635201 y[1] (closed_form) = 0.0527877986359 0.0425580357124 absolute error = 3.948e-06 relative error = 0.005822 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.438 Order of pole (three term test) = 1.031e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = 0.0526656174772 0.0427563215756 y[1] (closed_form) = 0.0526625838434 0.0427592165728 absolute error = 4.193e-06 relative error = 0.006182 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.839 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.862 Order of pole (three term test) = 1.696e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = 0.0525163383746 0.0428510005305 y[1] (closed_form) = 0.0525135152065 0.0428539186007 absolute error = 4.060e-06 relative error = 0.00599 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.841 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.305 Order of pole (three term test) = 1.097e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3818 1.292 h = 0.001 0.001 y[1] (numeric) = 0.0524275262062 0.0429086285849 y[1] (closed_form) = 0.0524247220915 0.0429116270978 absolute error = 4.105e-06 relative error = 0.00606 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.842 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.81 Order of pole (three term test) = 1.062e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = 0.0524154507109 0.0429570018368 y[1] (closed_form) = 0.0524126692799 0.0429600365291 absolute error = 4.117e-06 relative error = 0.006074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.841 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.87 Order of pole (three term test) = 9.050e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3829 1.297 h = 0.003 0.006 y[1] (numeric) = 0.0522962121792 0.0430326549884 y[1] (closed_form) = 0.0522934429334 0.0430355174809 absolute error = 3.983e-06 relative error = 0.005881 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.843 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.442 Order of pole (three term test) = 9.392e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = 0.0521685310831 0.0432315424797 y[1] (closed_form) = 0.0521654371247 0.0432344211864 absolute error = 4.226e-06 relative error = 0.006237 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.842 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.864 Order of pole (three term test) = 3.454e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.386 1.308 h = 0.0001 0.003 y[1] (numeric) = 0.0520181172935 0.0433237850636 y[1] (closed_form) = 0.0520152327762 0.0433266910092 absolute error = 4.095e-06 relative error = 0.006048 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.843 Order of pole (given) = 3 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) = 1.123e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3861 1.311 h = 0.001 0.001 y[1] (numeric) = 0.0519286123845 0.04337996146 y[1] (closed_form) = 0.0519257452548 0.043382948015 absolute error = 4.140e-06 relative error = 0.006119 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.844 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.811 Order of pole (three term test) = 5.306e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3871 1.312 h = 0.001 0.003 y[1] (numeric) = 0.0519158322864 0.0434280569819 y[1] (closed_form) = 0.0519129870531 0.0434310800741 absolute error = 4.151e-06 relative error = 0.006133 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.844 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.595 Order of pole (three term test) = 1.484e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = 0.0518420658969 0.043511528196 y[1] (closed_form) = 0.0518391791616 0.0435144748958 absolute error = 4.125e-06 relative error = 0.006095 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.844 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.864 Order of pole (three term test) = 1.069e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3882 1.319 h = 0.003 0.006 y[1] (numeric) = 0.0517217291907 0.0435848253688 y[1] (closed_form) = 0.0517188802221 0.0435877084987 absolute error = 4.053e-06 relative error = 0.005993 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.845 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.446 Order of pole (three term test) = 4.789e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = 0.0515908345957 0.0437810563519 y[1] (closed_form) = 0.0515876614762 0.0437839480712 absolute error = 4.293e-06 relative error = 0.006345 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.844 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.866 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = 0.051439128524 0.043870465659 y[1] (closed_form) = 0.0514361635945 0.0438733894245 absolute error = 4.164e-06 relative error = 0.006159 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.846 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.308 Order of pole (three term test) = 1.140e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=859.8MB, alloc=44.3MB, time=10.76 x[1] = 2.3914 1.333 h = 0.001 0.001 y[1] (numeric) = 0.0513488343159 0.0439249538039 y[1] (closed_form) = 0.0513458848429 0.0439279583458 absolute error = 4.210e-06 relative error = 0.006231 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.847 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.812 Order of pole (three term test) = 3.249e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3924 1.334 h = 0.001 0.003 y[1] (numeric) = 0.0513352404155 0.0439727210915 y[1] (closed_form) = 0.051332311922 0.0439757625729 absolute error = 4.222e-06 relative error = 0.006246 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.846 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.601 Order of pole (three term test) = 1.757e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = 0.051260173579 0.044054719275 y[1] (closed_form) = 0.0512572054887 0.0440576836235 absolute error = 4.195e-06 relative error = 0.006206 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.846 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.867 Order of pole (three term test) = 7.714e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3935 1.341 h = 0.003 0.006 y[1] (numeric) = 0.0511388184829 0.0441257495893 y[1] (closed_form) = 0.0511358895279 0.0441286514388 absolute error = 4.123e-06 relative error = 0.006104 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.848 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.451 Order of pole (three term test) = 4.888e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = 0.0510047818204 0.0443192569716 y[1] (closed_form) = 0.0510015294961 0.044322159831 absolute error = 4.359e-06 relative error = 0.006452 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.847 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.868 Order of pole (three term test) = 3.597e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = 0.0508518534248 0.0444058113691 y[1] (closed_form) = 0.0508488079044 0.0444087510272 absolute error = 4.233e-06 relative error = 0.00627 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.31 Order of pole (three term test) = 1.165e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3967 1.355 h = 0.001 0.001 y[1] (numeric) = 0.0507608116431 0.044458597973 y[1] (closed_form) = 0.0507577796506 0.0444616185178 absolute error = 4.280e-06 relative error = 0.006343 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.814 Order of pole (three term test) = 1.564e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3977 1.356 h = 0.001 0.003 y[1] (numeric) = 0.050746414056 0.0445060190631 y[1] (closed_form) = 0.050743402118 0.0445090769212 absolute error = 4.292e-06 relative error = 0.006359 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.607 Order of pole (three term test) = 3.078e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = 0.0506700850515 0.0445865183843 y[1] (closed_form) = 0.0506670354358 0.0445894984274 absolute error = 4.264e-06 relative error = 0.006317 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.87 Order of pole (three term test) = 1.581e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3988 1.363 h = 0.003 0.006 y[1] (numeric) = 0.050547767498 0.0446552650547 y[1] (closed_form) = 0.0505447583498 0.0446581837056 absolute error = 4.192e-06 relative error = 0.006215 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.851 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.455 Order of pole (three term test) = 3.996e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = 0.0504106618764 0.0448459840814 y[1] (closed_form) = 0.0504073303579 0.0448488962152 absolute error = 4.425e-06 relative error = 0.006558 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.87 Order of pole (three term test) = 1.875e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = 0.0502565814708 0.0449296640578 y[1] (closed_form) = 0.0502534552374 0.0449326176834 absolute error = 4.301e-06 relative error = 0.00638 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.852 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.312 Order of pole (three term test) = 1.331e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.402 1.377 h = 0.001 0.001 y[1] (numeric) = 0.0501648340628 0.0449807370971 y[1] (closed_form) = 0.0501617194333 0.0449837716633 absolute error = 4.349e-06 relative error = 0.006454 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.852 Order of pole (given) = 3 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) = 1.599e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.403 1.378 h = 0.001 0.003 y[1] (numeric) = 0.0501496433869 0.0450277943916 y[1] (closed_form) = 0.0501465478797 0.0450308666166 absolute error = 4.361e-06 relative error = 0.006471 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.852 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.613 Order of pole (three term test) = 1.101e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.404 1.381 h = 0.0001 0.004 y[1] (numeric) = 0.0500720910927 0.0451067702347 y[1] (closed_form) = 0.0500689598391 0.045109764021 absolute error = 4.332e-06 relative error = 0.006428 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.852 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.874 Order of pole (three term test) = 8.070e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4041 1.385 h = 0.003 0.006 y[1] (numeric) = 0.0499488672789 0.0451732181693 y[1] (closed_form) = 0.0499457777875 0.0451761517044 absolute error = 4.260e-06 relative error = 0.006326 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.853 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.46 Order of pole (three term test) = 6.130e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = 0.0498087673944 0.0453610864705 y[1] (closed_form) = 0.049805356746 0.0453640060215 absolute error = 4.490e-06 relative error = 0.006664 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.853 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.872 Order of pole (three term test) = 3.836e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = 0.0496536055723 0.0454418746372 y[1] (closed_form) = 0.0496503985604 0.0454448403096 absolute error = 4.368e-06 relative error = 0.00649 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.854 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.314 Order of pole (three term test) = 1.487e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=905.7MB, alloc=44.3MB, time=11.34 x[1] = 2.4073 1.399 h = 0.001 0.001 y[1] (numeric) = 0.0495611946621 0.0454912233558 y[1] (closed_form) = 0.0495579973366 0.0454942699665 absolute error = 4.416e-06 relative error = 0.006565 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.855 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.816 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4083 1.4 h = 0.003 0.006 y[1] (numeric) = 0.0495452219623 0.0455378996369 y[1] (closed_form) = 0.0495420428208 0.0455409842234 absolute error = 4.430e-06 relative error = 0.006583 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.855 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.29 Order of pole (three term test) = 1.132e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = 0.0494031047392 0.0457241213396 y[1] (closed_form) = 0.0493995333563 0.0457269106462 absolute error = 4.532e-06 relative error = 0.006732 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.854 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.873 Order of pole (three term test) = 1.142e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = 0.0492471667938 0.0458029364051 y[1] (closed_form) = 0.0492437979539 0.0458057750239 absolute error = 4.405e-06 relative error = 0.00655 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.856 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.314 Order of pole (three term test) = 3.699e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4115 1.414 h = 0.001 0.001 y[1] (numeric) = 0.0491542802617 0.0458511088532 y[1] (closed_form) = 0.0491509197922 0.0458540284245 absolute error = 4.452e-06 relative error = 0.006623 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.857 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.817 Order of pole (three term test) = 1.223e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4125 1.415 h = 0.001 0.003 y[1] (numeric) = 0.0491377661725 0.0458975326089 y[1] (closed_form) = 0.0491344232457 0.0459004903813 absolute error = 4.464e-06 relative error = 0.006638 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.856 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.623 Order of pole (three term test) = 6.521e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = 0.0490581991806 0.045973913225 y[1] (closed_form) = 0.049054823776 0.04597679159 absolute error = 4.436e-06 relative error = 0.006598 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.857 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.88 Order of pole (three term test) = 1.506e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4136 1.422 h = 0.003 0.006 y[1] (numeric) = 0.0489335151121 0.0460364713621 y[1] (closed_form) = 0.0489301835975 0.0460392914447 absolute error = 4.365e-06 relative error = 0.006497 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.858 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.468 Order of pole (three term test) = 5.296e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = 0.0487884597591 0.0462194644716 y[1] (closed_form) = 0.0487848094288 0.0462222580805 absolute error = 4.597e-06 relative error = 0.00684 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.857 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.876 Order of pole (three term test) = 1.234e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = 0.0486315596549 0.0462953614017 y[1] (closed_form) = 0.0486281100044 0.0462982088385 absolute error = 4.473e-06 relative error = 0.006662 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.859 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.316 Order of pole (three term test) = 1.320e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4168 1.436 h = 0.001 0.001 y[1] (numeric) = 0.0485380807955 0.0463417931797 y[1] (closed_form) = 0.0485346376118 0.0463447214731 absolute error = 4.520e-06 relative error = 0.006735 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 3 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) = 1.401e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4178 1.437 h = 0.001 0.003 y[1] (numeric) = 0.0485208039629 0.0463878074589 y[1] (closed_form) = 0.048517377375 0.0463907742223 absolute error = 4.532e-06 relative error = 0.006752 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.631 Order of pole (three term test) = 1.680e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = 0.0484401202817 0.0464626035464 y[1] (closed_form) = 0.0484366631708 0.0464654904364 absolute error = 4.504e-06 relative error = 0.00671 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.884 Order of pole (three term test) = 8.564e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4189 1.444 h = 0.003 0.006 y[1] (numeric) = 0.0483146816061 0.0465228293461 y[1] (closed_form) = 0.0483112695746 0.0465256591801 absolute error = 4.433e-06 relative error = 0.006609 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.861 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.474 Order of pole (three term test) = 1.214e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = 0.0481668385513 0.0467028142347 y[1] (closed_form) = 0.0481631094795 0.0467056103191 absolute error = 4.661e-06 relative error = 0.006947 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.861 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.878 Order of pole (three term test) = 8.950e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.422 1.455 h = 0.0001 0.003 y[1] (numeric) = 0.048009047315 0.0467757813329 y[1] (closed_form) = 0.0480055169379 0.0467786356863 absolute error = 4.540e-06 relative error = 0.006773 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.863 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.318 Order of pole (three term test) = 2.600e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4221 1.458 h = 0.001 0.001 y[1] (numeric) = 0.0479150185369 0.0468204650835 y[1] (closed_form) = 0.0479114927347 0.046823400143 absolute error = 4.588e-06 relative error = 0.006848 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.864 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.82 Order of pole (three term test) = 1.233e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4231 1.459 h = 0.001 0.003 y[1] (numeric) = 0.0478969912136 0.0468660537488 y[1] (closed_form) = 0.0478934810567 0.0468690275187 absolute error = 4.600e-06 relative error = 0.006865 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.863 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.638 Order of pole (three term test) = 1.715e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=951.8MB, alloc=44.3MB, time=11.92 x[1] = 2.