|\^/| 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(x)/c(x)); > end; exact_soln_y := proc(x) return c(1.0)/(c(x)*c(x)*c(x)) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 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0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 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_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > 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_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, 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_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > 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_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, 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_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > 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_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, 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_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > 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_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, 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_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > 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_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, 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_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > 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_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, 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_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > 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_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, 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_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > 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_3D0[1]); > #emit pre div CONST - LINEAR $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp3[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp4[1] / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[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 div CONST - LINEAR $eq_no = 1 i = 2 > array_tmp2[2] := neg(array_tmp2[1])* array_x[2] / array_x[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 div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := (array_tmp2[2] - array_tmp3[1] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp4[2] := (array_tmp3[2] - array_tmp4[1] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp4[2] - array_tmp5[1] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp6[2] := array_tmp5[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_tmp6[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_tmp2[3] := neg(array_tmp2[2])* array_x[2] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp3[3] := (array_tmp2[3] - array_tmp3[2] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp4[3] := (array_tmp3[3] - array_tmp4[2] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp4[3] - array_tmp5[2] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp6[3] := array_tmp5[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_tmp6[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_tmp2[4] := neg(array_tmp2[3])* array_x[2] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp3[4] := (array_tmp2[4] - array_tmp3[3] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp4[4] := (array_tmp3[4] - array_tmp4[3] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp4[4] - array_tmp5[3] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp6[4] := array_tmp5[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_tmp6[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_tmp2[5] := neg(array_tmp2[4])* array_x[2] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp3[5] := (array_tmp2[5] - array_tmp3[4] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp4[5] := (array_tmp3[5] - array_tmp4[4] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp4[5] - array_tmp5[4] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp6[5] := array_tmp5[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_tmp6[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_tmp2[kkk] := array_tmp1[1] * array_x[kkk]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp3[kkk] := neg(ats(kkk,array_x,array_tmp3,2)) / array_x[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp4[kkk] := neg(ats(kkk,array_x,array_tmp4,2)) / array_x[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp5[kkk] := neg(ats(kkk,array_x,array_tmp5,2)) / array_x[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp6[kkk] := array_tmp5[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_tmp6[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_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, 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_3D0[1]); array_tmp2[1] := array_tmp1[1]/array_x[1]; array_tmp3[1] := array_tmp2[1]/array_x[1]; array_tmp4[1] := array_tmp3[1]/array_x[1]; array_tmp5[1] := array_tmp4[1]/array_x[1]; array_tmp6[1] := array_const_0D0[1] + array_tmp5[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp6[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] := neg(array_tmp2[1])*array_x[2]/array_x[1]; array_tmp3[2] := (-array_x[2]*array_tmp3[1] + array_tmp2[2])/array_x[1] ; array_tmp4[2] := (-array_x[2]*array_tmp4[1] + array_tmp3[2])/array_x[1] ; array_tmp5[2] := (-array_x[2]*array_tmp5[1] + array_tmp4[2])/array_x[1] ; array_tmp6[2] := array_tmp5[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp6[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_tmp2[3] := neg(array_tmp2[2])*array_x[2]/array_x[1]; array_tmp3[3] := (-array_x[2]*array_tmp3[2] + array_tmp2[3])/array_x[1] ; array_tmp4[3] := (-array_x[2]*array_tmp4[2] + array_tmp3[3])/array_x[1] ; array_tmp5[3] := (-array_x[2]*array_tmp5[2] + array_tmp4[3])/array_x[1] ; array_tmp6[3] := array_tmp5[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp6[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_tmp2[4] := neg(array_tmp2[3])*array_x[2]/array_x[1]; array_tmp3[4] := (-array_x[2]*array_tmp3[3] + array_tmp2[4])/array_x[1] ; array_tmp4[4] := (-array_x[2]*array_tmp4[3] + array_tmp3[4])/array_x[1] ; array_tmp5[4] := (-array_x[2]*array_tmp5[3] + array_tmp4[4])/array_x[1] ; array_tmp6[4] := array_tmp5[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp6[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_tmp2[5] := neg(array_tmp2[4])*array_x[2]/array_x[1]; array_tmp3[5] := (-array_x[2]*array_tmp3[4] + array_tmp2[5])/array_x[1] ; array_tmp4[5] := (-array_x[2]*array_tmp4[4] + array_tmp3[5])/array_x[1] ; array_tmp5[5] := (-array_x[2]*array_tmp5[4] + array_tmp4[5])/array_x[1] ; array_tmp6[5] := array_tmp5[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp6[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_tmp2[kkk] := array_tmp1[1]*array_x[kkk]; array_tmp3[kkk] := neg(ats(kkk, array_x, array_tmp3, 2))/array_x[1] ; array_tmp4[kkk] := neg(ats(kkk, array_x, array_tmp4, 2))/array_x[1] ; array_tmp5[kkk] := neg(ats(kkk, array_x, array_tmp5, 2))/array_x[1] ; array_tmp6[kkk] := array_tmp5[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_tmp6[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_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > 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:=32; > 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_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_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_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_3D0); > array_const_3D0[1] := c(3.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > # 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/sing5postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > 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 := -1.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_h := c(0.001);"); > omniout_str(ALWAYS,"glob_min_h := c(0.001);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);"); > 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(4.0);"); > 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(x)/c(x));"); > 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 := -1.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_h := c(0.001); > glob_min_h := c(0.001); > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(0.0); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(4.0); > 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 ( 3.0 ) / x / x / x / x ; "); > 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,"2017-11-26T16:24:17-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing5") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; ") > ; > 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,"sing5 diffeq.mxt") > ; > logitem_str(html_log_file,"sing5 maple results") > ; > logitem_str(html_log_file,"Poor Accuracy") > ; > 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_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, 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 := 32; 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_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_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_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_3D0); array_const_3D0[1] := c(3.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; 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/sing5postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 3.0 ) /\ x / x / x / x ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); 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 := -1.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_h := c(0.001);"); omniout_str(ALWAYS, "glob_min_h := c(0.001);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);"); 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(4.0);"); 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(x)/c(x));"); 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,"); 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omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.000 + 0.000 * I ];"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;"); omniout_str(ALWAYS, "it := x_delta[glob_nxt];"); omniout_str(ALWAYS, "return it;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := -1.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c(0.001); glob_min_h := c(0.001); glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(0.); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(4.0); 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 ( 3.0 ) \ / x / x / x / x ; "); 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, "2017-11-26T16:24:17-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing5"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\ g ( 3.0 ) / x / x / x / x ; "); 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, "sing5 diffeq.mxt"); logitem_str(html_log_file, "sing5 maple results") ; logitem_str(html_log_file, "Poor Accuracy"); 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/sing5postcpx.cpx################# diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=20; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -1.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c(0.001); glob_min_h := c(0.001); glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(0.0); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(4.0); 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(x)/c(x)); 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] = -1.1 0.1 h = 0.0001 0.005 y[1] (numeric) = -0.714817539794 -0.199355893225 y[1] (closed_form) = -0.714817539794 -0.199355893225 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 1.105 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.381 Order of pole (three term test) = 6.795e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0999 0.105 h = 0.0001 0.003 y[1] (numeric) = -0.71136408545 -0.208820511104 y[1] (closed_form) = -0.711347641449 -0.208812631546 absolute error = 1.823e-05 relative error = 0.00246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.105 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6632 Order of pole (three term test) = 6.383e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0998 0.108 h = 0.001 0.001 y[1] (numeric) = -0.709257449737 -0.21447895692 y[1] (closed_form) = -0.709260641056 -0.214480673719 absolute error = 3.624e-06 relative error = 0.0004891 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.105 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5207 Order of pole (three term test) = 1.913e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0988 0.109 h = 0.001 0.003 y[1] (numeric) = -0.710334487206 -0.217110841881 y[1] (closed_form) = -0.710348881996 -0.217114058172 absolute error = 1.475e-05 relative error = 0.001986 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.104 Order of pole (given) = 4 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) = 1.165e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0978 0.112 h = 0.0001 0.004 y[1] (numeric) = -0.709850838814 -0.223484655234 y[1] (closed_form) = -0.709842429756 -0.223483746919 absolute error = 8.458e-06 relative error = 0.001137 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.103 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.396 Order of pole (three term test) = 7.448e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0977 0.116 h = 0.003 0.006 y[1] (numeric) = -0.706789664049 -0.230989659859 y[1] (closed_form) = -0.706774595329 -0.230970158053 absolute error = 2.465e-05 relative error = 0.003315 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.104 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.851 Order of pole (three term test) = 5.847e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0947 0.122 h = 0.0001 0.005 y[1] (numeric) = -0.707267618069 -0.244529588235 y[1] (closed_form) = -0.707197836135 -0.24457746166 absolute error = 8.462e-05 relative error = 0.01131 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8212 Order of pole (three term test) = 3.617e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0946 0.127 h = 0.0001 0.003 y[1] (numeric) = -0.702950618096 -0.2538095755 y[1] (closed_form) = -0.702924860879 -0.25382135644 absolute error = 2.832e-05 relative error = 0.00379 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.102 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6614 Order of pole (three term test) = 5.859e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=36.0MB, alloc=40.3MB, time=0.47 x[1] = -1.0945 0.13 h = 0.001 0.001 y[1] (numeric) = -0.70036409565 -0.259336071196 y[1] (closed_form) = -0.700357144061 -0.259359544728 absolute error = 2.448e-05 relative error = 0.003278 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.102 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5193 Order of pole (three term test) = 1.135e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0935 0.131 h = 0.001 0.003 y[1] (numeric) = -0.701232680234 -0.262075075787 y[1] (closed_form) = -0.701236865798 -0.262101213077 absolute error = 2.647e-05 relative error = 0.003536 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.463 Order of pole (three term test) = 1.519e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0925 0.134 h = 0.0001 0.004 y[1] (numeric) = -0.700221563441 -0.268454332807 y[1] (closed_form) = -0.700203193324 -0.268473965125 absolute error = 2.689e-05 relative error = 0.003585 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.393 Order of pole (three term test) = 7.849e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0924 0.138 h = 0.003 0.006 y[1] (numeric) = -0.696522162102 -0.275758426215 y[1] (closed_form) = -0.696498998707 -0.275758642098 absolute error = 2.316e-05 relative error = 0.003092 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 4 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) = 7.640e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0894 0.144 h = 0.0001 0.005 y[1] (numeric) = -0.695889950439 -0.289425005993 y[1] (closed_form) = -0.695804754703 -0.289487423323 absolute error = 0.0001056 relative error = 0.01401 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.099 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8192 Order of pole (three term test) = 1.500e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0893 0.149 h = 0.0001 0.003 y[1] (numeric) = -0.69078182673 -0.298403519818 y[1] (closed_form) = -0.690744658119 -0.298434164613 absolute error = 4.817e-05 relative error = 0.006402 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.099 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6599 Order of pole (three term test) = 5.447e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0892 0.152 h = 0.001 0.001 y[1] (numeric) = -0.687725663464 -0.303747729078 y[1] (closed_form) = -0.687706205458 -0.303792074845 absolute error = 4.843e-05 relative error = 0.006441 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5181 Order of pole (three term test) = 1.036e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0882 0.153 h = 0.001 0.003 y[1] (numeric) = -0.688373352896 -0.306573115137 y[1] (closed_form) = -0.688364821134 -0.306621288733 absolute error = 4.892e-05 relative error = 0.006492 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.099 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.457 Order of pole (three term test) = 7.065e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0872 0.156 h = 0.0001 