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = 0.0478152315706 0.0469392452787 y[1] (closed_form) = 0.0478116928498 0.0469421387677 absolute error = 4.571e-06 relative error = 0.006822 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.863 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.888 Order of pole (three term test) = 9.828e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4242 1.466 h = 0.003 0.006 y[1] (numeric) = 0.047689094985 0.0469971298817 y[1] (closed_form) = 0.0476856024922 0.0469999675697 absolute error = 4.500e-06 relative error = 0.006721 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.865 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.479 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = 0.0475385440481 0.0471740532878 y[1] (closed_form) = 0.0475347364918 0.047176850036 absolute error = 4.724e-06 relative error = 0.007054 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.864 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.881 Order of pole (three term test) = 8.220e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = 0.047379932711 0.0472440809636 y[1] (closed_form) = 0.0473763217458 0.0472469403433 absolute error = 4.606e-06 relative error = 0.006884 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.866 Order of pole (given) = 3 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) = 1.332e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4274 1.48 h = 0.001 0.001 y[1] (numeric) = 0.0472853964351 0.0472870105879 y[1] (closed_form) = 0.0472817881661 0.0472899504695 absolute error = 4.654e-06 relative error = 0.00696 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.867 Order of pole (given) = 3 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) = 1.318e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = 0.047266631281 0.0473321579314 y[1] (closed_form) = 0.0472630377047 0.0473351367351 absolute error = 4.668e-06 relative error = 0.006978 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.866 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.94 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4285 1.485 h = 0.003 0.006 y[1] (numeric) = 0.0471399697064 0.0473881215074 y[1] (closed_form) = 0.047136420942 0.04739093822 absolute error = 4.531e-06 relative error = 0.006778 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.868 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.485 Order of pole (three term test) = 8.088e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = 0.0469871899988 0.047562338051 y[1] (closed_form) = 0.0469833281148 0.0475651077348 absolute error = 4.752e-06 relative error = 0.007108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.867 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.883 Order of pole (three term test) = 1.520e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = 0.0468279647067 0.0476298208703 y[1] (closed_form) = 0.04682429746 0.0476326568483 absolute error = 4.636e-06 relative error = 0.006941 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.869 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.322 Order of pole (three term test) = 8.202e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4317 1.499 h = 0.001 0.001 y[1] (numeric) = 0.046733046511 0.0476712313147 y[1] (closed_form) = 0.046729380359 0.047674147554 absolute error = 4.685e-06 relative error = 0.007017 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 3 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) = 1.299e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4327 1.5 h = 0.001 0.003 y[1] (numeric) = 0.0467136621964 0.0477159779648 y[1] (closed_form) = 0.0467100099139 0.0477189332745 absolute error = 4.698e-06 relative error = 0.007036 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.653 Order of pole (three term test) = 3.617e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = 0.0466300297395 0.0477861231792 y[1] (closed_form) = 0.0466263525462 0.0477889976284 absolute error = 4.667e-06 relative error = 0.006991 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.897 Order of pole (three term test) = 9.271e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4338 1.507 h = 0.003 0.006 y[1] (numeric) = 0.0465027733748 0.0478396267989 y[1] (closed_form) = 0.0464991444195 0.0478424478657 absolute error = 4.596e-06 relative error = 0.00689 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.872 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.491 Order of pole (three term test) = 5.882e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = 0.0463474378682 0.0480106905557 y[1] (closed_form) = 0.0463434981328 0.048013457582 absolute error = 4.814e-06 relative error = 0.007215 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.871 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.886 Order of pole (three term test) = 8.676e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = 0.0461875244669 0.0480752225115 y[1] (closed_form) = 0.0461837770545 0.0480780600376 absolute error = 4.700e-06 relative error = 0.007051 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.873 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.325 Order of pole (three term test) = 1.414e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.437 1.521 h = 0.001 0.001 y[1] (numeric) = 0.0460921776305 0.0481148713083 y[1] (closed_form) = 0.0460884294644 0.0481177887938 absolute error = 4.750e-06 relative error = 0.007129 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.874 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.825 Order of pole (three term test) = 1.337e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.438 1.522 h = 0.001 0.003 y[1] (numeric) = 0.0460720802424 0.0481591487523 y[1] (closed_form) = 0.0460683449918 0.048162105467 absolute error = 4.764e-06 relative error = 0.007148 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.874 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.662 Order of pole (three term test) = 7.896e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.439 1.525 h = 0.0001 0.004 y[1] (numeric) = 0.0459874904916 0.048227639641 y[1] (closed_form) = 0.0459837322898 0.0482305152541 absolute error = 4.732e-06 relative error = 0.007101 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.874 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.902 Order of pole (three term test) = 1.067e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=997.8MB, alloc=44.3MB, time=12.50 x[1] = 2.4391 1.529 h = 0.003 0.006 y[1] (numeric) = 0.0458596981754 0.0482787866181 y[1] (closed_form) = 0.0458559892387 0.0482816101763 absolute error = 4.661e-06 relative error = 0.007 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.875 Order of pole (given) = 3 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) = 6.055e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = 0.0457018897029 0.0484466517118 y[1] (closed_form) = 0.0456978725146 0.0484494143213 absolute error = 4.875e-06 relative error = 0.00732 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.875 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.889 Order of pole (three term test) = 8.935e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = 0.0455413588132 0.048508229159 y[1] (closed_form) = 0.0455375315252 0.0485110663856 absolute error = 4.764e-06 relative error = 0.00716 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.877 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.327 Order of pole (three term test) = 2.028e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4423 1.543 h = 0.001 0.001 y[1] (numeric) = 0.0454456255391 0.0485461137631 y[1] (closed_form) = 0.0454417956675 0.0485490305958 absolute error = 4.814e-06 relative error = 0.00724 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.878 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.827 Order of pole (three term test) = 1.405e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4433 1.544 h = 0.001 0.003 y[1] (numeric) = 0.0454248288016 0.0485899075879 y[1] (closed_form) = 0.0454210108918 0.0485928637804 absolute error = 4.829e-06 relative error = 0.007259 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.877 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.67 Order of pole (three term test) = 4.287e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = 0.0453393237013 0.0486567290533 y[1] (closed_form) = 0.0453354847965 0.0486596039607 absolute error = 4.796e-06 relative error = 0.007211 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.878 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.906 Order of pole (three term test) = 3.932e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4444 1.551 h = 0.003 0.006 y[1] (numeric) = 0.0452110517385 0.0487055169377 y[1] (closed_form) = 0.0452072630824 0.0487083411399 absolute error = 4.725e-06 relative error = 0.007111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.879 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.504 Order of pole (three term test) = 1.872e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = 0.0450508540128 0.0488701401064 y[1] (closed_form) = 0.045046759818 0.048872896561 absolute error = 4.936e-06 relative error = 0.007426 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.879 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.892 Order of pole (three term test) = 4.605e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = 0.0448897759852 0.0489287614428 y[1] (closed_form) = 0.0448858691631 0.0489315965403 absolute error = 4.827e-06 relative error = 0.00727 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.881 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.329 Order of pole (three term test) = 4.481e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4476 1.565 h = 0.001 0.001 y[1] (numeric) = 0.044793698324 0.0489648805309 y[1] (closed_form) = 0.0447897871085 0.0489677948306 absolute error = 4.878e-06 relative error = 0.00735 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.882 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.829 Order of pole (three term test) = 1.420e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4486 1.566 h = 0.001 0.003 y[1] (numeric) = 0.0447722163002 0.049008176793 y[1] (closed_form) = 0.0447683160943 0.0490111305553 absolute error = 4.892e-06 relative error = 0.00737 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.881 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.679 Order of pole (three term test) = 7.128e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = 0.0446858380028 0.0490733150194 y[1] (closed_form) = 0.0446819187527 0.0490761873699 absolute error = 4.859e-06 relative error = 0.007321 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.882 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.911 Order of pole (three term test) = 1.036e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4497 1.573 h = 0.003 0.006 y[1] (numeric) = 0.0445571424653 0.049119742985 y[1] (closed_form) = 0.0445532744036 0.0491225660009 absolute error = 4.789e-06 relative error = 0.007221 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.883 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.51 Order of pole (three term test) = 7.271e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = 0.0443946399839 0.0492810835947 y[1] (closed_form) = 0.0443904692755 0.0492838321789 absolute error = 4.995e-06 relative error = 0.007531 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.883 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.895 Order of pole (three term test) = 1.573e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = 0.0442330848296 0.0493367492385 y[1] (closed_form) = 0.0442290988655 0.0493395803968 absolute error = 4.889e-06 relative error = 0.007378 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.885 Order of pole (given) = 3 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) = 1.549e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4529 1.587 h = 0.001 0.001 y[1] (numeric) = 0.0441367046392 0.0493711026956 y[1] (closed_form) = 0.0441327124933 0.0493740126028 absolute error = 4.940e-06 relative error = 0.00746 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.886 Order of pole (given) = 3 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) = 2.931e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = 0.0441145517131 0.04941388793 y[1] (closed_form) = 0.044110569627 0.0494168373749 absolute error = 4.955e-06 relative error = 0.007481 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.885 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.99 Order of pole (three term test) = 1.274e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.454 1.592 h = 0.003 0.006 y[1] (numeric) = 0.0439855548982 0.0494583859 y[1] (closed_form) = 0.0439816342138 0.0494611822952 absolute error = 4.816e-06 relative error = 0.007276 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.887 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.517 Order of pole (three term test) = 6.660e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1043.8MB, alloc=44.3MB, time=13.08 x[1] = 2.457 1.598 h = 0.0001 0.005 y[1] (numeric) = 0.043821176463 0.0496168443952 y[1] (closed_form) = 0.0438169558386 0.0496195607386 absolute error = 5.019e-06 relative error = 0.007582 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.887 Order of pole (given) = 3 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) = 1.094e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = 0.0436593015331 0.0496699631797 y[1] (closed_form) = 0.0436552632675 0.0496727653703 absolute error = 4.915e-06 relative error = 0.007433 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.889 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.334 Order of pole (three term test) = 7.940e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4572 1.606 h = 0.001 0.001 y[1] (numeric) = 0.0435627152891 0.0497027947306 y[1] (closed_form) = 0.043558669327 0.0497056752205 absolute error = 4.967e-06 relative error = 0.007515 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 3 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) = 7.551e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4582 1.607 h = 0.001 0.003 y[1] (numeric) = 0.0435400029186 0.0497451219249 y[1] (closed_form) = 0.043535966201 0.0497480419838 absolute error = 4.982e-06 relative error = 0.007536 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.889 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.697 Order of pole (three term test) = 1.695e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = 0.0434521328974 0.049807086438 y[1] (closed_form) = 0.0434480807445 0.0498099250217 absolute error = 4.947e-06 relative error = 0.007485 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.922 Order of pole (three term test) = 5.393e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4593 1.614 h = 0.003 0.006 y[1] (numeric) = 0.0433228254622 0.0498491229483 y[1] (closed_form) = 0.0433188261112 0.0498519148074 absolute error = 4.877e-06 relative error = 0.007385 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.891 Order of pole (given) = 3 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) = 6.847e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = 0.0431563016728 0.0500042313209 y[1] (closed_form) = 0.0431520055922 0.0500069366738 absolute error = 5.077e-06 relative error = 0.007686 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.891 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.901 Order of pole (three term test) = 1.882e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = 0.0429940787005 0.0500544013006 y[1] (closed_form) = 0.0429899621741 0.0500571962478 absolute error = 4.976e-06 relative error = 0.007541 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.893 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.337 Order of pole (three term test) = 1.641e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4625 1.628 h = 0.001 0.001 y[1] (numeric) = 0.0428972671325 0.0500854706626 y[1] (closed_form) = 0.0428931411662 0.050088343367 absolute error = 5.028e-06 relative error = 0.007624 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.894 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.835 Order of pole (three term test) = 3.123e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4635 1.629 h = 0.001 0.003 y[1] (numeric) = 0.0428739115617 0.0501272632523 y[1] (closed_form) = 0.0428697938972 0.05013017555 absolute error = 5.043e-06 relative error = 0.007646 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.894 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.706 Order of pole (three term test) = 2.174e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = 0.0427852897879 0.0501875125666 y[1] (closed_form) = 0.0427811586125 0.0501903434218 absolute error = 5.008e-06 relative error = 0.007594 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.894 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.927 Order of pole (three term test) = 5.576e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4646 1.636 h = 0.003 0.006 y[1] (numeric) = 0.0426557173687 0.050227196244 y[1] (closed_form) = 0.0426516398069 0.0502299817948 absolute error = 4.938e-06 relative error = 0.007494 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.896 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.531 Order of pole (three term test) = 7.082e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = 0.0424871344108 0.0503789214208 y[1] (closed_form) = 0.0424827634938 0.0503816141406 absolute error = 5.134e-06 relative error = 0.00779 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.895 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.904 Order of pole (three term test) = 5.233e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = 0.0423246320509 0.050426148639 y[1] (closed_form) = 0.042320437794 0.0504289345981 absolute error = 5.035e-06 relative error = 0.007648 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.897 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.339 Order of pole (three term test) = 1.868e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4678 1.65 h = 0.001 0.001 y[1] (numeric) = 0.0422276362328 0.0504554590635 y[1] (closed_form) = 0.0422234308183 0.0504583221917 absolute error = 5.088e-06 relative error = 0.007733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.899 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.837 Order of pole (three term test) = 1.616e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4688 1.651 h = 0.001 0.003 y[1] (numeric) = 0.0422036526543 0.0504967049951 y[1] (closed_form) = 0.0421994546042 0.0504996077139 absolute error = 5.104e-06 relative error = 0.007755 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.898 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.716 Order of pole (three term test) = 3.870e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = 0.0421143216462 0.0505552302141 y[1] (closed_form) = 0.0421101119967 0.0505580515774 absolute error = 5.068e-06 relative error = 0.007702 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.898 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.933 Order of pole (three term test) = 1.154e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4699 1.658 h = 0.003 0.006 y[1] (numeric) = 0.0419845389009 0.0505925663049 y[1] (closed_form) = 0.0419803836317 0.0505953437985 absolute error = 4.998e-06 relative error = 0.007602 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.539 Order of pole (three term test) = 7.331e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1089.7MB, alloc=44.3MB, time=13.66 x[1] = 2.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = 0.0418139833798 0.0507408778542 y[1] (closed_form) = 0.0418095382883 0.0507435563262 absolute error = 5.190e-06 relative error = 0.007893 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.907 Order of pole (three term test) = 1.212e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.473 1.669 h = 0.0001 0.003 y[1] (numeric) = 0.0416512696993 0.0507851702629 y[1] (closed_form) = 0.0416469982886 0.0507879455147 absolute error = 5.094e-06 relative error = 0.007755 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.902 Order of pole (given) = 3 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) = 5.277e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4731 1.672 h = 0.001 0.001 y[1] (numeric) = 0.0415541303627 0.0508127261444 y[1] (closed_form) = 0.041549846104 0.0508155779323 absolute error = 5.147e-06 relative error = 0.007841 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.903 Order of pole (given) = 3 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) = 1.707e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4741 1.673 h = 0.001 0.003 y[1] (numeric) = 0.041529534218 0.0508534138677 y[1] (closed_form) = 0.0415252563918 0.0508563052171 absolute error = 5.163e-06 relative error = 0.007864 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.903 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.727 Order of pole (three term test) = 7.235e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = 0.0414395364856 0.050910207353 y[1] (closed_form) = 0.0414352489576 0.0509130174873 absolute error = 5.126e-06 relative error = 0.007809 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.903 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.939 Order of pole (three term test) = 8.456e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4752 1.68 h = 0.003 0.006 y[1] (numeric) = 0.0413095975885 0.050945202618 y[1] (closed_form) = 0.041305365162 0.0509479703302 absolute error = 5.057e-06 relative error = 0.00771 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.905 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.546 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = 0.0411371564365 0.0510900727443 y[1] (closed_form) = 0.0411326378734 0.0510927353825 absolute error = 5.245e-06 relative error = 0.007996 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.905 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.911 Order of pole (three term test) = 5.616e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = 0.0409742988543 0.05113144017 y[1] (closed_form) = 0.0409699509114 0.0511342030222 absolute error = 5.152e-06 relative error = 0.007862 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.907 Order of pole (given) = 3 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) = 3.647e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4784 1.694 h = 0.001 0.001 y[1] (numeric) = 0.0408770563526 0.0511572470258 y[1] (closed_form) = 0.0408726938998 0.0511600857375 absolute error = 5.205e-06 relative error = 0.007948 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.908 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.841 Order of pole (three term test) = 5.205e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = 0.0408518633123 0.0511973654987 y[1] (closed_form) = 0.040847506367 0.0512002437167 absolute error = 5.222e-06 relative error = 0.007972 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.907 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.06 Order of pole (three term test) = 1.509e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4795 1.699 h = 0.003 0.006 y[1] (numeric) = 0.0407218402126 0.051230452347 y[1] (closed_form) = 0.0407175594515 0.0512331884754 absolute error = 5.080e-06 relative error = 0.007763 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.909 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.554 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = 0.0405478871632 0.0513723189113 y[1] (closed_form) = 0.0405433236255 0.0513749449162 absolute error = 5.265e-06 relative error = 0.008045 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.909 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.914 Order of pole (three term test) = 1.643e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = 0.0403849938129 0.051411177248 y[1] (closed_form) = 0.0403805981602 0.0514139062987 absolute error = 5.174e-06 relative error = 0.007914 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.911 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.347 Order of pole (three term test) = 8.435e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4827 1.713 h = 0.001 0.001 y[1] (numeric) = 0.0402877152338 0.0514354832779 y[1] (closed_form) = 0.0402833036732 0.0514382875523 absolute error = 5.227e-06 relative error = 0.008001 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.912 Order of pole (given) = 3 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) = 1.804e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4837 1.714 h = 0.001 0.003 y[1] (numeric) = 0.0402620280659 0.0514750964554 y[1] (closed_form) = 0.0402576212237 0.0514779401571 absolute error = 5.245e-06 relative error = 0.008026 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.912 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.747 Order of pole (three term test) = 7.903e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = 0.0401709234397 0.0515286447753 y[1] (closed_form) = 0.0401665103794 0.0515314076848 absolute error = 5.207e-06 relative error = 0.007969 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.912 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.95 Order of pole (three term test) = 6.415e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4848 1.721 h = 0.003 0.006 y[1] (numeric) = 0.0400408639379 0.0515593070119 y[1] (closed_form) = 0.0400365071829 0.0515620302282 absolute error = 5.138e-06 relative error = 0.00787 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.914 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.562 Order of pole (three term test) = 8.151e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = 0.0398651878327 0.0516976884554 y[1] (closed_form) = 0.0398605522536 0.051700295766 absolute error = 5.319e-06 relative error = 0.008147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.914 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.918 Order of pole (three term test) = 1.348e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1135.7MB, alloc=44.3MB, time=14.23 x[1] = 2.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = 0.0397022739393 0.0517336457399 y[1] (closed_form) = 0.0396978030461 0.0517363593267 absolute error = 5.230e-06 relative error = 0.00802 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.916 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.35 Order of pole (three term test) = 6.193e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.488 1.735 h = 0.001 0.001 y[1] (numeric) = 0.039604966061 0.0517562163931 y[1] (closed_form) = 0.0396004776549 0.0517590044495 absolute error = 5.284e-06 relative error = 0.008108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.917 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.846 Order of pole (three term test) = 3.728e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.489 1.736 h = 0.001 0.003 y[1] (numeric) = 0.0395787118203 0.0517952413308 y[1] (closed_form) = 0.0395742272226 0.0517980687121 absolute error = 5.301e-06 relative error = 0.008133 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.917 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.758 Order of pole (three term test) = 5.804e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.49 1.739 h = 0.0001 0.004 y[1] (numeric) = 0.0394870617025 0.0518470434207 y[1] (closed_form) = 0.0394825727335 0.051849790298 absolute error = 5.263e-06 relative error = 0.008075 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.917 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.956 Order of pole (three term test) = 6.663e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4901 1.743 h = 0.003 0.006 y[1] (numeric) = 0.0393569977985 0.0518753929023 y[1] (closed_form) = 0.0393525657261 0.0518781015607 absolute error = 5.194e-06 relative error = 0.007977 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.919 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.57 Order of pole (three term test) = 8.468e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = 0.0391796859721 0.0520102689099 y[1] (closed_form) = 0.0391749791637 0.0520128560296 absolute error = 5.371e-06 relative error = 0.008248 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.919 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.922 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = 0.039016816763 0.0520433401145 y[1] (closed_form) = 0.0390122713725 0.0520460366297 absolute error = 5.285e-06 relative error = 0.008125 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.921 Order of pole (given) = 3 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) = 7.339e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4933 1.757 h = 0.001 0.001 y[1] (numeric) = 0.0389195186547 0.0520641839924 y[1] (closed_form) = 0.0389149541782 0.0520669541831 absolute error = 5.339e-06 relative error = 0.008214 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.922 Order of pole (given) = 3 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) = 4.332e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4943 1.758 h = 0.001 0.003 y[1] (numeric) = 0.0388927135578 0.0521026111225 y[1] (closed_form) = 0.0388881519888 0.0521054205108 absolute error = 5.357e-06 relative error = 0.00824 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.922 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.769 Order of pole (three term test) = 8.095e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = 0.0388005600219 0.0521526640932 y[1] (closed_form) = 0.0387959959077 0.0521553933154 absolute error = 5.318e-06 relative error = 0.008181 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.922 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.963 Order of pole (three term test) = 1.392e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4954 1.765 h = 0.003 0.006 y[1] (numeric) = 0.0386705435725 0.0521787131442 y[1] (closed_form) = 0.0386660369011 0.0521814056285 absolute error = 5.250e-06 relative error = 0.008083 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.924 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.579 Order of pole (three term test) = 1.761e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = 0.0384916833397 0.0523100659821 y[1] (closed_form) = 0.0384869061499 0.0523126314475 absolute error = 5.422e-06 relative error = 0.008349 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.924 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.925 Order of pole (three term test) = 3.258e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = 0.0383289231799 0.0523402678029 y[1] (closed_form) = 0.0383243040754 0.0523429456701 absolute error = 5.339e-06 relative error = 0.00823 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.926 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.357 Order of pole (three term test) = 4.735e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4986 1.779 h = 0.001 0.001 y[1] (numeric) = 0.0382316734041 0.0523593945402 y[1] (closed_form) = 0.0382270336735 0.0523621452506 absolute error = 5.394e-06 relative error = 0.00832 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.927 Order of pole (given) = 3 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) = 4.507e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4996 1.78 h = 0.001 0.003 y[1] (numeric) = 0.0382043338245 0.0523972148133 y[1] (closed_form) = 0.03819969611 0.0524000045698 absolute error = 5.412e-06 relative error = 0.008346 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.927 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.781 Order of pole (three term test) = 1.431e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = 0.038111718737 0.0524455169713 y[1] (closed_form) = 0.0381070802815 0.0524482269483 absolute error = 5.372e-06 relative error = 0.008286 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.927 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.969 Order of pole (three term test) = 1.442e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5007 1.787 h = 0.003 0.006 y[1] (numeric) = 0.0379818008989 0.0524692792804 y[1] (closed_form) = 0.0379772203871 0.0524719540054 absolute error = 5.304e-06 relative error = 0.008189 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.929 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.587 Order of pole (three term test) = 1.296e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = 0.0378014794681 0.0525970937745 y[1] (closed_form) = 0.0377966327791 0.0525996361561 absolute error = 5.473e-06 relative error = 0.00845 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.929 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.929 Order of pole (three term test) = 2.714e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1181.7MB, alloc=44.3MB, time=14.81 x[1] = 2.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = 0.03763889181 0.0526244445875 y[1] (closed_form) = 0.0376341998132 0.0526271022633 absolute error = 5.392e-06 relative error = 0.008335 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.931 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.36 Order of pole (three term test) = 3.118e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5039 1.801 h = 0.001 0.001 y[1] (numeric) = 0.037541728392 0.0526418648269 y[1] (closed_form) = 0.0375370142629 0.0526445944765 absolute error = 5.447e-06 relative error = 0.008425 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.933 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.853 Order of pole (three term test) = 2.968e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = 0.0375138708409 0.0526790697132 y[1] (closed_form) = 0.0375091578473 0.0526818382336 absolute error = 5.466e-06 relative error = 0.008452 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.932 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.13 Order of pole (three term test) = 7.304e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.505 1.806 h = 0.003 0.006 y[1] (numeric) = 0.0373840746623 0.0527009732621 y[1] (closed_form) = 0.0373794506057 0.0527036121941 absolute error = 5.324e-06 relative error = 0.00824 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.934 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.596 Order of pole (three term test) = 1.024e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.508 1.812 h = 0.0001 0.005 y[1] (numeric) = 0.0372026075193 0.0528257158566 y[1] (closed_form) = 0.0371977211769 0.0528282180425 absolute error = 5.490e-06 relative error = 0.008497 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.934 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.933 Order of pole (three term test) = 1.492e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = 0.0370402520557 0.0528506316476 y[1] (closed_form) = 0.0370355174072 0.0528532514841 absolute error = 5.411e-06 relative error = 0.008384 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.936 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.363 Order of pole (three term test) = 5.118e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5082 1.82 h = 0.001 0.001 y[1] (numeric) = 0.0369432131267 0.0528665938975 y[1] (closed_form) = 0.0369384550885 0.0528692849135 absolute error = 5.466e-06 relative error = 0.008476 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.938 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.855 Order of pole (three term test) = 4.872e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5092 1.821 h = 0.001 0.003 y[1] (numeric) = 0.0369149304956 0.0529032567452 y[1] (closed_form) = 0.0369101728462 0.0529059864523 absolute error = 5.485e-06 relative error = 0.008503 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.937 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.804 Order of pole (three term test) = 4.293e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = 0.0368215879795 0.0529482962338 y[1] (closed_form) = 0.0368168328766 0.052950947027 absolute error = 5.444e-06 relative error = 0.008441 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.938 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.982 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5103 1.828 h = 0.003 0.006 y[1] (numeric) = 0.0366920140204 0.0529678469874 y[1] (closed_form) = 0.0366873176564 0.052970465306 absolute error = 5.377e-06 relative error = 0.008345 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.939 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.605 Order of pole (three term test) = 1.011e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = 0.0365092474936 0.0530890307582 y[1] (closed_form) = 0.0365042933959 0.0530915073047 absolute error = 5.539e-06 relative error = 0.008596 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.94 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.937 Order of pole (three term test) = 2.280e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = 0.0363471797436 0.0531111347807 y[1] (closed_form) = 0.0363423738473 0.0531137316548 absolute error = 5.463e-06 relative error = 0.008488 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.942 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.366 Order of pole (three term test) = 8.606e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5135 1.842 h = 0.001 0.001 y[1] (numeric) = 0.0362502962467 0.053125413364 y[1] (closed_form) = 0.0362454655207 0.0531280804837 absolute error = 5.518e-06 relative error = 0.00858 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.943 Order of pole (given) = 3 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) = 5.082e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5145 1.843 h = 0.001 0.003 y[1] (numeric) = 0.0362215267591 0.0531614465348 y[1] (closed_form) = 0.0362166955627 0.0531641521278 absolute error = 5.537e-06 relative error = 0.008608 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.943 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.816 Order of pole (three term test) = 4.478e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = 0.0361278409557 0.0532047373001 y[1] (closed_form) = 0.0361230140386 0.0532073644981 absolute error = 5.496e-06 relative error = 0.008545 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.943 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.989 Order of pole (three term test) = 8.132e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5156 1.85 h = 0.003 0.006 y[1] (numeric) = 0.0359985075258 0.0532220482668 y[1] (closed_form) = 0.035993739721 0.0532246444813 absolute error = 5.429e-06 relative error = 0.008449 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.945 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.614 Order of pole (three term test) = 1.463e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = 0.03581452803 0.0533396652082 y[1] (closed_form) = 0.0358095071489 0.0533421147874 absolute error = 5.587e-06 relative error = 0.008695 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.945 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.941 Order of pole (three term test) = 7.663e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = 0.0356528085567 0.0533589803802 y[1] (closed_form) = 0.0356479323364 0.0533615528478 absolute error = 5.513e-06 relative error = 0.008591 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.948 Order of pole (given) = 3 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) = 7.804e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1227.7MB, alloc=44.3MB, time=15.38 x[1] = 2.5188 1.864 h = 0.001 0.001 y[1] (numeric) = 0.0355561168142 0.0533715886662 y[1] (closed_form) = 0.0355512143607 0.0533742304126 absolute error = 5.569e-06 relative error = 0.008684 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.949 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.86 Order of pole (three term test) = 1.678e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5198 1.865 h = 0.001 0.003 y[1] (numeric) = 0.0355268772683 0.0534069851155 y[1] (closed_form) = 0.0355219734979 0.0534096650953 absolute error = 5.588e-06 relative error = 0.008712 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.948 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.829 Order of pole (three term test) = 6.902e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = 0.035432888883 0.053448529906 y[1] (closed_form) = 0.0354279910972 0.0534511320537 absolute error = 5.546e-06 relative error = 0.008649 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.949 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.997 Order of pole (three term test) = 8.491e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5209 1.872 h = 0.003 0.006 y[1] (numeric) = 0.0353038440646 0.0534636196937 y[1] (closed_form) = 0.0352990057206 0.053466192348 absolute error = 5.480e-06 relative error = 0.008553 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.951 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.624 Order of pole (three term test) = 1.080e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = 0.0351187375927 0.0535776642451 y[1] (closed_form) = 0.0351136509287 0.053580085566 absolute error = 5.634e-06 relative error = 0.008794 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.951 