0.004 y[1] (numeric) = -0.686830640187 -0.3129034684 y[1] (closed_form) = -0.686800097584 -0.312942771337 absolute error = 4.978e-05 relative error = 0.006595 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.098 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.39 Order of pole (three term test) = 5.333e-31 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0871 0.16 h = 0.003 0.006 y[1] (numeric) = -0.682509668785 -0.319939532444 y[1] (closed_form) = -0.682476313036 -0.319958822158 absolute error = 3.853e-05 relative error = 0.005112 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.099 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.842 Order of pole (three term test) = 6.901e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0841 0.166 h = 0.0001 0.005 y[1] (numeric) = -0.680747623073 -0.333619088881 y[1] (closed_form) = -0.680645515316 -0.33369446943 absolute error = 0.0001269 relative error = 0.01674 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8176 Order of pole (three term test) = 2.520e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.084 0.171 h = 0.0001 0.003 y[1] (numeric) = -0.674875399394 -0.342212740656 y[1] (closed_form) = -0.674824804535 -0.342261187062 absolute error = 7.005e-05 relative error = 0.009258 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6587 Order of pole (three term test) = 7.260e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0839 0.174 h = 0.001 0.001 y[1] (numeric) = -0.671366136367 -0.347325303658 y[1] (closed_form) = -0.671331903067 -0.347389332702 absolute error = 7.261e-05 relative error = 0.009605 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.098 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5172 Order of pole (three term test) = 1.094e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0829 0.175 h = 0.001 0.003 y[1] (numeric) = -0.671782987406 -0.350214676036 y[1] (closed_form) = -0.67175932415 -0.350283675861 absolute error = 7.294e-05 relative error = 0.009628 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.453 Order of pole (three term test) = 2.003e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0819 0.178 h = 0.0001 0.004 y[1] (numeric) = -0.669711268499 -0.356440963756 y[1] (closed_form) = -0.66966643524 -0.356498784962 absolute error = 7.317e-05 relative error = 0.009644 % Correct digits = 4 memory used=82.2MB, alloc=44.3MB, time=1.06 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.387 Order of pole (three term test) = 6.730e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0818 0.182 h = 0.003 0.006 y[1] (numeric) = -0.664793795451 -0.363143604535 y[1] (closed_form) = -0.66474821066 -0.363181059348 absolute error = 5.900e-05 relative error = 0.007789 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 4 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) = 4.797e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0788 0.188 h = 0.0001 0.005 y[1] (numeric) = -0.661896246173 -0.376719502055 y[1] (closed_form) = -0.661775927073 -0.376806083641 absolute error = 0.0001482 relative error = 0.01947 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8164 Order of pole (three term test) = 3.000e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0787 0.193 h = 0.0001 0.003 y[1] (numeric) = -0.655297412942 -0.384847951406 y[1] (closed_form) = -0.655231499226 -0.384912882179 absolute error = 9.252e-05 relative error = 0.01218 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6577 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0786 0.196 h = 0.001 0.001 y[1] (numeric) = -0.651357768931 -0.389681399813 y[1] (closed_form) = -0.651306631482 -0.389763631085 absolute error = 9.684e-05 relative error = 0.01276 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5165 Order of pole (three term test) = 9.361e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0776 0.197 h = 0.0001 0.004 y[1] (numeric) = -0.651536586016 -0.392611062178 y[1] (closed_form) = -0.651495519877 -0.392699364973 absolute error = 9.738e-05 relative error = 0.0128 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.099 Order of pole (three term test) = 1.129e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0775 0.201 h = 0.003 0.006 y[1] (numeric) = -0.646156271171 -0.398993621902 y[1] (closed_form) = -0.646096969702 -0.399037872033 absolute error = 7.399e-05 relative error = 0.009744 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 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) = 1.891e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0745 0.207 h = 0.0001 0.005 y[1] (numeric) = -0.642290953799 -0.412372772463 y[1] (closed_form) = -0.642152549182 -0.412459495091 absolute error = 0.0001633 relative error = 0.0214 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8158 Order of pole (three term test) = 1.789e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0744 0.212 h = 0.0001 0.003 y[1] (numeric) = -0.635111137989 -0.420032046612 y[1] (closed_form) = -0.635029035322 -0.420101980561 absolute error = 0.0001078 relative error = 0.01416 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6573 Order of pole (three term test) = 4.802e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0743 0.215 h = 0.001 0.001 y[1] (numeric) = -0.630827791591 -0.424584687879 y[1] (closed_form) = -0.630758912364 -0.424673221429 absolute error = 0.0001122 relative error = 0.01475 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5162 Order of pole (three term test) = 1.655e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0733 0.216 h = 0.001 0.003 y[1] (numeric) = -0.630798114566 -0.427526456561 y[1] (closed_form) = -0.630738755859 -0.427621951421 absolute error = 0.0001124 relative error = 0.01476 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.448 Order of pole (three term test) = 6.271e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0723 0.219 h = 0.0001 0.004 y[1] (numeric) = -0.627775175658 -0.433407646706 y[1] (closed_form) = -0.627696991241 -0.433487986267 absolute error = 0.0001121 relative error = 0.0147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.385 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0722 0.223 h = 0.003 0.006 y[1] (numeric) = -0.621847850989 -0.439320764735 y[1] (closed_form) = -0.621772842938 -0.439380791589 absolute error = 9.607e-05 relative error = 0.01262 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 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) = 2.317e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0692 0.229 h = 0.0001 0.005 y[1] (numeric) = -0.616876451679 -0.452378659463 y[1] (closed_form) = -0.616718054029 -0.452472917095 absolute error = 0.0001843 relative error = 0.0241 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.093 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8152 Order of pole (three term test) = 4.293e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0691 0.234 h = 0.0001 0.003 y[1] (numeric) = -0.609066793022 -0.459437229646 y[1] (closed_form) = -0.608966322688 -0.459520563811 absolute error = 0.0001305 relative error = 0.01711 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6569 Order of pole (three term test) = 4.703e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=128.2MB, alloc=44.3MB, time=1.64 x[1] = -1.069 0.237 h = 0.001 0.001 y[1] (numeric) = -0.604411223106 -0.463630928156 y[1] (closed_form) = -0.604322022024 -0.463734185255 absolute error = 0.0001365 relative error = 0.01791 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5159 Order of pole (three term test) = 4.528e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.068 0.238 h = 0.001 0.003 y[1] (numeric) = -0.604138337356 -0.466566812391 y[1] (closed_form) = -0.604057913129 -0.466677997521 absolute error = 0.0001372 relative error = 0.01798 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.447 Order of pole (three term test) = 1.232e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.067 0.241 h = 0.0001 0.004 y[1] (numeric) = -0.600632094266 -0.472190698446 y[1] (closed_form) = -0.600534462304 -0.472284820389 absolute error = 0.0001356 relative error = 0.01775 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.384 Order of pole (three term test) = 1.745e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0669 0.245 h = 0.003 0.006 y[1] (numeric) = -0.594224190268 -0.477604212776 y[1] (closed_form) = -0.594131825976 -0.477678412022 absolute error = 0.0001185 relative error = 0.01554 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 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) = 4.481e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0639 0.251 h = 0.0001 0.005 y[1] (numeric) = -0.588182434833 -0.490227279384 y[1] (closed_form) = -0.588003434859 -0.490326970589 absolute error = 0.0002049 relative error = 0.02676 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.093 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8149 Order of pole (three term test) = 1.424e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0638 0.256 h = 0.0001 0.003 y[1] (numeric) = -0.579807055953 -0.496621746727 y[1] (closed_form) = -0.579686872371 -0.496716552199 absolute error = 0.0001531 relative error = 0.02005 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6567 Order of pole (three term test) = 1.477e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0637 0.259 h = 0.001 0.001 y[1] (numeric) = -0.574817614135 -0.500419271191 y[1] (closed_form) = -0.574706592168 -0.500535073643 absolute error = 0.0001604 relative error = 0.02105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5158 Order of pole (three term test) = 8.964e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0627 0.26 h = 0.001 0.003 y[1] (numeric) = -0.57430300096 -0.503324177362 y[1] (closed_form) = -0.574199896561 -0.503448777029 absolute error = 0.0001617 relative error = 0.02118 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.446 Order of pole (three term test) = 6.130e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0617 0.263 h = 0.0001 0.004 y[1] (numeric) = -0.570341813907 -0.50864172297 y[1] (closed_form) = -0.570223347044 -0.508747563142 absolute error = 0.0001589 relative error = 0.02079 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.384 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0616 0.267 h = 0.003 0.006 y[1] (numeric) = -0.563506907707 -0.513507966427 y[1] (closed_form) = -0.563395738529 -0.513594530671 absolute error = 0.0001409 relative error = 0.01848 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0586 0.273 h = 0.0001 0.005 y[1] (numeric) = -0.556444399546 -0.525587659476 y[1] (closed_form) = -0.556244452588 -0.525690633988 absolute error = 0.0002249 relative error = 0.02939 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.093 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.815 Order of pole (three term test) = 1.849e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0585 0.278 h = 0.0001 0.003 y[1] (numeric) = -0.547574890877 -0.531262975434 y[1] (closed_form) = -0.547433894644 -0.531367166511 absolute error = 0.0001753 relative error = 0.02298 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6569 Order of pole (three term test) = 4.795e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0584 0.281 h = 0.001 0.001 y[1] (numeric) = -0.542294281844 -0.534632088542 y[1] (closed_form) = -0.542160223527 -0.534758081527 absolute error = 0.000184 relative error = 0.02416 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5159 Order of pole (three term test) = 4.520e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0574 0.282 h = 0.001 0.003 y[1] (numeric) = -0.541542516447 -0.537481278469 y[1] (closed_form) = -0.541415415952 -0.537616824563 absolute error = 0.0001858 relative error = 0.02435 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.447 Order of pole (three term test) = 1.977e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=174.3MB, alloc=44.3MB, time=2.22 x[1] = -1.0564 0.285 h = 0.0001 0.004 y[1] (numeric) = -0.537160622799 -0.542447299071 y[1] (closed_form) = -0.537020199667 -0.542562631709 absolute error = 0.0001817 relative error = 0.0238 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.384 Order of pole (three term test) = 7.871e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0563 0.289 h = 0.003 0.006 y[1] (numeric) = -0.529957797324 -0.546725589489 y[1] (closed_form) = -0.529826604195 -0.546822538265 absolute error = 0.0001631 relative error = 0.02142 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 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) = 1.284e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0533 0.295 h = 0.0001 0.005 y[1] (numeric) = -0.521937165517 -0.558160345525 y[1] (closed_form) = -0.521716193918 -0.558264442805 absolute error = 0.0002443 relative error = 0.03197 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8155 Order of pole (three term test) = 1.454e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0532 0.3 h = 0.0001 0.003 y[1] (numeric) = -0.51265130301 -0.563070804889 y[1] (closed_form) = -0.512488661309 -0.563182176048 absolute error = 0.0001971 relative error = 0.02589 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6573 Order of pole (three term test) = 6.786e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0531 0.303 h = 0.001 0.001 y[1] (numeric) = -0.507125818616 -0.565984836754 y[1] (closed_form) = -0.506967815192 -0.566118532228 absolute error = 0.000207 relative error = 0.02724 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5163 Order of pole (three term test) = 4.621e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0521 0.304 h = 0.0001 0.004 y[1] (numeric) = -0.506144485018 -0.568754369133 y[1] (closed_form) = -0.505992396753 -0.568898247285 absolute error = 0.0002094 relative error = 0.0275 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.098 Order of pole (three term test) = 1.250e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.052 0.308 h = 0.003 0.006 y[1] (numeric) = -0.498688759206 -0.572526520486 y[1] (closed_form) = -0.498541901775 -0.572622976197 absolute error = 0.0001757 relative error = 0.02314 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 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) = 1.047e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.049 0.314 h = 0.0001 0.005 y[1] (numeric) = -0.489911816375 -0.583321281081 y[1] (closed_form) = -0.489675351726 -0.583416902644 absolute error = 0.0002551 relative error = 0.03349 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8163 Order of pole (three term test) = 1.497e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0489 0.319 h = 0.0001 0.003 y[1] (numeric) = -0.48034318766 -0.587540869643 y[1] (closed_form) = -0.480163857333 -0.587648841313 absolute error = 0.0002093 relative error = 0.02758 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.658 Order of pole (three term test) = 1.113e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0488 0.322 h = 0.001 0.001 y[1] (numeric) = -0.474651847965 -0.590044286617 y[1] (closed_form) = -0.474475145891 -0.590174772961 absolute error = 0.0002197 relative error = 0.02901 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5169 Order of pole (three term test) = 4.799e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0478 0.323 h = 0.001 0.003 y[1] (numeric) = -0.473482480112 -0.592724441012 y[1] (closed_form) = -0.473310738784 -0.592865529714 absolute error = 0.0002223 relative error = 0.0293 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.452 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0468 0.326 h = 0.0001 0.004 y[1] (numeric) = -0.468431561692 -0.596928736414 y[1] (closed_form) = -0.468250690259 -0.597047659728 absolute error = 0.0002165 relative error = 0.02853 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.387 Order of pole (three term test) = 1.959e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0467 0.33 h = 0.003 0.006 y[1] (numeric) = -0.460723486833 -0.600028923184 y[1] (closed_form) = -0.460555050492 -0.600131731155 absolute error = 0.0001973 relative error = 0.02609 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.84 Order of pole (three term test) = 7.845e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0437 0.336 h = 0.0001 0.005 y[1] (numeric) = -0.451136381422 -0.610015358957 y[1] (closed_form) = -0.450879464578 -0.610108191084 absolute error = 0.0002732 relative error = 0.03601 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8174 Order of pole (three term test) = 1.593e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=220.4MB, alloc=44.3MB, time=2.80 x[1] = -1.0436 0.341 h = 0.0001 0.003 y[1] (numeric) = -0.441307876125 -0.613413388656 y[1] (closed_form) = -0.441106131029 -0.613524253242 absolute error = 0.0002302 relative error = 0.03046 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.098 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.659 Order of pole (three term test) = 1.593e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0435 0.344 h = 0.001 0.001 y[1] (numeric) = -0.435464544231 -0.615428922524 y[1] (closed_form) = -0.435263100851 -0.615562286461 absolute error = 0.0002416 relative error = 0.03205 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.099 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5177 Order of pole (three term test) = 7.043e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0425 0.345 h = 0.001 0.003 y[1] (numeric) = -0.434087388992 -0.617988573138 y[1] (closed_form) = -0.433889763611 -0.618132909638 absolute error = 0.0002447 relative error = 