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.945 Order of pole (three term test) = 1.790e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.524 1.883 h = 0.0001 0.003 y[1] (numeric) = 0.0349574258726 0.0535942149841 y[1] (closed_form) = 0.0349524802853 0.0535967616371 absolute error = 5.563e-06 relative error = 0.008694 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.953 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.373 Order of pole (three term test) = 1.841e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5241 1.886 h = 0.001 0.001 y[1] (numeric) = 0.034860961565 0.0536051672429 y[1] (closed_form) = 0.0348559883783 0.0536077821767 absolute error = 5.619e-06 relative error = 0.008787 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.955 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.863 Order of pole (three term test) = 6.507e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5251 1.887 h = 0.001 0.003 y[1] (numeric) = 0.0348312688271 0.0536399204417 y[1] (closed_form) = 0.0348262934898 0.0536425733476 absolute error = 5.638e-06 relative error = 0.008816 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.954 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.842 Order of pole (three term test) = 6.907e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = 0.0347370181827 0.0536797231073 y[1] (closed_form) = 0.0347320505071 0.0536822987865 absolute error = 5.596e-06 relative error = 0.008752 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.955 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.004 Order of pole (three term test) = 1.255e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5262 1.894 h = 0.003 0.006 y[1] (numeric) = 0.034608309182 0.0536926115078 y[1] (closed_form) = 0.0346034012341 0.0536951591816 absolute error = 5.530e-06 relative error = 0.008657 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.957 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.633 Order of pole (three term test) = 1.129e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = 0.0344221612281 0.0538030805177 y[1] (closed_form) = 0.0344170098093 0.0538054723265 absolute error = 5.680e-06 relative error = 0.008892 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.957 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.95 Order of pole (three term test) = 1.183e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = 0.0342613156118 0.0538168926908 y[1] (closed_form) = 0.0342563016458 0.0538194121584 absolute error = 5.611e-06 relative error = 0.008796 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.959 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.376 Order of pole (three term test) = 6.086e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5294 1.908 h = 0.001 0.001 y[1] (numeric) = 0.0341651137545 0.0538262040638 y[1] (closed_form) = 0.0341600708609 0.0538287907843 absolute error = 5.668e-06 relative error = 0.00889 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.866 Order of pole (three term test) = 1.296e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = 0.0341349847407 0.0538603079969 y[1] (closed_form) = 0.0341299388765 0.0538629324073 absolute error = 5.688e-06 relative error = 0.008919 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.2 Order of pole (three term test) = 4.512e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5305 1.913 h = 0.003 0.006 y[1] (numeric) = 0.0340065881924 0.0538714122058 y[1] (closed_form) = 0.0340016418485 0.0538739206741 absolute error = 5.546e-06 relative error = 0.008706 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.962 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.642 Order of pole (three term test) = 1.314e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = 0.0338196543898 0.053978791765 y[1] (closed_form) = 0.0338144688694 0.0539811406614 absolute error = 5.693e-06 relative error = 0.008937 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.962 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.954 Order of pole (three term test) = 1.233e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = 0.0336592879945 0.0539902749315 y[1] (closed_form) = 0.0336542367536 0.0539927533516 absolute error = 5.627e-06 relative error = 0.008844 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.965 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.38 Order of pole (three term test) = 1.203e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5337 1.927 h = 0.001 0.001 y[1] (numeric) = 0.0335633588455 0.0539981903337 y[1] (closed_form) = 0.0335582775772 0.0540007350841 absolute error = 5.683e-06 relative error = 0.008938 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.966 Order of pole (given) = 3 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) = 3.819e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5347 1.928 h = 0.001 0.003 y[1] (numeric) = 0.0335328756936 0.0540317260512 y[1] (closed_form) = 0.0335277907638 0.0540343082228 absolute error = 5.703e-06 relative error = 0.008968 % Correct digits = 4 memory used=1273.8MB, alloc=44.3MB, time=15.96 Radius of convergence (given) for eq 1 = 3.966 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.867 Order of pole (three term test) = 2.027e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = 0.0334382635159 0.0540682989413 y[1] (closed_form) = 0.0334331892804 0.054070805141 absolute error = 5.659e-06 relative error = 0.008902 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.966 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.018 Order of pole (three term test) = 4.836e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5358 1.935 h = 0.003 0.006 y[1] (numeric) = 0.0333103275201 0.0540771529242 y[1] (closed_form) = 0.0333053134127 0.0540796338783 absolute error = 5.594e-06 relative error = 0.008808 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.968 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.652 Order of pole (three term test) = 3.691e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = 0.0331225097101 0.0541809583556 y[1] (closed_form) = 0.0331172614289 0.0541832755213 absolute error = 5.737e-06 relative error = 0.009034 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.968 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.958 Order of pole (three term test) = 2.041e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = 0.032962714526 0.0541897554355 y[1] (closed_form) = 0.0329575968396 0.0541922042323 absolute error = 5.673e-06 relative error = 0.008945 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.971 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.383 Order of pole (three term test) = 1.260e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.539 1.949 h = 0.001 0.001 y[1] (numeric) = 0.0328671109326 0.0541960607397 y[1] (closed_form) = 0.0328619619631 0.0541985747882 absolute error = 5.730e-06 relative error = 0.00904 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.972 Order of pole (given) = 3 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) = 6.325e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.54 1.95 h = 0.001 0.003 y[1] (numeric) = 0.0328362231134 0.0542289375555 y[1] (closed_form) = 0.0328310696894 0.0542314887061 absolute error = 5.750e-06 relative error = 0.009071 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.972 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.881 Order of pole (three term test) = 5.575e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.541 1.953 h = 0.0001 0.004 y[1] (numeric) = 0.0327414615433 0.05426378567 y[1] (closed_form) = 0.0327363204026 0.0542662615683 absolute error = 5.706e-06 relative error = 0.009004 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.972 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.026 Order of pole (three term test) = 5.065e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5411 1.957 h = 0.003 0.006 y[1] (numeric) = 0.0326139910245 0.0542705015889 y[1] (closed_form) = 0.0326089101764 0.0542729537148 absolute error = 5.642e-06 relative error = 0.00891 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.974 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.663 Order of pole (three term test) = 1.289e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = 0.0324253728428 0.0543707364016 y[1] (closed_form) = 0.0324200628979 0.0543730206927 absolute error = 5.780e-06 relative error = 0.009131 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.974 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.963 Order of pole (three term test) = 2.183e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = 0.0322662037861 0.0543768771123 y[1] (closed_form) = 0.032261020724 0.0543792950248 absolute error = 5.719e-06 relative error = 0.009045 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.977 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.387 Order of pole (three term test) = 6.959e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5443 1.971 h = 0.001 0.001 y[1] (numeric) = 0.0321709587324 0.0543815897763 y[1] (closed_form) = 0.0321657431709 0.0543840718363 absolute error = 5.776e-06 relative error = 0.009142 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.978 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.874 Order of pole (three term test) = 9.376e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5453 1.972 h = 0.001 0.003 y[1] (numeric) = 0.0321396832047 0.054413803124 y[1] (closed_form) = 0.0321344624108 0.0544163219481 absolute error = 5.797e-06 relative error = 0.009172 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.978 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.895 Order of pole (three term test) = 1.307e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = 0.0320448107803 0.054446934336 y[1] (closed_form) = 0.0320396038263 0.0544493786648 absolute error = 5.752e-06 relative error = 0.009105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.979 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.034 Order of pole (three term test) = 2.443e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5464 1.979 h = 0.003 0.006 y[1] (numeric) = 0.031917849277 0.0544515361619 y[1] (closed_form) = 0.0319127027386 0.0544539581838 absolute error = 5.688e-06 relative error = 0.009012 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.98 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.673 Order of pole (three term test) = 9.191e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = 0.0317285135855 0.0545482061107 y[1] (closed_form) = 0.0317231430957 0.0545504564223 absolute error = 5.823e-06 relative error = 0.009227 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.981 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.968 Order of pole (three term test) = 3.009e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = 0.0315700243167 0.0545517214195 y[1] (closed_form) = 0.0315647769741 0.0545541072257 absolute error = 5.764e-06 relative error = 0.009146 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.983 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.391 Order of pole (three term test) = 1.177e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5496 1.993 h = 0.001 0.001 y[1] (numeric) = 0.0314751700426 0.0545548596535 y[1] (closed_form) = 0.0314698890244 0.0545573084793 absolute error = 5.821e-06 relative error = 0.009242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.985 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.877 Order of pole (three term test) = 6.221e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5506 1.994 h = 0.001 0.003 y[1] (numeric) = 0.0314435237503 0.0545864054645 y[1] (closed_form) = 0.0314382367374 0.054588890698 absolute error = 5.842e-06 relative error = 0.009274 % Correct digits = 4 memory used=1319.8MB, alloc=44.3MB, time=16.54 Radius of convergence (given) for eq 1 = 3.984 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.909 Order of pole (three term test) = 6.130e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = 0.0313485784801 0.0546178286285 y[1] (closed_form) = 0.0313433068303 0.0546202401597 absolute error = 5.797e-06 relative error = 0.009205 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.985 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.042 Order of pole (three term test) = 1.246e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5517 2.001 h = 0.003 0.006 y[1] (numeric) = 0.0312221685224 0.0546203413163 y[1] (closed_form) = 0.0312169573705 0.0546227319973 absolute error = 5.733e-06 relative error = 0.009113 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.987 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.684 Order of pole (three term test) = 2.962e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = 0.031032197344 0.054713454354 y[1] (closed_form) = 0.0310267674482 0.0547156696207 absolute error = 5.864e-06 relative error = 0.009323 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.987 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.973 Order of pole (three term test) = 2.106e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = 0.0308744402392 0.0547143764246 y[1] (closed_form) = 0.0308691297357 0.0547167289424 absolute error = 5.808e-06 relative error = 0.009245 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.99 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.395 Order of pole (three term test) = 3.427e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5549 2.015 h = 0.001 0.001 y[1] (numeric) = 0.0307800082242 0.0547159591599 y[1] (closed_form) = 0.030774662909 0.054718373547 absolute error = 5.865e-06 relative error = 0.009343 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.991 Order of pole (given) = 3 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) = 9.797e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = 0.03074800808 0.0547468338575 y[1] (closed_form) = 0.0307426560239 0.0547492842784 absolute error = 5.886e-06 relative error = 0.009375 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.991 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.29 Order of pole (three term test) = 9.295e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.556 2.02 h = 0.003 0.006 y[1] (numeric) = 0.0306220832544 0.0547476581714 y[1] (closed_form) = 0.0306168390726 0.0547500070449 absolute error = 5.746e-06 relative error = 0.00916 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.993 Order of pole (given) = 3 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) = 1.482e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.559 2.026 h = 0.0001 0.005 y[1] (numeric) = 0.0304316722657 0.0548377112921 y[1] (closed_form) = 0.0304262139086 0.0548398817634 absolute error = 5.874e-06 relative error = 0.009366 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.993 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.977 Order of pole (three term test) = 1.719e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = 0.0302746166731 0.0548364373655 y[1] (closed_form) = 0.0302692744446 0.0548387464618 absolute error = 5.820e-06 relative error = 0.009291 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.996 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.398 Order of pole (three term test) = 8.011e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5592 2.034 h = 0.001 0.001 y[1] (numeric) = 0.0301805909492 0.0548367023916 y[1] (closed_form) = 0.0301752129779 0.0548390723376 absolute error = 5.877e-06 relative error = 0.009389 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.997 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.883 Order of pole (three term test) = 1.080e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5602 2.035 h = 0.001 0.003 y[1] (numeric) = 0.0301483077724 0.0548669929825 y[1] (closed_form) = 0.0301429224357 0.0548693986183 absolute error = 5.898e-06 relative error = 0.009421 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.997 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.937 Order of pole (three term test) = 1.064e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = 0.0300533462435 0.0548952648583 y[1] (closed_form) = 0.0300479790021 0.0548975983749 absolute error = 5.853e-06 relative error = 0.009352 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.997 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.058 Order of pole (three term test) = 1.101e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5613 2.042 h = 0.003 0.006 y[1] (numeric) = 0.0299280963772 0.0548939674758 y[1] (closed_form) = 0.029922789664 0.0548962828251 absolute error = 5.790e-06 relative error = 0.00926 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.999 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.705 Order of pole (three term test) = 1.817e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = 0.0297371999265 0.0549804851152 y[1] (closed_form) = 0.0297316843423 0.0549826186784 absolute error = 5.914e-06 relative error = 0.009461 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.982 Order of pole (three term test) = 1.180e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = 0.0295809700389 0.0549766813863 y[1] (closed_form) = 0.0295755668043 0.0549789551154 absolute error = 5.862e-06 relative error = 0.00939 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.002 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.402 Order of pole (three term test) = 1.584e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5645 2.056 h = 0.001 0.001 y[1] (numeric) = 0.0294874228282 0.0549754283023 y[1] (closed_form) = 0.0294819827908 0.0549777616938 absolute error = 5.919e-06 relative error = 0.009489 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.004 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.886 Order of pole (three term test) = 8.027e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5655 2.057 h = 0.001 0.003 y[1] (numeric) = 0.0294548171637 0.0550050426134 y[1] (closed_form) = 0.0294493690456 0.0550074112901 absolute error = 5.941e-06 relative error = 0.009521 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.003 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.952 Order of pole (three term test) = 6.408e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = 0.0293598882228 0.0550316373771 y[1] (closed_form) = 0.029354459623 0.0550339348219 absolute error = 5.895e-06 relative error = 0.009451 % Correct digits = 4 memory used=1365.7MB, alloc=44.3MB, time=17.11 Radius of convergence (given) for eq 1 = 4.004 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.066 Order of pole (three term test) = 1.501e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5666 2.064 h = 0.003 0.006 y[1] (numeric) = 0.0292353054825 0.0550283277624 y[1] (closed_form) = 0.0292299373809 0.0550306084643 absolute error = 5.833e-06 relative error = 0.00936 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.006 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.716 Order of pole (three term test) = 1.711e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = 0.0290440028302 0.0551113238717 y[1] (closed_form) = 0.0290384312067 0.0551134195751 absolute error = 5.953e-06 relative error = 0.009556 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.007 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.987 Order of pole (three term test) = 3.652e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = 0.0288886472037 0.0551050256129 y[1] (closed_form) = 0.0288831841424 0.0551072629085 absolute error = 5.903e-06 relative error = 0.009488 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.009 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.406 Order of pole (three term test) = 1.587e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5698 2.078 h = 0.001 0.001 y[1] (numeric) = 0.0287956077203 0.0551022752257 y[1] (closed_form) = 0.0287901068373 0.0551045709785 absolute error = 5.961e-06 relative error = 0.009587 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.011 Order of pole (given) = 3 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) = 1.269e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5708 2.079 h = 0.001 0.003 y[1] (numeric) = 0.0287626963017 0.0551312110524 y[1] (closed_form) = 0.02875718664 0.0551335416702 absolute error = 5.982e-06 relative error = 0.009621 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.967 Order of pole (three term test) = 1.581e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = 0.0286678356648 0.0551561410812 y[1] (closed_form) = 0.0286623469081 0.0551584013846 absolute error = 5.936e-06 relative error = 0.009549 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.011 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.075 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5719 2.086 h = 0.003 0.006 y[1] (numeric) = 0.0285439584903 0.0551508475729 y[1] (closed_form) = 0.028538530164 0.0551530925444 absolute error = 5.874e-06 relative error = 0.009459 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.013 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.728 Order of pole (three term test) = 3.449e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = 0.0283523278305 0.055230338101 y[1] (closed_form) = 0.0283467013698 0.0552323950328 absolute error = 5.991e-06 relative error = 0.00965 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.013 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.992 Order of pole (three term test) = 1.288e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.575 2.097 h = 0.0001 0.003 y[1] (numeric) = 0.0281978936509 0.0552215815724 y[1] (closed_form) = 0.0281923719606 0.055223781409 absolute error = 5.944e-06 relative error = 0.009586 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.016 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.41 Order of pole (three term test) = 1.320e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5751 2.1 h = 0.001 0.001 y[1] (numeric) = 0.0281053902958 0.0552173552855 y[1] (closed_form) = 0.0280998298062 0.0552196123576 absolute error = 6.001e-06 relative error = 0.009686 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.017 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.893 Order of pole (three term test) = 5.797e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5761 2.101 h = 0.001 0.003 y[1] (numeric) = 0.0280721897681 0.0552456108893 y[1] (closed_form) = 0.028066619819 0.0552479023914 absolute error = 6.023e-06 relative error = 0.009719 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.017 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.983 Order of pole (three term test) = 1.111e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = 0.0279774325053 0.0552688894044 y[1] (closed_form) = 0.0279718848111 0.0552711115383 absolute error = 5.976e-06 relative error = 0.009647 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.018 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.084 Order of pole (three term test) = 5.706e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5772 2.108 h = 0.003 0.006 y[1] (numeric) = 0.02785429824 0.0552616411157 y[1] (closed_form) = 0.0278488108715 0.0552638493144 absolute error = 5.915e-06 relative error = 0.009558 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.739 Order of pole (three term test) = 7.490e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = 0.027662416648 0.0553376439542 y[1] (closed_form) = 0.0276567365652 0.0553396612425 absolute error = 6.028e-06 relative error = 0.009743 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.997 Order of pole (three term test) = 1.910e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = 0.0275089497139 0.0553264663487 y[1] (closed_form) = 0.0275033706089 0.0553286277418 absolute error = 5.983e-06 relative error = 0.009683 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.023 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.415 Order of pole (three term test) = 4.398e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5804 2.122 h = 0.001 0.001 y[1] (numeric) = 0.0274170100648 0.0553207861298 y[1] (closed_form) = 0.0274113912241 0.0553230035219 absolute error = 6.041e-06 relative error = 0.009784 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.024 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.896 Order of pole (three term test) = 1.024e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = 0.0273835369702 0.0553483602305 y[1] (closed_form) = 0.0273779080069 0.0553506116033 absolute error = 6.063e-06 relative error = 0.009818 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.024 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.39 Order of pole (three term test) = 1.460e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5815 2.127 h = 0.003 0.006 y[1] (numeric) = 0.0272610402102 0.055339536676 y[1] (closed_form) = 0.0272555252599 0.0553417012642 absolute error = 5.925e-06 relative error = 0.009604 % Correct digits = 4 memory used=1411.8MB, alloc=44.3MB, time=17.68 Radius of convergence (given) for eq 1 = 4.026 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.75 Order of pole (three term test) = 8.518e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = 0.0270690446727 0.0554125514346 y[1] (closed_form) = 0.0270633417269 0.0554145228424 absolute error = 6.034e-06 relative error = 0.009784 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.027 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.002 Order of pole (three term test) = 1.478e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = 0.0269164741363 0.0553993325404 y[1] (closed_form) = 0.0269108688934 0.0554014489515 absolute error = 5.991e-06 relative error = 0.009728 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.029 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.418 Order of pole (three term test) = 1.031e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5847 2.141 h = 0.001 0.001 y[1] (numeric) = 0.026825058108 0.0553924259698 y[1] (closed_form) = 0.0268194123712 0.0553945972941 absolute error = 6.049e-06 relative error = 0.009828 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.031 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.899 Order of pole (three term test) = 4.398e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5857 2.142 h = 0.001 0.003 y[1] (numeric) = 0.0267913716854 0.055419409793 y[1] (closed_form) = 0.0267857152752 0.055421614693 absolute error = 6.071e-06 relative error = 0.009863 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.031 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.013 Order of pole (three term test) = 1.226e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = 0.026696917087 0.0554396553687 y[1] (closed_form) = 0.0266912853322 0.0554417927478 absolute error = 6.024e-06 relative error = 0.00979 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.031 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.101 Order of pole (three term test) = 1.577e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5868 2.149 h = 0.003 0.006 y[1] (numeric) = 0.0265752832187 0.0554288594958 y[1] (closed_form) = 0.0265697114831 0.0554309854945 absolute error = 5.964e-06 relative error = 0.009702 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.033 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.762 Order of pole (three term test) = 8.284e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = 0.0263831767559 0.0554984257167 y[1] (closed_form) = 0.0263774224885 0.0555003559796 absolute error = 6.069e-06 relative error = 0.009877 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.034 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.007 Order of pole (three term test) = 4.483e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = 0.0262316544787 0.0554828577564 y[1] (closed_form) = 0.0262259941308 0.0554849340164 absolute error = 6.029e-06 relative error = 0.009824 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.037 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.423 Order of pole (three term test) = 9.736e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.59 2.163 h = 0.001 0.001 y[1] (numeric) = 0.0261408509749 0.0554745398266 y[1] (closed_form) = 0.0261351492736 0.0554766697398 absolute error = 6.087e-06 relative error = 0.009925 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.038 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.903 Order of pole (three term test) = 4.641e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.591 2.164 h = 0.001 0.003 y[1] (numeric) = 0.0261069224499 0.055500841149 y[1] (closed_form) = 0.0261012094459 0.0555030041644 absolute error = 6.109e-06 relative error = 0.00996 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.038 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.029 Order of pole (three term test) = 1.447e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.592 2.167 h = 0.0001 0.004 y[1] (numeric) = 0.0260126676244 0.0555194778185 y[1] (closed_form) = 0.0260069805174 0.055521574333 absolute error = 6.061e-06 relative error = 0.009886 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.039 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.11 Order of pole (three term test) = 1.665e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5921 2.171 h = 0.003 0.006 y[1] (numeric) = 0.025891876959 0.0555068147412 y[1] (closed_form) = 0.0258862496659 0.0555089012249 absolute error = 6.002e-06 relative error = 0.009799 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.041 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.774 Order of pole (three term test) = 7.648e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = 0.0256997331584 0.0555729555415 y[1] (closed_form) = 0.0256939288137 0.0555748439015 absolute error = 6.104e-06 relative error = 0.009969 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.041 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.013 Order of pole (three term test) = 1.699e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = 0.0255493008886 0.0555550780609 y[1] (closed_form) = 0.0255435866893 0.0555571133031 absolute error = 6.066e-06 relative error = 0.00992 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.044 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.427 Order of pole (three term test) = 1.854e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5953 2.185 h = 0.001 0.001 y[1] (numeric) = 0.0254591350809 0.0555453721655 y[1] (closed_form) = 0.0254533787098 0.05554745979 absolute error = 6.123e-06 relative error = 0.01002 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.046 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.906 Order of pole (three term test) = 1.471e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5963 2.186 h = 0.001 0.003 y[1] (numeric) = 0.0254249806241 0.0555709909689 y[1] (closed_form) = 0.0254192123393 0.0555731112102 absolute error = 6.146e-06 relative error = 0.01006 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.045 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.045 Order of pole (three term test) = 6.836e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = 0.0253309579638 0.0555880349222 y[1] (closed_form) = 0.0253252167794 0.0555900897056 absolute error = 6.098e-06 relative error = 0.009982 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.046 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.119 Order of pole (three term test) = 1.760e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5974 2.193 h = 0.003 0.006 y[1] (numeric) = 0.0252110434995 0.055573536325 y[1] (closed_form) = 0.0252053618899 0.0555755824092 absolute error = 6.039e-06 relative error = 0.009896 % Correct digits = 4 memory used=1457.7MB, alloc=44.3MB, time=18.26 Radius of convergence (given) for eq 1 = 4.048 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.787 Order of pole (three term test) = 6.723e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = 0.025018934653 0.0556362765395 y[1] (closed_form) = 0.0250130814831 0.0556381222783 absolute error = 6.137e-06 relative error = 0.01006 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.049 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.018 Order of pole (three term test) = 3.351e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = 0.0248696327079 0.0556161298089 y[1] (closed_form) = 0.0248638659218 0.0556181232077 absolute error = 6.102e-06 relative error = 0.01002 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.051 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.432 Order of pole (three term test) = 1.215e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6006 2.207 h = 0.001 0.001 y[1] (numeric) = 0.0247801289173 0.0556050597815 y[1] (closed_form) = 0.0247743191821 0.0556071042823 absolute error = 6.159e-06 relative error = 0.01012 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.053 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.91 Order of pole (three term test) = 5.181e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6016 2.208 h = 0.001 0.003 y[1] (numeric) = 0.0247457645473 0.055629996472 y[1] (closed_form) = 0.0247399423059 0.0556320730928 absolute error = 6.181e-06 relative error = 0.01015 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.053 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.062 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = 0.0246520057147 0.0556454645959 y[1] (closed_form) = 0.0246462117383 0.0556474768234 absolute error = 6.133e-06 relative error = 0.01008 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.053 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.129 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6027 2.215 h = 0.003 0.006 y[1] (numeric) = 0.0245329993073 0.0556291627285 y[1] (closed_form) = 0.0245272646342 0.0556311675693 absolute error = 6.075e-06 relative error = 0.009992 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.056 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.799 Order of pole (three term test) = 1.920e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = 0.0243409963723 0.0556885288494 y[1] (closed_form) = 0.0243350956357 0.055690331288 absolute error = 6.170e-06 relative error = 0.01015 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.056 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.024 Order of pole (three term test) = 1.786e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = 0.0241928636317 0.0556661538103 y[1] (closed_form) = 0.0241870455332 0.055668104581 absolute error = 6.136e-06 relative error = 0.01011 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.059 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.436 Order of pole (three term test) = 2.072e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6059 2.229 h = 0.001 0.001 y[1] (numeric) = 0.0241040453248 0.0556537438926 y[1] (closed_form) = 0.0240981835405 0.0556557444771 absolute error = 6.194e-06 relative error = 0.01021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.061 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.913 Order of pole (three term test) = 7.751e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = 0.0240694868967 0.0556779992909 y[1] (closed_form) = 0.0240636120323 0.0556800314877 absolute error = 6.216e-06 relative error = 0.01025 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.49 Order of pole (three term test) = 8.213e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.607 2.234 h = 0.003 0.006 y[1] (numeric) = 0.0239512487092 0.0556602484943 y[1] (closed_form) = 0.0239454918607 0.0556622086859 absolute error = 6.081e-06 relative error = 0.01004 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.062 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.811 Order of pole (three term test) = 5.572e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.61 2.24 h = 0.0001 0.005 y[1] (numeric) = 0.0237594324468 0.055716735129 y[1] (closed_form) = 0.0237535142887 0.0557184913439 absolute error = 6.173e-06 relative error = 0.01019 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.063 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.029 Order of pole (three term test) = 2.597e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = 0.0236123620202 0.0556924898256 y[1] (closed_form) = 0.0236065232846 0.0556943948235 absolute error = 6.142e-06 relative error = 0.01015 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.066 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.44 Order of pole (three term test) = 5.441e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6102 2.248 h = 0.001 0.001 y[1] (numeric) = 0.0235241674522 0.0556789548056 y[1] (closed_form) = 0.0235182844449 0.055680908495 absolute error = 6.199e-06 relative error = 0.01026 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.067 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.916 Order of pole (three term test) = 1.153e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6112 2.249 h = 0.001 0.003 y[1] (numeric) = 0.0234894626433 0.0557026226787 y[1] (closed_form) = 0.0234835660832 0.0557046075289 absolute error = 6.222e-06 relative error = 0.01029 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.067 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.094 Order of pole (three term test) = 1.679e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = 0.0233962947136 0.0557152097528 y[1] (closed_form) = 0.0233904284686 0.055717132256 absolute error = 6.173e-06 relative error = 0.01022 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.068 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.147 Order of pole (three term test) = 4.628e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6123 2.256 h = 0.003 0.006 y[1] (numeric) = 0.0232790793934 0.0556956516735 y[1] (closed_form) = 0.0232732718481 0.0556975691753 absolute error = 6.116e-06 relative error = 0.01013 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 3 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) = 1.319e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = 0.0230874970426 0.0557488185192 y[1] (closed_form) = 0.0230815336794 0.0557505302888 absolute error = 6.204e-06 relative error = 0.01028 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.071 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.035 Order of pole (three term test) = 3.928e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1503.8MB, alloc=44.3MB, time=18.83 x[1] = 2.