0.0324 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.098 Order of pole (given) = 4 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) = 1.380e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0415 0.348 h = 0.0001 0.004 y[1] (numeric) = -0.428740448218 -0.621740640175 y[1] (closed_form) = -0.428536068657 -0.621862166194 absolute error = 0.0002378 relative error = 0.03148 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.098 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.389 Order of pole (three term test) = 3.948e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0414 0.352 h = 0.003 0.006 y[1] (numeric) = -0.420854078961 -0.62418147314 y[1] (closed_form) = -0.420663610131 -0.624288362504 absolute error = 0.0002184 relative error = 0.02901 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.099 Order of pole (given) = 4 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) = 5.126e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0384 0.358 h = 0.0001 0.005 y[1] (numeric) = -0.410549246497 -0.633287176292 y[1] (closed_form) = -0.410272520231 -0.633375235507 absolute error = 0.0002904 relative error = 0.03848 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.098 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8188 Order of pole (three term test) = 4.958e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0383 0.363 h = 0.0001 0.003 y[1] (numeric) = -0.400548023882 -0.635848062202 y[1] (closed_form) = -0.400323847855 -0.635959499329 absolute error = 0.0002503 relative error = 0.03331 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6602 Order of pole (three term test) = 5.524e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0382 0.366 h = 0.001 0.001 y[1] (numeric) = -0.394604323926 -0.637366892671 y[1] (closed_form) = -0.394378165719 -0.637500531204 absolute error = 0.0002627 relative error = 0.03504 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5186 Order of pole (three term test) = 1.512e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0372 0.367 h = 0.001 0.003 y[1] (numeric) = -0.393034467173 -0.639786603434 y[1] (closed_form) = -0.392810959458 -0.639931439289 absolute error = 0.0002663 relative error = 0.03547 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.46 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0362 0.37 h = 0.0001 0.004 y[1] (numeric) = -0.387441546233 -0.643062601157 y[1] (closed_form) = -0.387213696234 -0.643184281904 absolute error = 0.0002583 relative error = 0.03441 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.392 Order of pole (three term test) = 1.129e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0361 0.374 h = 0.003 0.006 y[1] (numeric) = -0.379446347949 -0.64483532367 y[1] (closed_form) = -0.379233677729 -0.644943998601 absolute error = 0.0002388 relative error = 0.03192 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.102 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.847 Order of pole (three term test) = 7.741e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0331 0.38 h = 0.0001 0.005 y[1] (numeric) = -0.368523414887 -0.653000384261 y[1] (closed_form) = -0.36822774191 -0.65308181091 absolute error = 0.0003067 relative error = 0.0409 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8206 Order of pole (three term test) = 1.772e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.033 0.385 h = 0.0001 0.003 y[1] (numeric) = -0.358436929922 -0.654719425041 y[1] (closed_form) = -0.358190589437 -0.654829152709 absolute error = 0.0002697 relative error = 0.03613 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.102 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6617 Order of pole (three term test) = 1.201e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0329 0.388 h = 0.001 0.001 y[1] (numeric) = -0.352444589767 -0.655739153866 y[1] (closed_form) = -0.352194064701 -0.655870514956 absolute error = 0.0002829 relative error = 0.038 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.103 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5198 Order of pole (three term test) = 5.756e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=266.6MB, alloc=44.3MB, time=3.38 x[1] = -1.0319 0.389 h = 0.001 0.003 y[1] (numeric) = -0.350699186034 -0.658001682867 y[1] (closed_form) = -0.350450140275 -0.658144320518 absolute error = 0.000287 relative error = 0.03849 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.103 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.466 Order of pole (three term test) = 1.361e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0309 0.392 h = 0.0001 0.004 y[1] (numeric) = -0.344912267776 -0.66078428984 y[1] (closed_form) = -0.344661284385 -0.660903726183 absolute error = 0.000278 relative error = 0.03729 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.103 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.396 Order of pole (three term test) = 1.015e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0308 0.396 h = 0.003 0.006 y[1] (numeric) = -0.336877417568 -0.661888727517 y[1] (closed_form) = -0.336642659976 -0.661996908278 absolute error = 0.0002585 relative error = 0.0348 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.104 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.851 Order of pole (three term test) = 3.745e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0278 0.402 h = 0.0001 0.005 y[1] (numeric) = -0.325441273414 -0.669066458034 y[1] (closed_form) = -0.325127712556 -0.669139542723 absolute error = 0.000322 relative error = 0.04328 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.104 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8228 Order of pole (three term test) = 1.924e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0277 0.407 h = 0.0001 0.003 y[1] (numeric) = -0.315355735628 -0.669949614264 y[1] (closed_form) = -0.315087767843 -0.670055427857 absolute error = 0.0002881 relative error = 0.03891 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.105 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6635 Order of pole (three term test) = 9.147e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0276 0.41 h = 0.001 0.001 y[1] (numeric) = -0.30936568211 -0.670474121939 y[1] (closed_form) = -0.309091444527 -0.670600749355 absolute error = 0.0003021 relative error = 0.04091 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.106 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5213 Order of pole (three term test) = 1.404e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0266 0.411 h = 0.0001 0.004 y[1] (numeric) = -0.307463595321 -0.672564657345 y[1] (closed_form) = -0.307189682639 -0.672702498334 absolute error = 0.0003066 relative error = 0.04146 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.106 Order of pole (given) = 4 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) = 2.157e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0265 0.415 h = 0.003 0.006 y[1] (numeric) = -0.299447713905 -0.673128328184 y[1] (closed_form) = -0.2991997188 -0.673228873757 absolute error = 0.0002676 relative error = 0.03632 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.107 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.856 Order of pole (three term test) = 8.658e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0235 0.421 h = 0.0001 0.005 y[1] (numeric) = -0.287668625785 -0.679424850052 y[1] (closed_form) = -0.287346200771 -0.679484153707 absolute error = 0.0003278 relative error = 0.04444 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.107 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8251 Order of pole (three term test) = 9.410e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0234 0.426 h = 0.0001 0.003 y[1] (numeric) = -0.277660580858 -0.679602439311 y[1] (closed_form) = -0.277380132527 -0.679697790069 absolute error = 0.0002962 relative error = 0.04035 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.109 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6654 Order of pole (three term test) = 1.585e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0233 0.429 h = 0.001 0.001 y[1] (numeric) = -0.271717759269 -0.679709193265 y[1] (closed_form) = -0.271429377737 -0.679824446338 absolute error = 0.0003106 relative error = 0.04243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.11 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5228 Order of pole (three term test) = 6.889e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0223 0.43 h = 0.001 0.003 y[1] (numeric) = -0.269699172237 -0.681640267879 y[1] (closed_form) = -0.269410153048 -0.681766558129 absolute error = 0.0003154 relative error = 0.04303 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.109 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.48 Order of pole (three term test) = 9.528e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0213 0.433 h = 0.0001 0.004 y[1] (numeric) = -0.263698321943 -0.683480541557 y[1] (closed_form) = -0.26341167264 -0.683584330259 absolute error = 0.0003049 relative error = 0.04161 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.109 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.404 Order of pole (three term test) = 1.246e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0212 0.437 h = 0.003 0.006 y[1] (numeric) = -0.255775478915 -0.683370562166 y[1] (closed_form) = -0.255506353272 -0.683466557475 absolute error = 0.0002857 relative error = 0.03916 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.111 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.862 Order of pole (three term test) = 1.319e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0182 0.443 h = 0.0001 0.005 y[1] (numeric) = -0.243685730307 -0.68863048589 y[1] (closed_form) = -0.243347830576 -0.688678754138 absolute error = 0.0003413 relative error = 0.04673 % Correct digits = 3 memory used=312.7MB, alloc=44.3MB, time=3.97 Radius of convergence (given) for eq 1 = 1.11 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8278 Order of pole (three term test) = 6.621e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0181 0.448 h = 0.0001 0.003 y[1] (numeric) = -0.233830483533 -0.688010845633 y[1] (closed_form) = -0.23353008543 -0.688098519191 absolute error = 0.0003129 relative error = 0.04307 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.112 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6676 Order of pole (three term test) = 1.583e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.018 0.451 h = 0.001 0.001 y[1] (numeric) = -0.227979502685 -0.687645793844 y[1] (closed_form) = -0.227669386899 -0.687752149815 absolute error = 0.0003278 relative error = 0.04525 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.113 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5246 Order of pole (three term test) = 8.153e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.017 0.452 h = 0.001 0.003 y[1] (numeric) = -0.225842654087 -0.689384573205 y[1] (closed_form) = -0.225530828891 -0.689501658697 absolute error = 0.0003331 relative error = 0.04591 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.113 Order of pole (given) = 4 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) = 2.120e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.016 0.455 h = 0.0001 0.004 y[1] (numeric) = -0.219798624721 -0.690718859285 y[1] (closed_form) = -0.21949133108 -0.690814179027 absolute error = 0.0003217 relative error = 0.04439 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.113 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.409 Order of pole (three term test) = 9.864e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0159 0.459 h = 0.003 0.006 y[1] (numeric) = -0.212021772233 -0.68998514839 y[1] (closed_form) = -0.211732370926 -0.69007457281 absolute error = 0.0003029 relative error = 0.04196 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.115 Order of pole (given) = 4 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) = 8.024e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0129 0.465 h = 0.0001 0.005 y[1] (numeric) = -0.199730229245 -0.694200662404 y[1] (closed_form) = -0.199378316022 -0.694236719232 absolute error = 0.0003538 relative error = 0.04898 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.115 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8309 Order of pole (three term test) = 3.729e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0128 0.47 h = 0.0001 0.003 y[1] (numeric) = -0.190102719251 -0.692816923757 y[1] (closed_form) = -0.189783565298 -0.692895123289 absolute error = 0.0003286 relative error = 0.04574 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.117 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6702 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0127 0.473 h = 0.001 0.001 y[1] (numeric) = -0.18438770952 -0.691999890159 y[1] (closed_form) = -0.184057247344 -0.692095378237 absolute error = 0.000344 relative error = 0.04803 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.118 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5266 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0117 0.474 h = 0.001 0.003 y[1] (numeric) = -0.182154153606 -0.693539236275 y[1] (closed_form) = -0.181820977143 -0.693645029698 absolute error = 0.0003496 relative error = 0.04875 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.117 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.498 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0107 0.477 h = 0.0001 0.004 y[1] (numeric) = -0.176117528322 -0.694375026307 y[1] (closed_form) = -0.175790896321 -0.694460021415 absolute error = 0.0003375 relative error = 0.04711 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.118 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.414 Order of pole (three term test) = 3.468e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0106 0.481 h = 0.003 0.006 y[1] (numeric) = -0.168544254136 -0.693046522877 y[1] (closed_form) = -0.168235650633 -0.693127508074 absolute error = 0.0003191 relative error = 0.04473 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.119 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.876 Order of pole (three term test) = 4.256e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0076 0.487 h = 0.0001 0.005 y[1] (numeric) = -0.156157589612 -0.696222782519 y[1] (closed_form) = -0.155793206819 -0.696245657245 absolute error = 0.0003651 relative error = 0.05117 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.119 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8343 Order of pole (three term test) = 6.021e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0075 0.492 h = 0.0001 0.003 y[1] (numeric) = -0.146826676367 -0.694115863622 y[1] (closed_form) = -0.146490136929 -0.694182983482 absolute error = 0.0003432 relative error = 0.04837 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.121 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.673 Order of pole (three term test) = 2.040e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0074 0.495 h = 0.001 0.001 y[1] (numeric) = -0.141288148818 -0.692871224598 y[1] (closed_form) = -0.140938921129 -0.69295409765 absolute error = 0.0003589 relative error = 0.05076 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.122 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5288 Order of pole (three term test) = 9.961e-31 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=359.0MB, alloc=44.3MB, time=4.55 x[1] = -1.0064 0.496 h = 0.001 0.003 y[1] (numeric) = -0.13897962703 -0.694206720561 y[1] (closed_form) = -0.138626760382 -0.694299371507 absolute error = 0.0003648 relative error = 0.05153 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.122 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.509 Order of pole (three term test) = 4.122e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0054 0.499 h = 0.0001 0.004 y[1] (numeric) = -0.132998601266 -0.694557173256 y[1] (closed_form) = -0.132654117309 -0.694630196443 absolute error = 0.0003521 relative error = 0.04979 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.122 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.42 Order of pole (three term test) = 3.559e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0053 0.503 h = 0.003 0.006 y[1] (numeric) = -0.12568138147 -0.692668633569 y[1] (closed_form) = -0.125354839912 -0.692739488695 absolute error = 0.0003341 relative error = 0.04746 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.124 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.885 Order of pole (three term test) = 1.048e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0023 0.509 h = 0.0001 0.005 y[1] (numeric) = -0.113302399839 -0.694823000489 y[1] (closed_form) = -0.112927143794 -0.694831929805 absolute error = 0.0003754 relative error = 0.05332 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.124 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8381 Order of pole (three term test) = 1.869e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0022 0.514 h = 0.0001 0.003 y[1] (numeric) = -0.10433003674 -0.692040499176 y[1] (closed_form) = -0.103977626421 -0.692095141938 absolute error = 0.0003566 relative error = 0.05096 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.126 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.676 Order of pole (three term test) = 2.360e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0021 0.517 h = 0.001 0.001 y[1] (numeric) = -0.0990044048379 -0.690396527889 y[1] (closed_form) = -0.0986381476223 -0.69046528059 absolute error = 0.0003727 relative error = 0.05343 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.128 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5313 Order of pole (three term test) = 1.159e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0011 0.518 h = 0.0001 0.004 y[1] (numeric) = -0.0966424731973 -0.691526401658 y[1] (closed_form) = -0.0962717432822 -0.691604316223 absolute error = 0.0003788 relative error = 0.05425 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.127 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.189 Order of pole (three term test) = 1.990e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.001 0.522 h = 0.003 0.006 y[1] (numeric) = -0.0895704594449 -0.689209617783 y[1] (closed_form) = -0.089236306907 -0.689268473369 absolute error = 0.0003393 relative error = 0.04882 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.129 Order of pole (given) = 4 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) = 7.598e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.998 0.528 h = 0.0001 0.005 y[1] (numeric) = -0.0772880449597 -0.690508531291 y[1] (closed_form) = -0.0769114509916 -0.690503012996 absolute error = 0.0003766 relative error = 0.05421 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.129 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8417 Order of pole (three term test) = 5.644e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9979 0.533 h = 0.0001 0.003 y[1] (numeric) = -0.0686753599943 -0.687191988922 y[1] (closed_form) = -0.0683173039708 -0.687232891843 absolute error = 0.0003604 relative error = 0.05218 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.131 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.679 Order of pole (three term test) = 1.360e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9978 0.536 h = 0.001 0.001 y[1] (numeric) = -0.0635629862567 -0.68523242974 y[1] (closed_form) = -0.0631902881689 -0.685285957348 absolute error = 0.0003765 relative error = 0.05471 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.133 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5336 Order of pole (three term test) = 1.331e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9968 0.537 h = 0.001 0.003 y[1] (numeric) = -0.0611743782239 -0.686185519687 y[1] (closed_form) = -0.0607965772597 -0.686247611582 absolute error = 0.0003829 relative error = 0.05557 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.132 Order of pole (given) = 4 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) = 5.814e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9958 0.54 h = 0.0001 0.004 y[1] (numeric) = -0.0554193686892 -0.685686894413 y[1] (closed_form) = -0.0550528221385 -0.685731985308 absolute error = 0.0003693 relative error = 0.05368 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.133 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.433 Order of pole (three term test) = 1.068e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9957 0.544 h = 0.003 0.006 y[1] (numeric) = -0.0487039212911 -0.682869132787 y[1] (closed_form) = -0.0483545981566 -0.682915267229 absolute error = 0.0003524 relative error = 0.05147 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.135 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.902 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=405.3MB, alloc=44.3MB, time=5.13 x[1] = -0.9927 0.55 h = 0.0001 0.005 y[1] (numeric) = -0.0366047594343 -0.683208495986 y[1] (closed_form) = -0.0362203074665 -0.683188171335 absolute error = 0.000385 relative error = 0.05627 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.135 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8461 Order of pole (three term test) = 4.704e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9926 0.555 h = 0.0001 0.003 y[1] (numeric) = -0.0284448483641 -0.679319152456 y[1] (closed_form) = -0.0280740195013 -0.679345587502 absolute error = 0.0003718 relative error = 0.05468 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.137 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6826 Order of pole (three term test) = 1.606e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9925 0.558 h = 0.001 0.001 y[1] (numeric) = -0.0236006752075 -0.677021137335 y[1] (closed_form) = -0.0232144679557 -0.677058444724 absolute error = 0.000388 relative error = 0.05727 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.139 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5364 Order of pole (three term test) = 1.582e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9915 0.559 h = 0.001 0.003 y[1] (numeric) = -0.0211970757815 -0.677772106556 y[1] (closed_form) = -0.0208051209357 -0.677817240586 absolute error = 0.0003945 relative error = 0.05818 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.138 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.545 Order of pole (three term test) = 4.544e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9905 0.562 h = 0.0001 0.004 y[1] (numeric) = -0.0156164717328 -0.676852434098 y[1] (closed_form) = -0.0152370154058 -0.676882138962 absolute error = 0.0003806 relative error = 0.05622 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.139 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.441 Order of pole (three term test) = 5.663e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9904 0.566 h = 0.003 0.006 y[1] (numeric) = -0.00927383302956 -0.673598287225 y[1] (closed_form) = -0.00891097121247 -0.673630608872 absolute error = 0.0003643 relative error = 0.05408 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.141 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.912 Order of pole (three term test) = 1.060e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9874 0.572 h = 0.0001 0.005 y[1] (numeric) = 0.00255788306627 -0.673024274875 y[1] (closed_form) = 0.00294860234031 -0.672988945791 absolute error = 0.0003923 relative error = 0.05829 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.141 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8507 Order of pole (three term test) = 5.606e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9873 0.577 h = 0.0001 0.003 y[1] (numeric) = 0.010225580632 -0.66862209841 y[1] (closed_form) = 0.0106074421209 -0.668633308027 absolute error = 0.000382 relative error = 0.05713 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.144 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6864 Order of pole (three term test) = 2.712e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9872 0.58 h = 0.001 0.001 y[1] (numeric) = 0.0147784358631 -0.666021077568 y[1] (closed_form) = 0.0151761896613 -0.666041392625 absolute error = 0.0003983 relative error = 0.05978 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.145 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5394 Order of pole (three term test) = 5.949e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9862 0.581 h = 0.001 0.003 y[1] (numeric) = 0.01717779899 -0.666574842271 y[1] (closed_form) = 0.0175818386606 -0.666602203259 absolute error = 0.000405 relative error = 0.06073 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.145 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.559 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9852 0.584 h = 0.0001 0.004 y[1] (numeric) = 0.0225503446525 -0.665263503676 y[1] (closed_form) = 0.0229408637363 -0.665277084474 absolute error = 0.0003908 relative error = 0.0587 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.145 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.449 Order of pole (three term test) = 7.913e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9851 0.588 h = 0.003 0.006 y[1] (numeric) = 0.028491503616 -0.661621306354 y[1] (closed_form) = 0.0288662064245 -0.661638946549 absolute error = 0.0003751 relative error = 0.05664 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.147 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.923 Order of pole (three term test) = 9.007e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9821 0.594 h = 0.0001 0.005 y[1] (numeric) = 0.0399799123512 -0.660187663558 y[1] (closed_form) = 0.0403753553656 -0.660137308742 absolute error = 0.0003986 relative error = 0.06027 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.148 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8557 Order of pole (three term test) = 7.048e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.982 0.599 h = 0.0001 0.003 y[1] (numeric) = 0.0471241235702 -0.655334646893 y[1] (closed_form) = 0.0475152598972 -0.655330095483 absolute error = 0.0003912 relative error = 0.05953 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.15 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6904 Order of pole (three term test) = 6.544e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=451.6MB, alloc=44.3MB, time=5.72 x[1] = -0.9819 0.602 h = 0.001 0.001 y[1] (numeric) = 0.0513673518532 -0.652467229344 y[1] (closed_form) = 0.0517746805374 -0.652470030979 absolute error = 0.0004073 relative error = 0.06223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.152 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5426 Order of pole (three term test) = 6.817e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9809 0.603 h = 0.001 0.003 y[1] (numeric) = 0.0537445463916 -0.652830627202 y[1] (closed_form) = 0.0541585922846 -0.652839666587 absolute error = 0.0004141 relative error = 0.06322 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.151 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.575 Order of pole (three term test) = 9.952e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9799 0.606 h = 0.0001 0.004 y[1] (numeric) = 0.0588799393113 -0.651159550487 y[1] (closed_form) = 0.0592796639735 -0.651156503855 absolute error = 0.0003997 relative error = 0.06114 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.152 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.458 Order of pole (three term test) = 1.643e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9798 0.61 h = 0.003 0.006 y[1] (numeric) = 0.0643973924505 -0.64717886692 y[1] (closed_form) = 0.0647822047098 -0.647181178877 absolute error = 0.0003848 relative error = 0.05917 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.154 Order of pole (given) = 4 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9768 0.616 h = 0.0001 0.005 y[1] (numeric) = 0.0754755419204 -0.644945492794 y[1] (closed_form) = 0.0758742312989 -0.644880252773 absolute error = 0.000404 relative error = 0.06222 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.155 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8609 Order of pole (three term test) = 8.212e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9767 0.621 h = 0.0001 0.003 y[1] (numeric) = 0.0820730305335 -0.639704517411 y[1] (closed_form) = 0.0824716955106 -0.639683883219 absolute error = 0.0003992 relative error = 0.06189 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.157 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6947 Order of pole (three term test) = 2.820e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9766 0.624 h = 0.001 0.001 y[1] (numeric) = 0.085993048861 -0.63660780612 y[1] (closed_form) = 0.0864080046106 -0.636592813311 absolute error = 0.0004152 relative error = 0.06463 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.159 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.546 Order of pole (three term test) = 1.109e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9756 0.625 h = 0.0001 0.004 y[1] (numeric) = 0.0883316192385 -0.636789340402 y[1] (closed_form) = 0.0887536183586 -0.63677976448 absolute error = 0.0004221 relative error = 0.06565 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.159 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.278 Order of pole (three term test) = 1.460e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9755 0.629 h = 0.003 0.006 y[1] (numeric) = 0.093490022839 -0.632569613437 y[1] (closed_form) = 0.093876107529 -0.632559339733 absolute error = 0.0003862 relative error = 0.0604 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.161 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.946 Order of pole (three term test) = 1.306e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9725 0.635 h = 0.0001 0.005 y[1] (numeric) = 0.104160011825 -0.629705273532 y[1] (closed_form) = 0.104554352238 -0.629628481789 absolute error = 0.0004017 relative error = 0.06295 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.161 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8659 Order of pole (three term test) = 9.867e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9724 0.64 h = 0.0001 0.003 y[1] (numeric) = 0.110270614656 -0.624187355995 y[1] (closed_form) = 0.110668346857 -0.62415376649 absolute error = 0.0003991 relative error = 0.06297 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.164 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6987 Order of pole (three term test) = 4.798e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9723 0.643 h = 0.001 0.001 y[1] (numeric) = 0.113902897542 -0.620926895521 y[1] (closed_form) = 0.11431683604 -0.620897526112 absolute error = 0.000415 relative error = 0.06573 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.166 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5492 Order of pole (three term test) = 1.204e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9713 0.644 h = 0.001 0.003 y[1] (numeric) = 0.116194269063 -0.620960468459 y[1] (closed_form) = 0.116615440554 -0.620935807443 absolute error = 0.0004219 relative error = 0.06678 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.165 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.606 Order of pole (three term test) = 1.035e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9703 0.647 h = 0.0001 0.004 y[1] (numeric) = 0.120823596337 -0.618714235126 y[1] (closed_form) = 0.121229545571 -0.618680663336 absolute error = 0.0004073 relative error = 0.06461 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.166 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.476 Order of pole (three term test) = 2.424e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9702 0.651 h = 0.003 0.006 y[1] (numeric) = 0.125512180669 -0.614241633671 y[1] (closed_form) = 0.125905162179 -0.614215416229 absolute error = 0.0003939 relative error = 0.06282 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.168 Order of pole (given) = 4 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) = 3.224e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=497.7MB, alloc=44.3MB, time=6.31 x[1] = -0.9672 0.657 h = 0.0001 0.005 y[1] (numeric) = 0.135672871447 -0.610701092491 y[1] (closed_form) = 0.136067942584 -0.61061006501 absolute error = 0.0004054 relative error = 0.06481 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.169 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8717 Order of pole (three term test) = 1.565e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9671 0.662 h = 0.0001 0.003 y[1] (numeric) = 0.141214554229 -0.604911125015 y[1] (closed_form) = 0.141616686273 -0.604861399572 absolute error = 0.0004052 relative error = 0.06523 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.172 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7034 Order of pole (three term test) = 4.704e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.967 0.665 h = 0.001 0.001 y[1] (numeric) = 0.144510711123 -0.601489700575 y[1] (closed_form) = 0.144928816126 -0.601442619751 absolute error = 0.0004207 relative error = 0.06801 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.174 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5529 Order of pole (three term test) = 9.269e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.966 0.666 h = 0.001 0.003 y[1] (numeric) = 0.146737331506 -0.601360897042 y[1] (closed_form) = 0.147162811471 -0.601317716669 absolute error = 0.0004277 relative error = 0.06908 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.173 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.624 Order of pole (three term test) = 1.163e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.965 0.669 h = 0.0001 0.004 y[1] (numeric) = 0.151072369766 -0.598854345927 y[1] (closed_form) = 0.151482418104 -0.598803918816 absolute error = 0.0004131 relative error = 0.06689 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.174 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.486 Order of pole (three term test) = 6.031e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9649 0.673 h = 0.003 0.006 y[1] (numeric) = 0.155307961766 -0.594184358323 y[1] (closed_form) = 0.155706171308 -0.594142139194 absolute error = 0.0004004 relative error = 0.0652 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.176 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.972 Order of pole (three term test) = 4.017e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9619 0.679 h = 0.0001 0.005 y[1] (numeric) = 0.164919055965 -0.59003730211 y[1] (closed_form) = 0.165313647357 -0.589932545953 absolute error = 0.0004083 relative error = 0.06664 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.177 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8778 Order of pole (three term test) = 1.534e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9618 0.684 h = 0.0001 0.003 y[1] (numeric) = 0.169889534289 -0.584035175881 y[1] (closed_form) = 0.170294489618 -0.583969527989 absolute error = 0.0004102 relative error = 0.06744 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.18 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7084 Order of pole (three term