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = 0.0229416638238 0.0557224231187 y[1] (closed_form) = 0.0229357761759 0.055724284152 absolute error = 6.175e-06 relative error = 0.01025 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.074 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.445 Order of pole (three term test) = 9.519e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6155 2.27 h = 0.001 0.001 y[1] (numeric) = 0.0228541958227 0.0557075945516 y[1] (closed_form) = 0.022848263242 0.0557095029773 absolute error = 6.232e-06 relative error = 0.01035 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.075 Order of pole (given) = 3 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) = 1.366e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6165 2.271 h = 0.001 0.003 y[1] (numeric) = 0.022819325965 0.0557305839121 y[1] (closed_form) = 0.0228133792927 0.0557325229733 absolute error = 6.255e-06 relative error = 0.01039 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.075 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.112 Order of pole (three term test) = 9.933e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = 0.0227265080688 0.0557416473843 y[1] (closed_form) = 0.0227205927642 0.0557435252163 absolute error = 6.206e-06 relative error = 0.01031 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.076 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.157 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6176 2.278 h = 0.003 0.006 y[1] (numeric) = 0.022610285192 0.0557203813721 y[1] (closed_form) = 0.0226044282282 0.0557222554566 absolute error = 6.149e-06 relative error = 0.01023 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.078 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.837 Order of pole (three term test) = 2.795e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = 0.022419003682 0.0557702593077 y[1] (closed_form) = 0.0224129963833 0.055771926064 absolute error = 6.234e-06 relative error = 0.01037 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.079 Order of pole (given) = 3 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) = 2.081e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = 0.0222744424157 0.0557417563657 y[1] (closed_form) = 0.0222685071495 0.0557435727655 absolute error = 6.207e-06 relative error = 0.01034 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.082 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.45 Order of pole (three term test) = 7.309e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6208 2.292 h = 0.001 0.001 y[1] (numeric) = 0.0221877219878 0.0557256594786 y[1] (closed_form) = 0.0221817411677 0.0557275219677 absolute error = 6.264e-06 relative error = 0.01044 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.083 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.924 Order of pole (three term test) = 7.236e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6218 2.293 h = 0.001 0.003 y[1] (numeric) = 0.0221527024049 0.0557479722751 y[1] (closed_form) = 0.0221467069734 0.0557498648657 absolute error = 6.287e-06 relative error = 0.01048 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.083 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.13 Order of pole (three term test) = 1.058e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = 0.0220602632646 0.0557575314228 y[1] (closed_form) = 0.022054300214 0.0557593639181 absolute error = 6.238e-06 relative error = 0.0104 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.084 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.167 Order of pole (three term test) = 2.324e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6229 2.3 h = 0.003 0.006 y[1] (numeric) = 0.0219450602437 0.0557345915034 y[1] (closed_form) = 0.0219391551462 0.0557364214833 absolute error = 6.182e-06 relative error = 0.01032 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.086 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.85 Order of pole (three term test) = 8.888e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = 0.0217541450438 0.0557812128278 y[1] (closed_form) = 0.0217480950805 0.0557828340403 absolute error = 6.263e-06 relative error = 0.01046 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.087 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.047 Order of pole (three term test) = 6.979e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.626 2.311 h = 0.0001 0.003 y[1] (numeric) = 0.0216108890317 0.0557506453706 y[1] (closed_form) = 0.0216049074453 0.0557524165083 absolute error = 6.238e-06 relative error = 0.01043 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.455 Order of pole (three term test) = 4.318e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6261 2.314 h = 0.001 0.001 y[1] (numeric) = 0.0215249363244 0.0557333056797 y[1] (closed_form) = 0.0215189086028 0.0557351216006 absolute error = 6.295e-06 relative error = 0.01054 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.091 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.928 Order of pole (three term test) = 4.805e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6271 2.315 h = 0.001 0.003 y[1] (numeric) = 0.0214897821369 0.0557549442354 y[1] (closed_form) = 0.0214837393029 0.0557567897158 absolute error = 6.318e-06 relative error = 0.01057 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.091 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.148 Order of pole (three term test) = 9.623e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = 0.0213977496918 0.0557630188827 y[1] (closed_form) = 0.0213917402126 0.0557648054163 absolute error = 6.269e-06 relative error = 0.0105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.092 Order of pole (given) = 3 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) = 4.931e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6282 2.322 h = 0.003 0.006 y[1] (numeric) = 0.0212835927896 0.0557384394456 y[1] (closed_form) = 0.0212776408483 0.0557402246736 absolute error = 6.214e-06 relative error = 0.01041 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.094 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.864 Order of pole (three term test) = 9.429e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = 0.0210931078827 0.0557818378153 y[1] (closed_form) = 0.0210870165264 0.0557834129915 absolute error = 6.292e-06 relative error = 0.01055 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.095 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.053 Order of pole (three term test) = 2.001e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1549.7MB, alloc=44.3MB, time=19.41 x[1] = 2.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = 0.0209511889866 0.0557492492905 y[1] (closed_form) = 0.0209451623815 0.0557509745769 absolute error = 6.269e-06 relative error = 0.01053 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.098 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.459 Order of pole (three term test) = 3.055e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6314 2.336 h = 0.001 0.001 y[1] (numeric) = 0.0208660232899 0.055730692571 y[1] (closed_form) = 0.0208599500075 0.055732461333 absolute error = 6.326e-06 relative error = 0.01063 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.099 Order of pole (given) = 3 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) = 7.322e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = 0.0208307494063 0.055751659573 y[1] (closed_form) = 0.0208246605294 0.0557534573452 absolute error = 6.349e-06 relative error = 0.01067 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.099 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.6 Order of pole (three term test) = 8.978e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6325 2.341 h = 0.003 0.006 y[1] (numeric) = 0.0207174692188 0.0557257667793 y[1] (closed_form) = 0.0207115003577 0.0557275070307 absolute error = 6.217e-06 relative error = 0.01046 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.101 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.876 Order of pole (three term test) = 1.483e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = 0.0205274425994 0.0557664250138 y[1] (closed_form) = 0.02052133901 0.0557679542945 absolute error = 6.292e-06 relative error = 0.01059 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.102 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.058 Order of pole (three term test) = 1.747e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = 0.0203867224299 0.0557321483153 y[1] (closed_form) = 0.0203806804959 0.0557338277471 absolute error = 6.271e-06 relative error = 0.01057 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.105 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.464 Order of pole (three term test) = 1.140e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6357 2.355 h = 0.001 0.001 y[1] (numeric) = 0.020302263035 0.0557125745059 y[1] (closed_form) = 0.0202961740039 0.0557142962815 absolute error = 6.328e-06 relative error = 0.01067 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.107 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.935 Order of pole (three term test) = 1.537e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6367 2.356 h = 0.001 0.003 y[1] (numeric) = 0.0202669058402 0.0557329646903 y[1] (closed_form) = 0.0202608008216 0.0557347149925 absolute error = 6.351e-06 relative error = 0.01071 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.106 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.182 Order of pole (three term test) = 1.309e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = 0.0201757189118 0.0557383371279 y[1] (closed_form) = 0.020169648942 0.0557400306651 absolute error = 6.302e-06 relative error = 0.01063 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.107 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.197 Order of pole (three term test) = 1.139e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6378 2.363 h = 0.003 0.006 y[1] (numeric) = 0.0200635931165 0.055710812689 y[1] (closed_form) = 0.0200575798275 0.0557125071047 absolute error = 6.247e-06 relative error = 0.01055 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.89 Order of pole (three term test) = 4.980e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = 0.0198741113764 0.0557483147162 y[1] (closed_form) = 0.0198679687622 0.0557497971576 absolute error = 6.319e-06 relative error = 0.01068 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.111 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.064 Order of pole (three term test) = 1.174e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = 0.0197347832682 0.055712099087 y[1] (closed_form) = 0.019728698747 0.0557137316911 absolute error = 6.300e-06 relative error = 0.01066 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.113 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.469 Order of pole (three term test) = 8.562e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.641 2.377 h = 0.001 0.001 y[1] (numeric) = 0.0196511441927 0.0556913570054 y[1] (closed_form) = 0.0196450121043 0.0556930306463 absolute error = 6.356e-06 relative error = 0.01076 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.115 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.939 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.642 2.378 h = 0.001 0.003 y[1] (numeric) = 0.0196156944073 0.0557110817387 y[1] (closed_form) = 0.0196095458847 0.0557127833454 absolute error = 6.380e-06 relative error = 0.0108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.115 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.201 Order of pole (three term test) = 5.698e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.643 2.381 h = 0.0001 0.004 y[1] (numeric) = 0.0195249894615 0.0557150294321 y[1] (closed_form) = 0.0195188768494 0.055716675456 absolute error = 6.330e-06 relative error = 0.01072 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.116 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.208 Order of pole (three term test) = 6.564e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6431 2.385 h = 0.003 0.006 y[1] (numeric) = 0.0194139781793 0.0556859657814 y[1] (closed_form) = 0.0194079217594 0.0556876138263 absolute error = 6.277e-06 relative error = 0.01064 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.118 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.904 Order of pole (three term test) = 8.369e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = 0.0192251009142 0.0557203487807 y[1] (closed_form) = 0.0192189205414 0.0557217839951 absolute error = 6.345e-06 relative error = 0.01076 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.119 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.071 Order of pole (three term test) = 2.012e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = 0.0190871926383 0.0556822385862 y[1] (closed_form) = 0.019081066833 0.0556838238848 absolute error = 6.328e-06 relative error = 0.01075 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.122 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.474 Order of pole (three term test) = 1.287e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1595.7MB, alloc=44.3MB, time=19.99 x[1] = 2.6463 2.399 h = 0.001 0.001 y[1] (numeric) = 0.0190043907352 0.0556603545777 y[1] (closed_form) = 0.0189982169305 0.0556619796079 absolute error = 6.384e-06 relative error = 0.01085 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.123 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.943 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6473 2.4 h = 0.001 0.003 y[1] (numeric) = 0.0189688626112 0.0556794175247 y[1] (closed_form) = 0.0189626719445 0.0556810699542 absolute error = 6.407e-06 relative error = 0.01089 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.123 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.22 Order of pole (three term test) = 1.714e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = 0.0188786645009 0.0556819621114 y[1] (closed_form) = 0.0188725105677 0.0556835601499 absolute error = 6.358e-06 relative error = 0.01081 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.124 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.218 Order of pole (three term test) = 3.490e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6484 2.407 h = 0.003 0.006 y[1] (numeric) = 0.0187687895929 0.0556513946642 y[1] (closed_form) = 0.0187626913394 0.0556529958418 absolute error = 6.305e-06 relative error = 0.01074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.126 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.918 Order of pole (three term test) = 3.583e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = 0.0185805748361 0.0556826969331 y[1] (closed_form) = 0.018574357967 0.0556840845686 absolute error = 6.370e-06 relative error = 0.01085 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.127 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.077 Order of pole (three term test) = 6.639e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = 0.0184441127513 0.0556427367746 y[1] (closed_form) = 0.0184379469635 0.0556442743276 absolute error = 6.355e-06 relative error = 0.01084 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.479 Order of pole (three term test) = 9.686e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6516 2.421 h = 0.001 0.001 y[1] (numeric) = 0.0183621640317 0.0556197373331 y[1] (closed_form) = 0.0183559498499 0.0556213133153 absolute error = 6.411e-06 relative error = 0.01095 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.132 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.947 Order of pole (three term test) = 9.243e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6526 2.422 h = 0.001 0.003 y[1] (numeric) = 0.0183265715789 0.0556381424791 y[1] (closed_form) = 0.0183203401259 0.0556397452896 absolute error = 6.434e-06 relative error = 0.01098 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.132 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.239 Order of pole (three term test) = 1.290e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = 0.01823690435 0.0556393059959 y[1] (closed_form) = 0.0182307104146 0.0556408556152 absolute error = 6.385e-06 relative error = 0.0109 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.133 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.229 Order of pole (three term test) = 4.255e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6537 2.429 h = 0.003 0.006 y[1] (numeric) = 0.0181281865543 0.055607270345 y[1] (closed_form) = 0.0181220477636 0.0556088241969 absolute error = 6.332e-06 relative error = 0.01083 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.135 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.932 Order of pole (three term test) = 1.327e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = 0.0179406907619 0.0556355312382 y[1] (closed_form) = 0.0179344386543 0.0556368709779 absolute error = 6.394e-06 relative error = 0.01094 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.136 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.083 Order of pole (three term test) = 1.265e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = 0.017805699826 0.055593765907 y[1] (closed_form) = 0.0177994953547 0.0555952553118 absolute error = 6.381e-06 relative error = 0.01093 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.139 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.484 Order of pole (three term test) = 1.031e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6569 2.443 h = 0.001 0.001 y[1] (numeric) = 0.0177246194658 0.0555696776472 y[1] (closed_form) = 0.0177183662425 0.055571204183 absolute error = 6.437e-06 relative error = 0.01104 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.141 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.951 Order of pole (three term test) = 9.841e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = 0.0176889764449 0.0555874292873 y[1] (closed_form) = 0.0176827055601 0.055588982076 absolute error = 6.460e-06 relative error = 0.01107 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.71 Order of pole (three term test) = 6.862e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.658 2.448 h = 0.003 0.006 y[1] (numeric) = 0.0175812217852 0.0555542213093 y[1] (closed_form) = 0.0175750710874 0.055555730501 absolute error = 6.333e-06 relative error = 0.01087 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.143 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.945 Order of pole (three term test) = 6.999e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.661 2.454 h = 0.0001 0.005 y[1] (numeric) = 0.0173944244222 0.0555799060134 y[1] (closed_form) = 0.0173881649389 0.0555812007759 absolute error = 6.392e-06 relative error = 0.01098 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.144 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.089 Order of pole (three term test) = 1.606e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = 0.017260739501 0.0555366407326 y[1] (closed_form) = 0.0172545247279 0.0555380848358 absolute error = 6.380e-06 relative error = 0.01097 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.147 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.489 Order of pole (three term test) = 4.364e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6612 2.462 h = 0.001 0.001 y[1] (numeric) = 0.017180430652 0.0555116472141 y[1] (closed_form) = 0.0171741668632 0.055513127331 absolute error = 6.436e-06 relative error = 0.01108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.148 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.954 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1641.8MB, alloc=44.3MB, time=20.57 x[1] = 2.6622 2.463 h = 0.001 0.003 y[1] (numeric) = 0.0171447626382 0.0555288396211 y[1] (closed_form) = 0.0171384808736 0.0555303454887 absolute error = 6.460e-06 relative error = 0.01112 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.148 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.276 Order of pole (three term test) = 1.453e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = 0.0170561602981 0.0555275001485 y[1] (closed_form) = 0.0170499173936 0.0555289550828 absolute error = 6.410e-06 relative error = 0.01104 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.149 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.25 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6633 2.47 h = 0.003 0.006 y[1] (numeric) = 0.0169496634877 0.0554928420187 y[1] (closed_form) = 0.0169434746631 0.0554943031462 absolute error = 6.359e-06 relative error = 0.01096 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.151 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.96 Order of pole (three term test) = 6.752e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = 0.016763685411 0.0555155618089 y[1] (closed_form) = 0.016757393016 0.0555168081921 absolute error = 6.415e-06 relative error = 0.01106 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.153 