test) = 5.266e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9617 0.687 h = 0.001 0.001 y[1] (numeric) = 0.172848281741 -0.580488072069 y[1] (closed_form) = 0.173268824444 -0.580423590106 absolute error = 0.0004255 relative error = 0.07024 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.182 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5568 Order of pole (three term test) = 1.038e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9607 0.688 h = 0.001 0.003 y[1] (numeric) = 0.174998517889 -0.580208658328 y[1] (closed_form) = 0.17542648747 -0.580147291545 absolute error = 0.0004323 relative error = 0.07133 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.182 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.642 Order of pole (three term test) = 7.211e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9597 0.691 h = 0.0001 0.004 y[1] (numeric) = 0.179027846106 -0.577477218792 y[1] (closed_form) = 0.179440356319 -0.577410213776 absolute error = 0.0004179 relative error = 0.06912 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.183 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.496 Order of pole (three term test) = 1.892e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9596 0.695 h = 0.003 0.006 y[1] (numeric) = 0.182810661628 -0.572656596047 y[1] (closed_form) = 0.183212497295 -0.572598496566 absolute error = 0.000406 relative error = 0.06753 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.185 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.986 Order of pole (three term test) = 1.071e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9566 0.701 h = 0.0001 0.005 y[1] (numeric) = 0.191840927086 -0.567973674628 y[1] (closed_form) = 0.192233937726 -0.567855790346 absolute error = 0.0004103 relative error = 0.06844 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.186 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8841 Order of pole (three term test) = 1.924e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9565 0.706 h = 0.0001 0.003 y[1] (numeric) = 0.196244198116 -0.561816719451 y[1] (closed_form) = 0.196650494872 -0.561735515995 absolute error = 0.0004143 relative error = 0.06962 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.189 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7136 Order of pole (three term test) = 6.646e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=544.0MB, alloc=44.3MB, time=6.90 x[1] = -0.9564 0.709 h = 0.001 0.001 y[1] (numeric) = 0.198867935361 -0.558177701898 y[1] (closed_form) = 0.199289301604 -0.558096295194 absolute error = 0.0004292 relative error = 0.07242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.191 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5609 Order of pole (three term test) = 6.559e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9554 0.71 h = 0.001 0.003 y[1] (numeric) = 0.200931905648 -0.557760085102 y[1] (closed_form) = 0.20136066832 -0.557681040408 absolute error = 0.000436 relative error = 0.07353 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.19 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.662 Order of pole (three term test) = 9.115e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9544 0.713 h = 0.0001 0.004 y[1] (numeric) = 0.204648273536 -0.554838692776 y[1] (closed_form) = 0.205061714021 -0.554755544363 absolute error = 0.0004217 relative error = 0.0713 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.191 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.507 Order of pole (three term test) = 1.437e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9543 0.717 h = 0.003 0.006 y[1] (numeric) = 0.207983299823 -0.549911954691 y[1] (closed_form) = 0.20838724489 -0.549838257847 absolute error = 0.0004106 relative error = 0.06983 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.194 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.001 Order of pole (three term test) = 1.318e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9513 0.723 h = 0.0001 0.005 y[1] (numeric) = 0.216410183547 -0.54476365043 y[1] (closed_form) = 0.216800625889 -0.544633314216 absolute error = 0.0004116 relative error = 0.07022 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.195 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8908 Order of pole (three term test) = 4.890e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9512 0.728 h = 0.0001 0.003 y[1] (numeric) = 0.220255870396 -0.538506034648 y[1] (closed_form) = 0.220662134414 -0.538409776146 absolute error = 0.0004175 relative error = 0.07175 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.198 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7189 Order of pole (three term test) = 1.196e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9511 0.731 h = 0.001 0.001 y[1] (numeric) = 0.222550293406 -0.534807001139 y[1] (closed_form) = 0.222970997066 -0.534709288964 absolute error = 0.0004319 relative error = 0.07455 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5652 Order of pole (three term test) = 8.517e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9501 0.732 h = 0.0001 0.004 y[1] (numeric) = 0.224519844553 -0.534263987092 y[1] (closed_form) = 0.224947840281 -0.534167923643 absolute error = 0.0004386 relative error = 0.07568 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.199 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.393 Order of pole (three term test) = 1.026e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.95 0.736 h = 0.003 0.006 y[1] (numeric) = 0.227495260745 -0.529282360729 y[1] (closed_form) = 0.22789559821 -0.529198436532 absolute error = 0.000409 relative error = 0.07099 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.202 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.015 Order of pole (three term test) = 8.879e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.947 0.742 h = 0.0001 0.005 y[1] (numeric) = 0.235386540221 -0.523796440755 y[1] (closed_form) = 0.235769826379 -0.523658882137 absolute error = 0.0004072 relative error = 0.07091 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.203 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8969 Order of pole (three term test) = 6.087e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9469 0.747 h = 0.0001 0.003 y[1] (numeric) = 0.238763379574 -0.517499186088 y[1] (closed_form) = 0.239164329042 -0.517393341853 absolute error = 0.0004147 relative error = 0.07275 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.206 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7239 Order of pole (three term test) = 1.075e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9468 0.75 h = 0.001 0.001 y[1] (numeric) = 0.240780880558 -0.513776182863 y[1] (closed_form) = 0.241195640438 -0.513667917279 absolute error = 0.0004287 relative error = 0.07554 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.208 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5691 Order of pole (three term test) = 3.124e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9458 0.751 h = 0.001 0.003 y[1] (numeric) = 0.242662627387 -0.513136850833 y[1] (closed_form) = 0.243084529376 -0.513029658965 absolute error = 0.0004353 relative error = 0.07668 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.208 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.7 Order of pole (three term test) = 1.478e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9448 0.754 h = 0.0001 0.004 y[1] (numeric) = 0.245789052834 -0.50995517078 y[1] (closed_form) = 0.246196279906 -0.509846479276 absolute error = 0.0004215 relative error = 0.07444 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.209 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.529 Order of pole (three term test) = 1.619e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=590.2MB, alloc=44.3MB, time=7.49 x[1] = -0.9447 0.758 h = 0.0001 0.004 y[1] (numeric) = 0.248318088251 -0.504945098259 y[1] (closed_form) = 0.248717994446 -0.504846482793 absolute error = 0.0004119 relative error = 0.07319 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.211 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.211 Order of pole (three term test) = 1.434e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9446 0.762 h = 0.003 0.006 y[1] (numeric) = 0.250767417867 -0.49995897156 y[1] (closed_form) = 0.251167324063 -0.499860356094 absolute error = 0.0004119 relative error = 0.07363 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.214 Order of pole (given) = 4 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) = 6.345e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9416 0.768 h = 0.0001 0.005 y[1] (numeric) = 0.257916476126 -0.49410644928 y[1] (closed_form) = 0.258295233115 -0.493958620739 absolute error = 0.0004066 relative error = 0.07294 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.215 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9059 Order of pole (three term test) = 5.916e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9415 0.773 h = 0.0001 0.003 y[1] (numeric) = 0.260678561796 -0.487820854858 y[1] (closed_form) = 0.261076983688 -0.48770141415 absolute error = 0.0004159 relative error = 0.07519 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.218 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7312 Order of pole (three term test) = 1.562e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9414 0.776 h = 0.001 0.001 y[1] (numeric) = 0.262332904683 -0.484103881464 y[1] (closed_form) = 0.26274417759 -0.483980872171 absolute error = 0.0004293 relative error = 0.07795 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.22 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5748 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9404 0.777 h = 0.001 0.003 y[1] (numeric) = 0.264087616162 -0.483351137795 y[1] (closed_form) = 0.264505749274 -0.483228485835 absolute error = 0.0004358 relative error = 0.0791 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.22 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.728 Order of pole (three term test) = 1.997e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9394 0.78 h = 0.0001 0.004 y[1] (numeric) = 0.26684447554 -0.480070596762 y[1] (closed_form) = 0.267248580181 -0.479947878941 absolute error = 0.0004223 relative error = 0.07688 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.221 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.545 Order of pole (three term test) = 1.177e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9393 0.784 h = 0.003 0.006 y[1] (numeric) = 0.268893545755 -0.475084896391 y[1] (closed_form) = 0.269291648498 -0.474972387154 absolute error = 0.0004137 relative error = 0.07577 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.223 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.051 Order of pole (three term test) = 1.412e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9363 0.79 h = 0.0001 0.005 y[1] (numeric) = 0.275421225906 -0.468970001622 y[1] (closed_form) = 0.275795156569 -0.468812094182 absolute error = 0.0004059 relative error = 0.07463 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.225 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9133 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9362 0.795 h = 0.0001 0.003 y[1] (numeric) = 0.277684133301 -0.462723336865 y[1] (closed_form) = 0.278079133063 -0.462591016641 absolute error = 0.0004166 relative error = 0.07718 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.228 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7372 Order of pole (three term test) = 6.410e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9361 0.798 h = 0.001 0.001 y[1] (numeric) = 0.279043557842 -0.459028547944 y[1] (closed_form) = 0.27945056598 -0.458891795305 absolute error = 0.0004294 relative error = 0.07991 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5795 Order of pole (three term test) = 3.731e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9351 0.799 h = 0.001 0.003 y[1] (numeric) = 0.280689627931 -0.45818964983 y[1] (closed_form) = 0.281103225385 -0.458052695569 absolute error = 0.0004357 relative error = 0.08107 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.75 Order of pole (three term test) = 3.115e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9341 0.802 h = 0.0001 0.004 y[1] (numeric) = 0.283141430964 -0.454846315238 y[1] (closed_form) = 0.283541608126 -0.454710408598 absolute error = 0.0004226 relative error = 0.07887 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.231 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.558 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.934 0.806 h = 0.003 0.006 y[1] (numeric) = 0.284801641969 -0.449903107467 y[1] (closed_form) = 0.285196886056 -0.449777435231 absolute error = 0.0004147 relative error = 0.07787 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.234 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.068 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.931 0.812 h = 0.0001 0.005 y[1] (numeric) = 0.290714145873 -0.443586551793 y[1] (closed_form) = 0.291082714508 -0.443419379695 absolute error = 0.0004047 relative error = 0.0763 % Correct digits = 3 memory used=636.5MB, alloc=44.3MB, time=8.08 Radius of convergence (given) for eq 1 = 1.235 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.921 Order of pole (three term test) = 1.588e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9309 0.817 h = 0.0001 0.003 y[1] (numeric) = 0.292502887517 -0.437416524115 y[1] (closed_form) = 0.292893591793 -0.437272155962 absolute error = 0.0004165 relative error = 0.07914 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.239 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7434 Order of pole (three term test) = 7.801e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9308 0.82 h = 0.001 0.001 y[1] (numeric) = 0.293582102043 -0.433766133721 y[1] (closed_form) = 0.293983936176 -0.433616594152 absolute error = 0.0004288 relative error = 0.08184 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.24 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5844 Order of pole (three term test) = 9.771e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9298 0.821 h = 0.001 0.003 y[1] (numeric) = 0.295117549276 -0.432853400567 y[1] (closed_form) = 0.295525664092 -0.432703155544 absolute error = 0.0004349 relative error = 0.083 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.24 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.774 Order of pole (three term test) = 4.817e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9288 0.824 h = 0.0001 0.004 y[1] (numeric) = 0.297272820546 -0.429473997209 y[1] (closed_form) = 0.297668194646 -0.429325796962 absolute error = 0.0004222 relative error = 0.08082 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.242 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.571 Order of pole (three term test) = 2.713e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9287 0.828 h = 0.003 0.006 y[1] (numeric) = 0.29856471058 -0.424601839291 y[1] (closed_form) = 0.298956165494 -0.424463798452 absolute error = 0.0004151 relative error = 0.07995 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.244 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.086 Order of pole (three term test) = 1.230e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9257 0.834 h = 0.0001 0.005 y[1] (numeric) = 0.303873589988 -0.41814052358 y[1] (closed_form) = 0.304236361969 -0.417964903297 absolute error = 0.000403 relative error = 0.07796 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.246 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9289 Order of pole (three term test) = 9.390e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9256 0.839 h = 0.0001 0.003 y[1] (numeric) = 0.305215344386 -0.412080485325 y[1] (closed_form) = 0.305601004125 -0.411924938286 absolute error = 0.0004158 relative error = 0.08108 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.249 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7498 Order of pole (three term test) = 7.262e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9255 0.842 h = 0.001 0.001 y[1] (numeric) = 0.306030325894 -0.408494150267 y[1] (closed_form) = 0.306426216739 -0.408332813584 absolute error = 0.0004275 relative error = 0.08374 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.251 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5895 Order of pole (three term test) = 6.435e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9245 0.843 h = 0.001 0.003 y[1] (numeric) = 0.307454415383 -0.407519422061 y[1] (closed_form) = 0.307856248822 -0.407356931763 absolute error = 0.0004334 relative error = 0.08489 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.251 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.798 Order of pole (three term test) = 4.489e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9235 0.846 h = 0.0001 0.004 y[1] (numeric) = 0.309323693731 -0.404128444702 y[1] (closed_form) = 0.309713520452 -0.403968879758 absolute error = 0.0004212 relative error = 0.08275 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.252 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.585 Order of pole (three term test) = 1.239e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9234 0.85 h = 0.003 0.006 y[1] (numeric) = 0.31026932501 -0.399352454236 y[1] (closed_form) = 0.310656184252 -0.399202885161 absolute error = 0.0004148 relative error = 0.082 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.255 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.104 Order of pole (three term test) = 6.370e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9204 0.856 h = 0.0001 0.005 y[1] (numeric) = 0.314990734897 -0.392799135912 y[1] (closed_form) = 0.315347370283 -0.392615875847 absolute error = 0.000401 relative error = 0.07962 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.257 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.937 Order of pole (three term test) = 7.416e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9203 0.861 h = 0.0001 0.003 y[1] (numeric) = 0.315914243837 -0.386878131157 y[1] (closed_form) = 0.316294230441 -0.38671229603 absolute error = 0.0004146 relative error = 0.08299 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.26 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7564 Order of pole (three term test) = 4.489e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9202 0.864 h = 0.001 0.001 y[1] (numeric) = 0.316481885474 -0.383372979356 y[1] (closed_form) = 0.316871198212 -0.383200851491 absolute error = 0.0004257 relative error = 0.08561 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.262 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5947 Order of pole (three term test) = 1.348e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=682.6MB, alloc=44.3MB, time=8.67 x[1] = -0.9192 0.865 h = 0.0001 0.004 y[1] (numeric) = 0.317794998499 -0.382347515112 y[1] (closed_form) = 0.318189894037 -0.382173840652 absolute error = 0.0004314 relative error = 0.08675 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.262 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.571 Order of pole (three term test) = 1.577e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9191 0.869 h = 0.003 0.006 y[1] (numeric) = 0.318474788715 -0.377666957371 y[1] (closed_form) = 0.318855251491 -0.377511689135 absolute error = 0.0004109 relative error = 0.08316 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.265 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.121 Order of pole (three term test) = 1.371e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9161 0.875 h = 0.0001 0.005 y[1] (numeric) = 0.322706113473 -0.371080031148 y[1] (closed_form) = 0.323055419008 -0.370894369061 absolute error = 0.0003956 relative error = 0.08043 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.267 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9444 Order of pole (three term test) = 4.767e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.916 0.88 h = 0.0001 0.003 y[1] (numeric) = 0.32329546075 -0.365303252054 y[1] (closed_form) = 0.323668276409 -0.36513281884 absolute error = 0.0004099 relative error = 0.08401 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.27 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7624 Order of pole (three term test) = 7.821e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9159 0.883 h = 0.001 0.001 y[1] (numeric) = 0.323665387829 -0.361882476256 y[1] (closed_form) = 0.324046750849 -0.361705414889 absolute error = 0.0004205 relative error = 0.08658 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.272 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5994 Order of pole (three term test) = 1.097e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9149 0.884 h = 0.001 0.003 y[1] (numeric) = 0.324883601434 -0.360823151773 y[1] (closed_form) = 0.325270221805 -0.360644253215 absolute error = 0.000426 relative error = 0.08772 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.272 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.845 Order of pole (three term test) = 7.659e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9139 0.887 h = 0.0001 0.004 y[1] (numeric) = 0.326254597829 -0.357470973602 y[1] (closed_form) = 0.32663067652 -0.357296326582 absolute error = 0.0004147 relative error = 0.08566 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.274 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.611 Order of pole (three term test) = 1.034e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9138 0.891 h = 0.003 0.006 y[1] (numeric) = 0.326619667071 -0.352932745895 y[1] (closed_form) = 0.326994363199 -0.352767587092 absolute error = 0.0004095 relative error = 0.08513 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.276 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.14 Order of pole (three term test) = 7.704e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9108 0.897 h = 0.0001 0.005 y[1] (numeric) = 0.330303852571 -0.346339997793 y[1] (closed_form) = 0.330646625472 -0.346148151344 absolute error = 0.0003928 relative error = 0.08206 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.278 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.953 Order of pole (three term test) = 2.122e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9107 0.902 h = 0.0001 0.003 y[1] (numeric) = 0.330530976521 -0.340744905386 y[1] (closed_form) = 0.330897260966 -0.340565856962 absolute error = 0.0004077 relative error = 0.08586 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.282 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7693 Order of pole (three term test) = 7.392e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9106 0.905 h = 0.001 0.001 y[1] (numeric) = 0.330686490365 -0.337430498666 y[1] (closed_form) = 0.331060438197 -0.337244514005 absolute error = 0.0004176 relative error = 0.08837 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.284 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6049 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9096 0.906 h = 0.001 0.003 y[1] (numeric) = 0.33179706785 -0.33633955939 y[1] (closed_form) = 0.332175891843 -0.336151443116 absolute error = 0.000423 relative error = 0.0895 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.284 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.871 Order of pole (three term test) = 1.449e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9086 0.909 h = 0.0001 0.004 y[1] (numeric) = 0.332920355458 -0.333032953568 y[1] (closed_form) = 0.333289444062 -0.332849651469 absolute error = 0.0004121 relative error = 0.08749 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.285 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.626 Order of pole (three term test) = 1.920e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9085 0.913 h = 0.003 0.006 y[1] (numeric) = 0.333006913059 -0.328644203048 y[1] (closed_form) = 0.333375369494 -0.328470039576 absolute error = 0.0004075 relative error = 0.08708 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.288 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.159 Order of pole (three term test) = 3.667e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=729.0MB, alloc=44.3MB, time=9.26 x[1] = -0.9055 0.919 h = 0.0001 0.005 y[1] (numeric) = 0.336169294348 -0.322085646159 y[1] (closed_form) = 0.336505424842 -0.321888356159 absolute error = 0.0003898 relative error = 0.0837 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.29 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9618 Order of pole (three term test) = 3.322e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9054 0.924 h = 0.0001 0.003 y[1] (numeric) = 0.336064504331 -0.31668978184 y[1] (closed_form) = 0.336423939168 -0.316502998144 absolute error = 0.0004051 relative error = 0.0877 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.294 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7765 Order of pole (three term test) = 3.970e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9053 0.927 h = 0.001 0.001 y[1] (numeric) = 0.336023420598 -0.313492121762 y[1] (closed_form) = 0.336389659137 -0.313298186942 absolute error = 0.0004144 relative error = 0.09015 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.296 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6105 Order of pole (three term test) = 1.261e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9043 0.928 h = 0.001 0.003 y[1] (numeric) = 0.337029198507 -0.312378794886 y[1] (closed_form) = 0.337399928739 -0.312182483441 absolute error = 0.0004195 relative error = 0.09126 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.296 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.897 Order of pole (three term test) = 1.377e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9033 0.931 h = 0.0001 0.004 y[1] (numeric) = 0.337919824244 -0.309133382498 y[1] (closed_form) = 0.338281627059 -0.308942346787 absolute error = 0.0004091 relative error = 0.08931 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.297 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.641 Order of pole (three term test) = 1.096e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9032 0.935 h = 0.003 0.006 y[1] (numeric) = 0.33775183506 -0.304906918216 y[1] (closed_form) = 0.338113683221 -0.304724627884 absolute error = 0.0004052 relative error = 0.08902 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.179 Order of pole (three term test) = 6.943e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9002 0.941 h = 0.0001 0.005 y[1] (numeric) = 0.340419719802 -0.298418110094 y[1] (closed_form) = 0.340749163827 -0.298216083161 absolute error = 0.0003865 relative error = 0.08534 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.302 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9708 Order of pole (three term test) = 1.384e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9001 0.946 h = 0.0001 0.003 y[1] (numeric) = 0.340013070121 -0.29323542719 y[1] (closed_form) = 0.340365430426 -0.293041765046 absolute error = 0.0004021 relative error = 0.08952 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.306 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7838 Order of pole (three term test) = 4.016e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9 0.949 h = 0.001 0.001 y[1] (numeric) = 0.339793057462 -0.290162785374 y[1] (closed_form) = 0.340151393549 -0.289961841742 absolute error = 0.0004108 relative error = 0.09192 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.308 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6162 Order of pole (three term test) = 1.352e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.899 0.95 h = 0.001 0.003 y[1] (numeric) = 0.340697488829 -0.289035526842 y[1] (closed_form) = 0.341059933908 -0.288832007959 absolute error = 0.0004157 relative error = 0.09301 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.308 Order of pole (given) = 4 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.898 0.953 h = 0.0001 0.004 y[1] (numeric) = 0.341370951732 -0.285864755446 y[1] (closed_form) = 0.341725269067 -0.285666879466 absolute error = 0.0004058 relative error = 0.09112 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.309 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.657 Order of pole (three term test) = 4.932e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8979 0.957 h = 0.003 0.006 y[1] (numeric) = 0.340972073757 -0.28181062692 y[1] (closed_form) = 0.341327041776 -0.281621069457 absolute error = 0.0004024 relative error = 0.09094 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.312 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.2 Order of pole (three term test) = 6.632e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8949 0.963 h = 0.0001 0.005 y[1] (numeric) = 0.343174173001 -0.275422777248 y[1] (closed_form) = 0.343496944575 -0.275216682139 absolute error = 0.000383 relative error = 0.08701 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.315 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9801 Order of pole (three term test) = 1.162e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8948 0.968 h = 0.0001 0.003 y[1] (numeric) = 0.342495131106 -0.270463909693 y[1] (closed_form) = 0.342840276852 -0.270264195222 absolute error = 0.0003988 relative error = 0.09134 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.318 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7912 Order of pole (three term test) = 7.249e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=775.3MB, alloc=44.3MB, time=9.85 x[1] = -0.8947 0.971 h = 0.001 0.001 y[1] (numeric) = 0.342113517091 -0.267522609033 y[1] (closed_form) = 0.342463848403 -0.267315558416 absolute error = 0.0004069 relative error = 0.09367 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.32 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6221 Order of pole (three term test) = 1.799e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8937 0.972 h = 0.0001 0.004 y[1] (numeric) = 0.342920554972 -0.266389096298 y[1] (closed_form) = 0.343274618668 -0.266179314855 absolute error = 0.0004115 relative error = 0.09474 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.32 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.736 Order of pole (three term test) = 1.834e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8936 0.976 h = 0.003 0.006 y[1] (numeric) = 0.34235032901 -0.262481902356 y[1] (closed_form) = 0.342698806722 -0.26228993039 absolute error = 0.0003979 relative error = 0.09219 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.323 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.219 Order of pole (three term test) = 1.786e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8906 0.982 h = 0.0001 0.005 y[1] (numeric) = 0.344176809715 -0.256207811876 y[1] (closed_form) = 0.344493504583 -0.256001885623 absolute error = 0.0003778 relative error = 0.08801 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.326 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9883 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8905 0.987 h = 0.0001 0.003 y[1] (numeric) = 0.343289027831 -0.251450570476 y[1] (closed_form) = 0.343627505361 -0.251249454372 absolute error = 0.0003937 relative error = 0.09249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.329 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7979 Order of pole (three term test) = 1.006e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8904 0.99 h = 0.001 0.001 y[1] (numeric) = 0.34278344197 -0.248627675094 y[1] (closed_form) = 0.343126458973 -0.248419238446 absolute error = 0.0004014 relative error = 0.09475 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.332 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6273 Order of pole (three term test) = 1.490e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8894 0.991 h = 0.001 0.003 y[1] (numeric) = 0.343510149778 -0.24749542551 y[1] (closed_form) = 0.343856581432 -0.247284160218 absolute error = 0.0004058 relative error = 0.0958 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.332 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.978 Order of pole (three term test) = 6.595e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8884 0.994 h = 0.0001 0.004 y[1] (numeric) = 0.343822514713 -0.244494482124 y[1] (closed_form) = 0.344162258673 -0.24428930789 absolute error = 0.0003969 relative error = 0.09404 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.333 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.687 Order of pole (three term test) = 1.226e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8883 0.998 h = 0.003 0.006 y[1] (numeric) = 0.343057154133 -0.240781353552 y[1] (closed_form) = 0.343398484025 -0.240583639604 absolute error = 0.0003945 relative error = 0.09408 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.336 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.24 Order of pole (three term test) = 4.714e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8853 1.004 h = 0.0001 0.005 y[1] (numeric) = 0.344473552254 -0.234654950238 y[1] (closed_form) = 0.344783737041 -0.234446089791 absolute error = 0.0003739 relative error = 0.08969 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.339 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9979 Order of pole (three term test) = 9.306e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8852 1.009 h = 0.0001 0.003 y[1] (numeric) = 0.343365786627 -0.230133131513 y[1] (closed_form) = 0.343696993813 -0.229927398582 absolute error = 0.0003899 relative error = 0.09429 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.342 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8056 Order of pole (three term test) = 4.348e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8851 1.012 h = 0.001 0.001 y[1] (numeric) = 0.342729430864 -0.227448537853 y[1] (closed_form) = 0.343064469189 -0.227235546888 absolute error = 0.000397 relative error = 0.09648 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.344 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6334 Order of pole (three term test) = 7.177e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8841 1.013 h = 0.001 0.003 y[1] (numeric) = 0.343367138206 -0.226322220295 y[1] (closed_form) = 0.343705235459 -0.226106315555 absolute error = 0.0004012 relative error = 0.09751 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.345 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.006 Order of pole (three term test) = 7.735e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8831 1.016 h = 0.0001 0.004 y[1] (numeric) = 0.343507228396 -0.223423204547 y[1] (closed_form) = 0.343839371195 -0.223213529427 absolute error = 0.0003928 relative error = 0.09582 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.346 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.703 Order of pole (three term test) = 2.672e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.883 1.02 h = 0.003 0.006 y[1] (numeric) = 0.342574976466 -0.219897653525 y[1] (closed_form) = 0.342909116335 -0.219694964028 absolute error = 0.0003908 relative error = 