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.096 Order of pole (three term test) = 1.127e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = 0.0166315138558 0.0554705753141 y[1] (closed_form) = 0.0166252628091 0.055471970633 absolute error = 6.405e-06 relative error = 0.01106 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.156 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.494 Order of pole (three term test) = 1.300e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6665 2.484 h = 0.001 0.001 y[1] (numeric) = 0.0165520990867 0.0554445428907 y[1] (closed_form) = 0.0165457987334 0.0554459729357 absolute error = 6.461e-06 relative error = 0.01117 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.157 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.959 Order of pole (three term test) = 1.115e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6675 2.485 h = 0.001 0.003 y[1] (numeric) = 0.0165164053687 0.0554610907249 y[1] (closed_form) = 0.0165100866836 0.0554625459393 absolute error = 6.484e-06 relative error = 0.01121 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.157 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.295 Order of pole (three term test) = 1.556e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = 0.0164283979543 0.0554584354216 y[1] (closed_form) = 0.0164221188044 0.0554598409184 absolute error = 6.435e-06 relative error = 0.01112 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.158 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.261 Order of pole (three term test) = 3.991e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6686 2.492 h = 0.003 0.006 y[1] (numeric) = 0.0163231110385 0.0554224117758 y[1] (closed_form) = 0.0163168853745 0.0554238244863 absolute error = 6.384e-06 relative error = 0.01105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.975 Order of pole (three term test) = 1.610e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = 0.0161380041276 0.0554422086761 y[1] (closed_form) = 0.016131680059 0.0554434064602 absolute error = 6.436e-06 relative error = 0.01115 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.162 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.102 Order of pole (three term test) = 1.140e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = 0.016007366959 0.0553955460442 y[1] (closed_form) = 0.0160010809238 0.05539689228 absolute error = 6.429e-06 relative error = 0.01115 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.164 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.265e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6718 2.506 h = 0.001 0.001 y[1] (numeric) = 0.0159288590972 0.0553685015228 y[1] (closed_form) = 0.0159225234995 0.0553698812039 absolute error = 6.484e-06 relative error = 0.01125 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.166 Order of pole (given) = 3 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6728 2.507 h = 0.001 0.003 y[1] (numeric) = 0.0158931526889 0.055384409898 y[1] (closed_form) = 0.0158867984217 0.0553858141649 absolute error = 6.508e-06 relative error = 0.01129 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.166 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.315 Order of pole (three term test) = 1.652e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = 0.0158057611193 0.0553804620599 y[1] (closed_form) = 0.0157994470248 0.0553818178281 absolute error = 6.458e-06 relative error = 0.01121 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.167 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.273 Order of pole (three term test) = 9.519e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6739 2.514 h = 0.003 0.006 y[1] (numeric) = 0.0157017005944 0.0553431088332 y[1] (closed_form) = 0.0156954393731 0.05534447281 absolute error = 6.408e-06 relative error = 0.01114 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.169 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.99 Order of pole (three term test) = 7.681e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = 0.0155175151201 0.0553600256925 y[1] (closed_form) = 0.0155111606079 0.0553611746901 absolute error = 6.458e-06 relative error = 0.01123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.171 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.109 Order of pole (three term test) = 1.672e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.677 2.525 h = 0.0001 0.003 y[1] (numeric) = 0.0153884320131 0.0553117320245 y[1] (closed_form) = 0.0153821122678 0.0553130289135 absolute error = 6.451e-06 relative error = 0.01124 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.173 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.505 Order of pole (three term test) = 1.330e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6771 2.528 h = 0.001 0.001 y[1] (numeric) = 0.0153108430824 0.0552837022343 y[1] (closed_form) = 0.0153044735532 0.0552850312955 absolute error = 6.507e-06 relative error = 0.01134 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.175 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.967 Order of pole (three term test) = 1.361e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1687.8MB, alloc=44.3MB, time=21.14 x[1] = 2.6781 2.529 h = 0.001 0.003 y[1] (numeric) = 0.0152751367282 0.0552989765294 y[1] (closed_form) = 0.0152687482099 0.0553003295909 absolute error = 6.530e-06 relative error = 0.01138 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.175 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.336 Order of pole (three term test) = 8.816e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = 0.0151883811166 0.0552937597125 y[1] (closed_form) = 0.0151820333713 0.0552950654966 absolute error = 6.481e-06 relative error = 0.0113 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.176 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.284 Order of pole (three term test) = 9.089e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6792 2.536 h = 0.003 0.006 y[1] (numeric) = 0.0150855624102 0.0552551128508 y[1] (closed_form) = 0.0150792669077 0.0552564278121 absolute error = 6.431e-06 relative error = 0.01123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.178 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.005 Order of pole (three term test) = 5.798e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = 0.014902347032 0.0552691932839 y[1] (closed_form) = 0.0148959632967 0.0552702933398 absolute error = 6.478e-06 relative error = 0.01132 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.116 Order of pole (three term test) = 1.369e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = 0.0147748363325 0.0552193136655 y[1] (closed_form) = 0.0147684841479 0.0552205609783 absolute error = 6.473e-06 relative error = 0.01132 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.183 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.51 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6824 2.55 h = 0.001 0.001 y[1] (numeric) = 0.0146981775636 0.0551903254334 y[1] (closed_form) = 0.0146917754073 0.0551916036542 absolute error = 6.529e-06 relative error = 0.01143 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.184 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.971 Order of pole (three term test) = 1.366e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = 0.0146624837342 0.0552049712809 y[1] (closed_form) = 0.0146560622872 0.0552062729154 absolute error = 6.552e-06 relative error = 0.01147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.184 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.84 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6835 2.555 h = 0.003 0.006 y[1] (numeric) = 0.0145606932616 0.0551652951258 y[1] (closed_form) = 0.014554390548 0.0551665663101 absolute error = 6.430e-06 relative error = 0.01127 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.187 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.019 Order of pole (three term test) = 1.375e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = 0.0143783837111 0.0551769818402 y[1] (closed_form) = 0.014371997069 0.0551780383405 absolute error = 6.473e-06 relative error = 0.01135 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.188 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.122 Order of pole (three term test) = 1.655e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = 0.0142522583394 0.0551257921546 y[1] (closed_form) = 0.0142459005295 0.055126995271 absolute error = 6.471e-06 relative error = 0.01136 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.191 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.515 Order of pole (three term test) = 1.506e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6867 2.569 h = 0.001 0.001 y[1] (numeric) = 0.0141764196007 0.055096011639 y[1] (closed_form) = 0.0141700116988 0.0550972445812 absolute error = 6.525e-06 relative error = 0.01147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.193 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.975 Order of pole (three term test) = 5.723e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6877 2.57 h = 0.001 0.003 y[1] (numeric) = 0.0141407537169 0.0551101215815 y[1] (closed_form) = 0.0141343262859 0.0551113774283 absolute error = 6.549e-06 relative error = 0.01151 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.192 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.374 Order of pole (three term test) = 8.234e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = 0.0140552467036 0.0551026150681 y[1] (closed_form) = 0.014048861051 0.055103825918 absolute error = 6.499e-06 relative error = 0.01143 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.193 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.306 Order of pole (three term test) = 1.544e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6888 2.577 h = 0.003 0.006 y[1] (numeric) = 0.0139547905909 0.055061671808 y[1] (closed_form) = 0.0139484559536 0.0550628935594 absolute error = 6.451e-06 relative error = 0.01136 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.196 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.034 Order of pole (three term test) = 9.290e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = 0.0137735368511 0.0550706056298 y[1] (closed_form) = 0.013767123231 0.0550716129963 absolute error = 6.492e-06 relative error = 0.01144 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.197 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.129 Order of pole (three term test) = 4.907e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = 0.0136490140163 0.0550179138956 y[1] (closed_form) = 0.0136426261102 0.0550190671133 absolute error = 6.491e-06 relative error = 0.01145 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.521 Order of pole (three term test) = 1.791e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.692 2.591 h = 0.001 0.001 y[1] (numeric) = 0.0135741239445 0.0549872248847 y[1] (closed_form) = 0.0135676858192 0.0549884066829 absolute error = 6.546e-06 relative error = 0.01156 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.202 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.98 Order of pole (three term test) = 1.537e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.693 2.592 h = 0.001 0.003 y[1] (numeric) = 0.0135384929756 0.055000717637 y[1] (closed_form) = 0.0135320350525 0.0550019217522 absolute error = 6.569e-06 relative error = 0.0116 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.202 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.395 Order of pole (three term test) = 4.270e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1733.8MB, alloc=44.3MB, time=21.72 x[1] = 2.694 2.595 h = 0.0001 0.004 y[1] (numeric) = 0.0134536747522 0.0549920109356 y[1] (closed_form) = 0.0134472591042 0.0549931712751 absolute error = 6.520e-06 relative error = 0.01152 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.203 Order of pole (given) = 3 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) = 7.784e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6941 2.599 h = 0.003 0.006 y[1] (numeric) = 0.0133544983928 0.0549498767956 y[1] (closed_form) = 0.0133481330849 0.0549510489294 absolute error = 6.472e-06 relative error = 0.01145 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.205 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.05 Order of pole (three term test) = 7.024e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = 0.0131743445074 0.0549561031966 y[1] (closed_form) = 0.0131679050989 0.0549570613614 absolute error = 6.510e-06 relative error = 0.01152 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.207 Order of pole (given) = 3 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) = 5.249e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = 0.0130514388603 0.0549019542291 y[1] (closed_form) = 0.0130450221017 0.0549030574134 absolute error = 6.511e-06 relative error = 0.01154 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.527 Order of pole (three term test) = 3.832e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6973 2.613 h = 0.001 0.001 y[1] (numeric) = 0.0129775064786 0.0548703834094 y[1] (closed_form) = 0.0129710394053 0.0548715139401 absolute error = 6.565e-06 relative error = 0.01164 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.211 Order of pole (given) = 3 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) = 1.636e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6983 2.614 h = 0.001 0.003 y[1] (numeric) = 0.0129419220905 0.0548832652631 y[1] (closed_form) = 0.0129354349678 0.0548844175234 absolute error = 6.589e-06 relative error = 0.01168 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.211 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.417 Order of pole (three term test) = 1.938e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = 0.0128578096942 0.054873382674 y[1] (closed_form) = 0.0128513653082 0.0548744923776 absolute error = 6.539e-06 relative error = 0.0116 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.212 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.33 Order of pole (three term test) = 1.178e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6994 2.621 h = 0.003 0.006 y[1] (numeric) = 0.0127599245289 0.0548300933411 y[1] (closed_form) = 0.012753529794 0.0548312157054 absolute error = 6.492e-06 relative error = 0.01153 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.215 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.066 Order of pole (three term test) = 1.011e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = 0.0125809129378 0.0548336583415 y[1] (closed_form) = 0.0125744489184 0.0548345672659 absolute error = 6.528e-06 relative error = 0.0116 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.216 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.143 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = 0.0124596378768 0.0547780967975 y[1] (closed_form) = 0.0124531934985 0.0547791498452 absolute error = 6.530e-06 relative error = 0.01162 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.219 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.532 Order of pole (three term test) = 1.556e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7026 2.635 h = 0.001 0.001 y[1] (numeric) = 0.0123866714601 0.054745670768 y[1] (closed_form) = 0.0123801767026 0.0547467499399 absolute error = 6.584e-06 relative error = 0.01173 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.221 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.989 Order of pole (three term test) = 1.401e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7036 2.636 h = 0.001 0.003 y[1] (numeric) = 0.0123511450329 0.0547579482244 y[1] (closed_form) = 0.0123446299914 0.0547590485392 absolute error = 6.607e-06 relative error = 0.01177 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.221 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.438 Order of pole (three term test) = 7.731e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = 0.0122677547183 0.0547469141806 y[1] (closed_form) = 0.0122612828403 0.054747973155 absolute error = 6.558e-06 relative error = 0.01169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.222 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.342 Order of pole (three term test) = 6.428e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7047 2.643 h = 0.003 0.006 y[1] (numeric) = 0.0121711711952 0.0547025052083 y[1] (closed_form) = 0.0121647482663 0.0547035776831 absolute error = 6.512e-06 relative error = 0.01162 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.224 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.082 Order of pole (three term test) = 1.617e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = 0.0119933427403 0.0547034553229 y[1] (closed_form) = 0.0119868552748 0.0547043149966 absolute error = 6.544e-06 relative error = 0.01169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.226 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.15 Order of pole (three term test) = 1.203e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = 0.0118737104335 0.0546465256665 y[1] (closed_form) = 0.0118672396566 0.0546475285055 absolute error = 6.548e-06 relative error = 0.01171 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.229 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.538 Order of pole (three term test) = 1.001e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7079 2.657 h = 0.001 0.001 y[1] (numeric) = 0.0118017175214 0.0546132709181 y[1] (closed_form) = 0.0117951963308 0.0546142986716 absolute error = 6.602e-06 relative error = 0.01182 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.231 Order of pole (given) = 3 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) = 5.930e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = 0.0117662601473 0.0546249506772 y[1] (closed_form) = 0.0117597184551 0.0546259989881 absolute error = 6.625e-06 relative error = 0.01186 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.97 Order of pole (three term test) = 1.707e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1779.8MB, alloc=44.3MB, time=22.29 x[1] = 2.709 2.662 h = 0.003 0.006 y[1] (numeric) = 0.0116707498691 0.0545796544004 y[1] (closed_form) = 0.0116643240529 0.0545806844656 absolute error = 6.508e-06 relative error = 0.01166 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.233 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.096 Order of pole (three term test) = 4.959e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.712 2.668 h = 0.0001 0.005 y[1] (numeric) = 0.0114940016957 0.0545784060206 y[1] (closed_form) = 0.011487515364 0.0545792239752 absolute error = 6.538e-06 relative error = 0.01172 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.234 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.157 Order of pole (three term test) = 7.454e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = 0.0113758078186 0.0545203539164 y[1] (closed_form) = 0.0113693356924 0.0545213141296 absolute error = 6.543e-06 relative error = 0.01175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.237 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.543 Order of pole (three term test) = 7.527e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7122 2.676 h = 0.001 0.001 y[1] (numeric) = 0.0113046677972 0.0544864186557 y[1] (closed_form) = 0.0112981452652 0.054487402753 absolute error = 6.596e-06 relative error = 0.01185 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.239 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.997 Order of pole (three term test) = 2.819e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7132 2.677 h = 0.001 0.003 y[1] (numeric) = 0.0112692855307 0.0544975904425 y[1] (closed_form) = 0.0112627423299 