0.09596 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.349 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.262 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=821.6MB, alloc=44.3MB, time=10.43 x[1] = -0.88 1.026 h = 0.0001 0.005 y[1] (numeric) = 0.343611338718 -0.213938740676 y[1] (closed_form) = 0.343915153412 -0.213727494887 absolute error = 0.00037 relative error = 0.09139 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.352 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.008 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8799 1.031 h = 0.0001 0.003 y[1] (numeric) = 0.342309999245 -0.209655084735 y[1] (closed_form) = 0.342633990376 -0.20944544392 absolute error = 0.0003859 relative error = 0.0961 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.355 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8135 Order of pole (three term test) = 4.417e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8798 1.034 h = 0.001 0.001 y[1] (numeric) = 0.341558418134 -0.207110477759 y[1] (closed_form) = 0.341885579321 -0.206893692723 absolute error = 0.0003925 relative error = 0.09821 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.358 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6396 Order of pole (three term test) = 9.045e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8788 1.035 h = 0.001 0.003 y[1] (numeric) = 0.342111934641 -0.205995609618 y[1] (closed_form) = 0.342441813728 -0.205775858378 absolute error = 0.0003964 relative error = 0.09921 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.358 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.036 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8778 1.038 h = 0.0001 0.004 y[1] (numeric) = 0.342094981555 -0.203204698921 y[1] (closed_form) = 0.342419606196 -0.202991250708 absolute error = 0.0003885 relative error = 0.0976 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.359 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.72 Order of pole (three term test) = 1.761e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8777 1.042 h = 0.003 0.006 y[1] (numeric) = 0.34101636212 -0.199868236306 y[1] (closed_form) = 0.341343333624 -0.199661295786 absolute error = 0.000387 relative error = 0.09785 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.362 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.284 Order of pole (three term test) = 1.556e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8747 1.048 h = 0.0001 0.005 y[1] (numeric) = 0.341702478445 -0.194093096487 y[1] (closed_form) = 0.342000094608 -0.193879971212 absolute error = 0.0003661 relative error = 0.09311 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.365 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.018 Order of pole (three term test) = 1.938e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8746 1.053 h = 0.0001 0.003 y[1] (numeric) = 0.340232598981 -0.190048137929 y[1] (closed_form) = 0.340549480228 -0.189835251558 absolute error = 0.0003818 relative error = 0.09791 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.369 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8216 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8745 1.056 h = 0.001 0.001 y[1] (numeric) = 0.339380533613 -0.187643905205 y[1] (closed_form) = 0.33969997232 -0.187424031927 absolute error = 0.0003878 relative error = 0.09995 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.646 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8735 1.057 h = 0.001 0.003 y[1] (numeric) = 0.339854803978 -0.186545303167 y[1] (closed_form) = 0.340176636119 -0.18632244035 absolute error = 0.0003915 relative error = 0.1009 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.066 Order of pole (three term test) = 1.192e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8725 1.06 h = 0.0001 0.004 y[1] (numeric) = 0.339695597591 -0.183867133406 y[1] (closed_form) = 0.340012838627 -0.183650589404 absolute error = 0.0003841 relative error = 0.09939 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.373 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.737 Order of pole (three term test) = 3.859e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8724 1.064 h = 0.003 0.006 y[1] (numeric) = 0.338490014381 -0.180719608265 y[1] (closed_form) = 0.338809894766 -0.18050909641 absolute error = 0.0003829 relative error = 0.09975 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.376 Order of pole (given) = 4 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) = 9.756e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8694 1.07 h = 0.0001 0.005 y[1] (numeric) = 0.338855122903 -0.175141273384 y[1] (closed_form) = 0.339146737886 -0.174926731884 absolute error = 0.000362 relative error = 0.09487 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.379 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.028 Order of pole (three term test) = 5.955e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8693 1.075 h = 0.0001 0.003 y[1] (numeric) = 0.337240263517 -0.171333618538 y[1] (closed_form) = 0.337550185143 -0.171118100988 absolute error = 0.0003775 relative error = 0.09975 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.383 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8298 Order of pole (three term test) = 8.358e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=868.0MB, alloc=44.3MB, time=11.02 x[1] = -0.8692 1.078 h = 0.001 0.001 y[1] (numeric) = 0.336301593967 -0.169069012363 y[1] (closed_form) = 0.336613509308 -0.168846701421 absolute error = 0.000383 relative error = 0.1017 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.385 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6524 Order of pole (three term test) = 8.263e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8682 1.079 h = 0.0001 0.004 y[1] (numeric) = 0.336701626881 -0.16799082992 y[1] (closed_form) = 0.33701562911 -0.167765531705 absolute error = 0.0003865 relative error = 0.1027 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.385 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.918 Order of pole (three term test) = 2.201e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8681 1.083 h = 0.003 0.006 y[1] (numeric) = 0.335406087056 -0.16499685351 y[1] (closed_form) = 0.335720457516 -0.164786252729 absolute error = 0.0003784 relative error = 0.1012 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.388 Order of pole (given) = 4 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8651 1.089 h = 0.0001 0.005 y[1] (numeric) = 0.335520194085 -0.159599444969 y[1] (closed_form) = 0.335807334952 -0.159386485604 absolute error = 0.0003575 relative error = 0.09617 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.391 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.037 Order of pole (three term test) = 4.457e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.865 1.094 h = 0.0001 0.003 y[1] (numeric) = 0.333801008701 -0.155995033884 y[1] (closed_form) = 0.334105593853 -0.15578018047 absolute error = 0.0003727 relative error = 0.1011 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.395 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8371 Order of pole (three term test) = 1.101e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8649 1.097 h = 0.001 0.001 y[1] (numeric) = 0.33279985601 -0.153850085584 y[1] (closed_form) = 0.333105991233 -0.153628635111 absolute error = 0.0003778 relative error = 0.103 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.397 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6582 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8639 1.098 h = 0.001 0.003 y[1] (numeric) = 0.333140300934 -0.152793132946 y[1] (closed_form) = 0.333448274618 -0.152568718434 absolute error = 0.0003811 relative error = 0.1039 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.397 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.124 Order of pole (three term test) = 1.534e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8629 1.101 h = 0.0001 0.004 y[1] (numeric) = 0.332755240076 -0.150333725306 y[1] (closed_form) = 0.333059750704 -0.150115523474 absolute error = 0.0003746 relative error = 0.1025 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.399 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.77 Order of pole (three term test) = 8.168e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8628 1.105 h = 0.003 0.006 y[1] (numeric) = 0.331363140277 -0.147533587051 y[1] (closed_form) = 0.331670691284 -0.147320552568 absolute error = 0.0003741 relative error = 0.1031 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.402 Order of pole (given) = 4 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8598 1.111 h = 0.0001 0.005 y[1] (numeric) = 0.33120845077 -0.142349210842 y[1] (closed_form) = 0.331490012977 -0.142135584444 absolute error = 0.0003534 relative error = 0.09799 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.405 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.047 Order of pole (three term test) = 9.719e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8597 1.116 h = 0.0001 0.003 y[1] (numeric) = 0.329383952978 -0.138975035418 y[1] (closed_form) = 0.329681956854 -0.138758562702 absolute error = 0.0003683 relative error = 0.103 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.409 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8455 Order of pole (three term test) = 1.697e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8596 1.119 h = 0.001 0.001 y[1] (numeric) = 0.328319585136 -0.13696568416 y[1] (closed_form) = 0.328618665005 -0.136742857213 absolute error = 0.000373 relative error = 0.1048 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.411 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6648 Order of pole (three term test) = 1.056e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8586 1.12 h = 0.001 0.003 y[1] (numeric) = 0.328595111353 -0.135935199878 y[1] (closed_form) = 0.328895758817 -0.135709449795 absolute error = 0.000376 relative error = 0.1057 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.411 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.156 Order of pole (three term test) = 1.079e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8576 1.123 h = 0.0001 0.004 y[1] (numeric) = 0.328106837321 -0.133594443338 y[1] (closed_form) = 0.328404569457 -0.133374796231 absolute error = 0.00037 relative error = 0.1044 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.413 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.788 Order of pole (three term test) = 2.521e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=914.2MB, alloc=44.3MB, time=11.60 x[1] = -0.8575 1.127 h = 0.003 0.006 y[1] (numeric) = 0.326636561958 -0.130975332185 y[1] (closed_form) = 0.326937487087 -0.130760407958 absolute error = 0.0003698 relative error = 0.105 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.416 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.374 Order of pole (three term test) = 9.718e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8545 1.133 h = 0.0001 0.005 y[1] (numeric) = 0.326239516132 -0.126009269117 y[1] (closed_form) = 0.326515742927 -0.125795323271 absolute error = 0.0003494 relative error = 0.09985 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.419 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.058 Order of pole (three term test) = 8.493e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8544 1.138 h = 0.0001 0.003 y[1] (numeric) = 0.324328794081 -0.122859843861 y[1] (closed_form) = 0.32462045415 -0.122642228734 absolute error = 0.0003639 relative error = 0.1049 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.423 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8541 Order of pole (three term test) = 4.689e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8543 1.141 h = 0.001 0.001 y[1] (numeric) = 0.323212475914 -0.120982927576 y[1] (closed_form) = 0.323504784056 -0.120759219556 absolute error = 0.0003681 relative error = 0.1066 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.425 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6716 Order of pole (three term test) = 2.084e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8533 1.142 h = 0.001 0.003 y[1] (numeric) = 0.323427959218 -0.11998140612 y[1] (closed_form) = 0.323721583568 -0.119754832407 absolute error = 0.0003709 relative error = 0.1075 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.426 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.188 Order of pole (three term test) = 5.850e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8523 1.145 h = 0.0001 0.004 y[1] (numeric) = 0.322848764444 -0.117759354055 y[1] (closed_form) = 0.323139979869 -0.117538741869 absolute error = 0.0003653 relative error = 0.1063 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.427 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.806 Order of pole (three term test) = 1.247e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8522 1.149 h = 0.003 0.006 y[1] (numeric) = 0.321314983307 -0.115316633906 y[1] (closed_form) = 0.321609503861 -0.115100316738 absolute error = 0.0003654 relative error = 0.107 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.431 Order of pole (given) = 4 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) = 1.192e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8492 1.155 h = 0.0001 0.005 y[1] (numeric) = 0.320700774119 -0.110571977703 y[1] (closed_form) = 0.320971916959 -0.110358022872 absolute error = 0.0003454 relative error = 0.1018 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.434 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.069 Order of pole (three term test) = 8.751e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8491 1.16 h = 0.0001 0.003 y[1] (numeric) = 0.318721358242 -0.107640818063 y[1] (closed_form) = 0.31900693104 -0.107422491476 absolute error = 0.0003595 relative error = 0.1068 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.438 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8628 Order of pole (three term test) = 1.046e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.849 1.163 h = 0.001 0.001 y[1] (numeric) = 0.317563442733 -0.105892583208 y[1] (closed_form) = 0.317849280021 -0.105668438529 absolute error = 0.0003632 relative error = 0.1084 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.44 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6784 Order of pole (three term test) = 6.447e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.848 1.164 h = 0.001 0.003 y[1] (numeric) = 0.317723633346 -0.104922026588 y[1] (closed_form) = 0.318010554872 -0.104695087449 absolute error = 0.0003658 relative error = 0.1093 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.44 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.22 Order of pole (three term test) = 4.049e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.847 1.167 h = 0.0001 0.004 y[1] (numeric) = 0.317065058535 -0.102817873591 y[1] (closed_form) = 0.317350036632 -0.102596728383 absolute error = 0.0003607 relative error = 0.1082 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.442 Order of pole (given) = 4 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) = 1.526e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8469 1.171 h = 0.003 0.006 y[1] (numeric) = 0.315481217925 -0.100546176258 y[1] (closed_form) = 0.315769577042 -0.100328916858 absolute error = 0.000361 relative error = 0.109 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.445 Order of pole (given) = 4 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) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8439 1.177 h = 0.0001 0.005 y[1] (numeric) = 0.314673704275 -0.0960240908122 y[1] (closed_form) = 0.314940019448 -0.0958104023525 absolute error = 0.0003414 relative error = 0.1037 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.448 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.08 Order of pole (three term test) = 3.455e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8438 1.182 h = 0.0001 0.003 y[1] (numeric) = 0.312641599404 -0.0933039096912 y[1] (closed_form) = 0.312921355471 -0.09308525841 absolute error = 0.0003551 relative error = 0.1088 % Correct digits = 3 memory used=960.5MB, alloc=44.3MB, time=12.19 Radius of convergence (given) for eq 1 = 1.452 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8717 Order of pole (three term test) = 1.764e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8437 1.185 h = 0.001 0.001 y[1] (numeric) = 0.311451546016 -0.091680126388 y[1] (closed_form) = 0.311731225202 -0.0914559408164 absolute error = 0.0003584 relative error = 0.1103 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6854 Order of pole (three term test) = 2.017e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8427 1.186 h = 0.0001 0.004 y[1] (numeric) = 0.31156103843 -0.090742089499 y[1] (closed_form) = 0.311841588984 -0.0905151919667 absolute error = 0.0003608 relative error = 0.1111 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.116 Order of pole (three term test) = 3.505e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8426 1.19 h = 0.003 0.006 y[1] (numeric) = 0.309945665725 -0.0886059122776 y[1] (closed_form) = 0.310229869407 -0.0883899080628 absolute error = 0.000357 relative error = 0.1107 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 4 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) = 1.782e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8396 1.196 h = 0.0001 0.005 y[1] (numeric) = 0.308992445883 -0.0842769887718 y[1] (closed_form) = 