0.0544985945921 absolute error = 6.620e-06 relative error = 0.0119 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.239 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.479 Order of pole (three term test) = 6.223e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = 0.0111872924775 0.0544844882164 y[1] (closed_form) = 0.0111807931298 0.0544854532818 absolute error = 6.571e-06 relative error = 0.01181 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.365 Order of pole (three term test) = 7.213e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7143 2.684 h = 0.003 0.006 y[1] (numeric) = 0.0110931678326 0.0544381056682 y[1] (closed_form) = 0.0110867160872 0.0544390857173 absolute error = 6.526e-06 relative error = 0.01175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.243 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.113 Order of pole (three term test) = 1.024e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = 0.0109176740034 0.0544343305334 y[1] (closed_form) = 0.0109111663563 0.0544350993047 absolute error = 6.553e-06 relative error = 0.0118 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.244 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.164 Order of pole (three term test) = 7.828e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = 0.0108011418034 0.0543749925419 y[1] (closed_form) = 0.0107946455175 0.0543759025058 absolute error = 6.560e-06 relative error = 0.01183 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.247 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.549 Order of pole (three term test) = 5.004e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7175 2.698 h = 0.001 0.001 y[1] (numeric) = 0.0107309870929 0.0543402775714 y[1] (closed_form) = 0.0107244404203 0.0543412102354 absolute error = 6.613e-06 relative error = 0.01194 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.249 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.002 Order of pole (three term test) = 7.704e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7185 2.699 h = 0.001 0.003 y[1] (numeric) = 0.0106956936633 0.0543508647427 y[1] (closed_form) = 0.0106891261348 0.0543518168771 absolute error = 6.636e-06 relative error = 0.01198 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.249 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.501 Order of pole (three term test) = 9.434e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = 0.0106144646422 0.0543366816407 y[1] (closed_form) = 0.0106079412975 0.0543375958932 absolute error = 6.587e-06 relative error = 0.0119 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.378 Order of pole (three term test) = 8.033e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7196 2.706 h = 0.003 0.006 y[1] (numeric) = 0.0105216657895 0.0542892802757 y[1] (closed_form) = 0.0105151893137 0.0542902102756 absolute error = 6.543e-06 relative error = 0.01183 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.252 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.129 Order of pole (three term test) = 1.002e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = 0.0103474626215 0.0542830260082 y[1] (closed_form) = 0.0103409347834 0.0542837456629 absolute error = 6.567e-06 relative error = 0.01188 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.254 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.171 Order of pole (three term test) = 7.346e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = 0.0102326008783 0.0542224458527 y[1] (closed_form) = 0.0102260816162 0.0542233055792 absolute error = 6.576e-06 relative error = 0.01192 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.257 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.555 Order of pole (three term test) = 7.589e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7228 2.72 h = 0.001 0.001 y[1] (numeric) = 0.0101634369913 0.0541869772405 y[1] (closed_form) = 0.0101568673895 0.0541878584975 absolute error = 6.628e-06 relative error = 0.01202 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.259 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.007 Order of pole (three term test) = 3.241e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7238 2.721 h = 0.001 0.003 y[1] (numeric) = 0.0101282426577 0.0541969870003 y[1] (closed_form) = 0.0101216520287 0.0541978871483 absolute error = 6.652e-06 relative error = 0.01206 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.259 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.523 Order of pole (three term test) = 1.319e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = 0.0100477909735 0.0541817477364 y[1] (closed_form) = 0.0100412448269 0.0541826111983 absolute error = 6.603e-06 relative error = 0.01198 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.39 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1825.8MB, alloc=44.3MB, time=22.86 x[1] = 2.7249 2.728 h = 0.003 0.006 y[1] (numeric) = 0.00995632470097 0.0541333623391 y[1] (closed_form) = 0.0099498246804 0.0541342422858 absolute error = 6.559e-06 relative error = 0.01192 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.262 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.146 Order of pole (three term test) = 1.059e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = 0.00978344695346 0.0541246768582 y[1] (closed_form) = 0.00977690003416 0.0541253474883 absolute error = 6.581e-06 relative error = 0.01197 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.264 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.179 Order of pole (three term test) = 9.621e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.728 2.739 h = 0.0001 0.003 y[1] (numeric) = 0.00967026330837 0.0540628979504 y[1] (closed_form) = 0.00966372223922 0.0540637074791 absolute error = 6.591e-06 relative error = 0.012 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.267 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.561 Order of pole (three term test) = 1.038e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7281 2.742 h = 0.001 0.001 y[1] (numeric) = 0.0096020950763 0.0540267015852 y[1] (closed_form) = 0.00959550374147 0.0540275314899 absolute error = 6.643e-06 relative error = 0.01211 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.269 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.011 Order of pole (three term test) = 5.499e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7291 2.743 h = 0.001 0.003 y[1] (numeric) = 0.0095670098057 0.0540361412942 y[1] (closed_form) = 0.00956039728824 0.0540369895134 absolute error = 6.667e-06 relative error = 0.01215 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.269 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.545 Order of pole (three term test) = 6.944e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = 0.00948734802141 0.0540198706028 y[1] (closed_form) = 0.00948078025304 0.0540206833246 absolute error = 6.618e-06 relative error = 0.01207 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.403 Order of pole (three term test) = 8.857e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7302 2.75 h = 0.003 0.006 y[1] (numeric) = 0.00939722021521 0.0539705357038 y[1] (closed_form) = 0.00939069782158 0.0539713656213 absolute error = 6.575e-06 relative error = 0.012 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.272 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.163 Order of pole (three term test) = 2.262e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = 0.00922570110389 0.053959467177 y[1] (closed_form) = 0.00921913619748 0.0539600888992 absolute error = 6.594e-06 relative error = 0.01205 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.274 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.186 Order of pole (three term test) = 8.461e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = 0.00911420208457 0.0538965325896 y[1] (closed_form) = 0.00910764036282 0.0538972919874 absolute error = 6.606e-06 relative error = 0.01208 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.277 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.567 Order of pole (three term test) = 2.977e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7334 2.764 h = 0.001 0.001 y[1] (numeric) = 0.00904703367228 0.0538596341642 y[1] (closed_form) = 0.00904042178504 0.053860412799 absolute error = 6.658e-06 relative error = 0.01219 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.279 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.016 Order of pole (three term test) = 5.280e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = 0.00901206713945 0.0538685113292 y[1] (closed_form) = 0.00900543392949 0.0538693077053 absolute error = 6.681e-06 relative error = 0.01223 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.279 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.11 Order of pole (three term test) = 3.256e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7345 2.769 h = 0.003 0.006 y[1] (numeric) = 0.00892303910745 0.0538184274735 y[1] (closed_form) = 0.00891651774011 0.0538192167483 absolute error = 6.569e-06 relative error = 0.01204 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.281 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.178 Order of pole (three term test) = 1.204e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = 0.00875274249785 0.0538053631206 y[1] (closed_form) = 0.00874618231496 0.0538059452878 absolute error = 6.586e-06 relative error = 0.01208 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.283 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.193 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = 0.00864271101928 0.0537414881285 y[1] (closed_form) = 0.00863615179066 0.0537422068496 absolute error = 6.598e-06 relative error = 0.01212 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.286 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.573 Order of pole (three term test) = 1.178e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7377 2.783 h = 0.001 0.001 y[1] (numeric) = 0.00857641400623 0.0537040177708 y[1] (closed_form) = 0.00856980473202 0.0537047547631 absolute error = 6.650e-06 relative error = 0.01223 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.288 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.02 Order of pole (three term test) = 1.142e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7387 2.784 h = 0.001 0.003 y[1] (numeric) = 0.00854156377997 0.053712418398 y[1] (closed_form) = 0.00853493308129 0.0537131726394 absolute error = 6.673e-06 relative error = 0.01227 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.288 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.588 Order of pole (three term test) = 4.713e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = 0.00846341434422 0.0536943040032 y[1] (closed_form) = 0.00845682879483 0.0536950249394 absolute error = 6.625e-06 relative error = 0.01219 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.289 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.427 Order of pole (three term test) = 1.013e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7398 2.791 h = 0.003 0.006 y[1] (numeric) = 0.00837580012631 0.053643309316 y[1] (closed_form) = 0.00836925852629 0.0536440486923 absolute error = 6.583e-06 relative error = 0.01213 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.292 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.195 Order of pole (three term test) = 1.830e-27 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1871.8MB, alloc=44.3MB, time=23.44 x[1] = 2.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = 0.00820691932532 0.0536279524001 y[1] (closed_form) = 0.0082003431465 0.0536284859522 absolute error = 6.598e-06 relative error = 0.01216 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.293 Order of pole (given) = 3 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) = 9.683e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = 0.0080985812414 0.0535630009321 y[1] (closed_form) = 0.00809200346533 0.0535636697292 absolute error = 6.612e-06 relative error = 0.01221 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.296 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.579 Order of pole (three term test) = 4.475e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.743 2.805 h = 0.001 0.001 y[1] (numeric) = 0.00803328977606 0.0535248757784 y[1] (closed_form) = 0.00802666210096 0.0535255617383 absolute error = 6.663e-06 relative error = 0.01231 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.298 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.025 Order of pole (three term test) = 5.960e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.744 2.806 h = 0.001 0.003 y[1] (numeric) = 0.00799857541987 0.0535327282912 y[1] (closed_form) = 0.00799192620793 0.0535334309343 absolute error = 6.686e-06 relative error = 0.01235 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.298 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.611 Order of pole (three term test) = 4.220e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.745 2.809 h = 0.0001 0.004 y[1] (numeric) = 0.00792124752521 0.0535136532751 y[1] (closed_form) = 0.00791464364233 0.0535143237763 absolute error = 6.638e-06 relative error = 0.01227 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.299 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.44 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7451 2.813 h = 0.003 0.006 y[1] (numeric) = 0.00783498341556 0.0534618063127 y[1] (closed_form) = 0.00782842271147 0.0534624958906 absolute error = 6.597e-06 relative error = 0.01221 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.302 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.212 Order of pole (three term test) = 5.562e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = 0.00766754730989 0.0534442054393 y[1] (closed_form) = 0.00766095618233 0.053444690559 absolute error = 6.609e-06 relative error = 0.01224 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.304 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.208 Order of pole (three term test) = 1.041e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = 0.00756090611103 0.0533782194442 y[1] (closed_form) = 0.0075543108962 0.053378838457 absolute error = 6.624e-06 relative error = 0.01229 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.307 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.585 Order of pole (three term test) = 6.803e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7483 2.827 h = 0.001 0.001 y[1] (numeric) = 0.00749662253877 0.053339464534 y[1] (closed_form) = 0.00748997759532 0.0533400996182 absolute error = 6.675e-06 relative error = 0.01239 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.309 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.03 Order of pole (three term test) = 1.378e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7493 2.828 h = 0.001 0.003 y[1] (numeric) = 0.00746205289182 0.0533467767977 y[1] (closed_form) = 0.00745538631363 0.0533474280035 absolute error = 6.698e-06 relative error = 0.01244 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.309 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.634 Order of pole (three term test) = 6.417e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = 0.00738555633674 0.0533267657724 y[1] (closed_form) = 0.00737893523826 0.0533273859895 absolute error = 6.650e-06 relative error = 0.01235 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.453 Order of pole (three term test) = 7.024e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7504 2.835 h = 0.003 0.006 y[1] (numeric) = 0.00730064493636 0.0532740998803 y[1] (closed_form) = 0.00729406624086 0.053274739785 absolute error = 6.610e-06 relative error = 0.01229 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.312 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.23 Order of pole (three term test) = 1.525e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = 0.00713468093513 0.053254303729 y[1] (closed_form) = 0.00712807588898 0.0532547406207 absolute error = 6.619e-06 relative error = 0.01232 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.314 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.216 Order of pole (three term test) = 1.119e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = 0.00702973909965 0.053187324722 y[1] (closed_form) = 0.00702312753797 0.053187894114 absolute error = 6.636e-06 relative error = 0.01237 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.317 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.591 Order of pole (three term test) = 8.181e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7536 2.849 h = 0.001 0.001 y[1] (numeric) = 0.0069664651592 0.0531479648419 y[1] (closed_form) = 0.00695980406235 0.0531485492314 absolute error = 6.687e-06 relative error = 0.01247 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.319 Order of pole (given) = 3 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) = 3.495e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7546 2.85 h = 0.001 0.003 y[1] (numeric) = 0.0069320487708 0.0531547448293 y[1] (closed_form) = 0.00692536595545 0.0531553447833 absolute error = 6.710e-06 relative error = 0.01252 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.319 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.658 Order of pole (three term test) = 2.183e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = 0.00685639266568 0.0531338223306 y[1] (closed_form) = 0.0068497554523 0.0531343924384 absolute error = 6.662e-06 relative error = 0.01243 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.467 Order of pole (three term test) = 1.356e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7557 2.857 h = 0.003 0.006 y[1] (numeric) = 0.00677283577506 0.0530803705043 y[1] (closed_form) = 0.00676624018434 0.0530809608854 absolute error = 6.622e-06 relative error = 0.01238 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.323 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.248 Order of pole (three term test) = 1.608e-28 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1917.9MB, alloc=44.3MB, time=24.01 x[1] = 2.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = 0.00660836982951 0.0530584277874 y[1] (closed_form) = 0.00660175187752 0.0530588166761 absolute error = 6.629e-06 relative error = 0.0124 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.325 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.224 Order of pole (three term test) = 4.818e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = 0.00650512885058 0.0529904968283 y[1] (closed_form) = 0.00649850201681 0.0529910167862 absolute error = 6.647e-06 relative error = 0.01245 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.328 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.598 Order of pole (three term test) = 1.113e-27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7589 2.871 h = 0.001 0.001 y[1] (numeric) = 0.00644286569002 0.052950556499 y[1] (closed_form) = 0.0064361895367 0.0529510903982 absolute error = 6.697e-06 relative error = 0.01256 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.04 Order of pole (three term test) = 3.761e-28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7599 2.872 h = 0.001 0.003 y[1] (numeric) = 0.00640861082094 0.0529568122806 y[1] (closed_form) = 0.00640191287915 0.0529573611922 absolute error = 6.720e-06 relative error = 0.0126 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 3 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.682 Order of pole (three term test) = 5.253e-28 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; Iterations = 754 Total Elapsed Time = 24 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 24 Seconds > quit memory used=1928.9MB, alloc=44.3MB, time=24.14