0.309255764759 -0.0840654484172 absolute error = 0.0003378 relative error = 0.1054 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.089 Order of pole (three term test) = 1.651e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8395 1.201 h = 0.0001 0.003 y[1] (numeric) = 0.306929057548 -0.0817324896532 y[1] (closed_form) = 0.307204977819 -0.0815155713523 absolute error = 0.000351 relative error = 0.1104 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8795 Order of pole (three term test) = 5.352e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8394 1.204 h = 0.001 0.001 y[1] (numeric) = 0.305719660513 -0.080212401709 y[1] (closed_form) = 0.305995245534 -0.0799902010383 absolute error = 0.000354 relative error = 0.1119 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.468 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6915 Order of pole (three term test) = 5.343e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8384 1.205 h = 0.001 0.003 y[1] (numeric) = 0.305789461432 -0.0793038259353 y[1] (closed_form) = 0.306065750628 -0.0790789938251 absolute error = 0.0003562 relative error = 0.1127 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.468 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.282 Order of pole (three term test) = 1.111e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8374 1.208 h = 0.0001 0.004 y[1] (numeric) = 0.305012619007 -0.0774151270125 y[1] (closed_form) = 0.305287722896 -0.0771957200436 absolute error = 0.0003519 relative error = 0.1117 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 4 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) = 1.212e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8373 1.212 h = 0.003 0.006 y[1] (numeric) = 0.303369220979 -0.0754457532241 y[1] (closed_form) = 0.303647760148 -0.0752295249671 absolute error = 0.0003526 relative error = 0.1127 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.473 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.47 Order of pole (three term test) = 9.665e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8343 1.218 h = 0.0001 0.005 y[1] (numeric) = 0.302263338555 -0.071337009786 y[1] (closed_form) = 0.30252231217 -0.0711261590338 absolute error = 0.000334 relative error = 0.1075 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.476 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.101 Order of pole (three term test) = 6.731e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8342 1.223 h = 0.0001 0.003 y[1] (numeric) = 0.300173050497 -0.0689882373055 y[1] (closed_form) = 0.300443683197 -0.0687716002331 absolute error = 0.0003467 relative error = 0.1125 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.48 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8886 Order of pole (three term test) = 1.051e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8341 1.226 h = 0.001 0.001 y[1] (numeric) = 0.298946778054 -0.0675837216357 y[1] (closed_form) = 0.299216806333 -0.0673620923037 absolute error = 0.0003493 relative error = 0.1139 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.483 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6986 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8331 1.227 h = 0.001 0.003 y[1] (numeric) = 0.298973946855 -0.0667094700828 y[1] (closed_form) = 0.299244500593 -0.0664853066636 absolute error = 0.0003514 relative error = 0.1146 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.483 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.316 Order of pole (three term test) = 2.074e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8321 1.23 h = 0.0001 0.004 y[1] (numeric) = 0.298146475227 -0.0649325675504 y[1] (closed_form) = 0.298416198128 -0.0647136137756 absolute error = 0.0003474 relative error = 0.1138 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.485 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.879 Order of pole (three term test) = 2.820e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1006.7MB, alloc=44.3MB, time=12.77 x[1] = -0.832 1.234 h = 0.003 0.006 y[1] (numeric) = 0.296484958134 -0.0631159786721 y[1] (closed_form) = 0.296758110547 -0.0628998547104 absolute error = 0.0003483 relative error = 0.1148 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.488 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.495 Order of pole (three term test) = 1.163e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.829 1.24 h = 0.0001 0.005 y[1] (numeric) = 0.295246216694 -0.0592243700795 y[1] (closed_form) = 0.295501100028 -0.0590143958762 absolute error = 0.0003302 relative error = 0.1096 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.492 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.112 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8289 1.245 h = 0.0001 0.003 y[1] (numeric) = 0.29314096388 -0.0570626730606 y[1] (closed_form) = 0.29340659623 -0.0568465897194 absolute error = 0.0003424 relative error = 0.1146 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.496 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8977 Order of pole (three term test) = 1.077e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8288 1.248 h = 0.001 0.001 y[1] (numeric) = 0.291904889207 -0.0557686837133 y[1] (closed_form) = 0.292169683101 -0.0555478974401 absolute error = 0.0003448 relative error = 0.1159 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.498 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7058 Order of pole (three term test) = 1.025e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8278 1.249 h = 0.001 0.003 y[1] (numeric) = 0.291893460047 -0.0549292736306 y[1] (closed_form) = 0.29215861793 -0.0547060559754 absolute error = 0.0003466 relative error = 0.1166 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.498 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.351 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8268 1.252 h = 0.0001 0.004 y[1] (numeric) = 0.291023958366 -0.0532611161406 y[1] (closed_form) = 0.291288604242 -0.0530428834401 absolute error = 0.000343 relative error = 0.1159 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.898 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8267 1.256 h = 0.003 0.006 y[1] (numeric) = 0.289353410585 -0.0515904011128 y[1] (closed_form) = 0.289621458466 -0.0513746712851 absolute error = 0.0003441 relative error = 0.117 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.504 Order of pole (given) = 4 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) = 1.864e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8237 1.262 h = 0.0001 0.005 y[1] (numeric) = 0.28800019545 -0.0479118071257 y[1] (closed_form) = 0.288251239196 -0.047702869801 absolute error = 0.0003266 relative error = 0.1118 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.507 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.123 Order of pole (three term test) = 8.475e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8236 1.267 h = 0.0001 0.003 y[1] (numeric) = 0.285890625253 -0.0459283146067 y[1] (closed_form) = 0.286151544107 -0.0457130223413 absolute error = 0.0003383 relative error = 0.1167 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.511 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.907 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8235 1.27 h = 0.001 0.001 y[1] (numeric) = 0.284651065697 -0.0447396713621 y[1] (closed_form) = 0.284910944602 -0.044519962207 absolute error = 0.0003403 relative error = 0.118 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.514 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7131 Order of pole (three term test) = 8.545e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8225 1.271 h = 0.001 0.003 y[1] (numeric) = 0.284604855907 -0.0439353339204 y[1] (closed_form) = 0.284864953723 -0.0437132998011 absolute error = 0.000342 relative error = 0.1187 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.514 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.385 Order of pole (three term test) = 2.003e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8215 1.274 h = 0.0001 0.004 y[1] (numeric) = 0.283701198851 -0.0423725175399 y[1] (closed_form) = 0.283961069759 -0.0421552377456 absolute error = 0.0003387 relative error = 0.118 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.516 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.918 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8214 1.278 h = 0.003 0.006 y[1] (numeric) = 0.282029712546 -0.0408406230307 y[1] (closed_form) = 0.282292939372 -0.0406255411146 absolute error = 0.0003399 relative error = 0.1192 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.519 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.547 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8184 1.284 h = 0.0001 0.005 y[1] (numeric) = 0.280579014743 -0.0373700293341 y[1] (closed_form) = 0.280826463793 -0.0371622647787 absolute error = 0.0003231 relative error = 0.1141 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.523 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.135 Order of pole (three term test) = 5.717e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1053.1MB, alloc=44.3MB, time=13.36 x[1] = -0.8183 1.289 h = 0.0001 0.003 y[1] (numeric) = 0.278474564153 -0.0355557596582 y[1] (closed_form) = 0.278731053466 -0.0353414632179 absolute error = 0.0003342 relative error = 0.119 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.527 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9164 Order of pole (three term test) = 2.004e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8182 1.292 h = 0.001 0.001 y[1] (numeric) = 0.277237126099 -0.0344672122224 y[1] (closed_form) = 0.277492403927 -0.0342487795647 absolute error = 0.000336 relative error = 0.1202 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.529 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7205 Order of pole (three term test) = 1.782e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8172 1.293 h = 0.0001 0.004 y[1] (numeric) = 0.277159731233 -0.0336979287606 y[1] (closed_form) = 0.277415098366 -0.0334772798332 absolute error = 0.0003375 relative error = 0.1208 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.328 Order of pole (three term test) = 6.272e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8171 1.297 h = 0.003 0.006 y[1] (numeric) = 0.275493035518 -0.0322742672409 y[1] (closed_form) = 0.275753407607 -0.0320610319469 absolute error = 0.0003365 relative error = 0.1212 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.533 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.57 Order of pole (three term test) = 9.583e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8141 1.303 h = 0.0001 0.005 y[1] (numeric) = 0.273973379136 -0.028979047541 y[1] (closed_form) = 0.274218998447 -0.0287734816936 absolute error = 0.0003203 relative error = 0.1162 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.536 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.145 Order of pole (three term test) = 1.079e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.814 1.308 h = 0.0001 0.003 y[1] (numeric) = 0.271881896731 -0.0273030388862 y[1] (closed_form) = 0.272135869397 -0.0270908473585 absolute error = 0.0003309 relative error = 0.121 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.541 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9247 Order of pole (three term test) = 9.588e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8139 1.311 h = 0.001 0.001 y[1] (numeric) = 0.270651372555 -0.0262963298627 y[1] (closed_form) = 0.270904011361 -0.0260802397031 absolute error = 0.0003324 relative error = 0.1222 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.543 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.727 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8129 1.312 h = 0.001 0.003 y[1] (numeric) = 0.270550256527 -0.0255573562108 y[1] (closed_form) = 0.270802886046 -0.0253391455217 absolute error = 0.0003338 relative error = 0.1227 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.543 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.451 Order of pole (three term test) = 8.306e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8119 1.315 h = 0.0001 0.004 y[1] (numeric) = 0.269602784424 -0.0241808219445 y[1] (closed_form) = 0.26985563191 -0.0239669274799 absolute error = 0.0003312 relative error = 0.1222 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.545 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.955 Order of pole (three term test) = 1.992e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8118 1.319 h = 0.003 0.006 y[1] (numeric) = 0.267949389206 -0.0228881376655 y[1] (closed_form) = 0.268205464104 -0.0226759318355 absolute error = 0.0003326 relative error = 0.1236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.549 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.597 Order of pole (three term test) = 3.998e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8088 1.325 h = 0.0001 0.005 y[1] (numeric) = 0.266360211323 -0.0197895928715 y[1] (closed_form) = 0.266602673209 -0.0195853920993 absolute error = 0.000317 relative error = 0.1186 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.552 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.157 Order of pole (three term test) = 1.657e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8087 1.33 h = 0.0001 0.003 y[1] (numeric) = 0.264288354639 -0.0182660284974 y[1] (closed_form) = 0.26453841308 -0.0180551325542 absolute error = 0.0003271 relative error = 0.1234 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.557 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9343 Order of pole (three term test) = 1.333e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8086 1.333 h = 0.001 0.001 y[1] (numeric) = 0.263068588949 -0.0173495934999 y[1] (closed_form) = 0.263317190942 -0.0171350650354 absolute error = 0.0003284 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.559 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7345 Order of pole (three term test) = 7.342e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8076 1.334 h = 0.001 0.003 y[1] (numeric) = 0.262942378853 -0.0166450509238 y[1] (closed_form) = 0.263190868177 -0.0164285115288 absolute error = 0.0003296 relative error = 0.125 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.559 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.487 Order of pole (three term test) = 1.155e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1099.4MB, alloc=44.3MB, time=13.94 x[1] = -0.8066 1.337 h = 0.0001 0.004 y[1] (numeric) = 0.261979486927 -0.0153627643918 y[1] (closed_form) = 0.262228394136 -0.0151503082164 absolute error = 0.0003272 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.561 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.976 Order of pole (three term test) = 1.380e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8065 1.341 h = 0.003 0.006 y[1] (numeric) = 0.260343276042 -0.0141885580309 y[1] (closed_form) = 0.26059532678 -0.0139775462356 absolute error = 0.0003287 relative error = 0.126 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.565 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.623 Order of pole (three term test) = 5.633e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8035 1.347 h = 0.0001 0.005 y[1] (numeric) = 0.258697809789 -0.0112799809291 y[1] (closed_form) = 0.258937336431 -0.0110772227231 absolute error = 0.0003138 relative error = 0.1211 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.568 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.169 Order of pole (three term test) = 1.483e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8034 1.352 h = 0.0001 0.003 y[1] (numeric) = 0.256651996973 -0.00990004452386 y[1] (closed_form) = 0.256898406128 -0.00969056973217 absolute error = 0.0003234 relative error = 0.1258 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.573 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9439 Order of pole (three term test) = 5.143e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8033 1.355 h = 0.001 0.001 y[1] (numeric) = 0.255446820523 -0.00906871703011 y[1] (closed_form) = 0.255691673551 -0.0088558664766 absolute error = 0.0003244 relative error = 0.1268 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.575 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7422 Order of pole (three term test) = 5.104e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8023 1.356 h = 0.001 0.003 y[1] (numeric) = 0.255298475956 -0.00839805155259 y[1] (closed_form) = 0.25554312562 -0.00818329885768 absolute error = 0.0003255 relative error = 0.1273 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.576 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.523 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8013 1.359 h = 0.0001 0.004 y[1] (numeric) = 0.254325525384 -0.00720590780136 y[1] (closed_form) = 0.254570767108 -0.00699500821244 absolute error = 0.0003235 relative error = 0.127 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.578 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.996 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8012 1.363 h = 0.003 0.006 y[1] (numeric) = 0.252711334312 -0.00614325121983 y[1] (closed_form) = 0.252959626867 -0.00593357163705 absolute error = 0.000325 relative error = 0.1284 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.581 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.651 Order of pole (three term test) = 1.650e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7982 1.369 h = 0.0001 0.005 y[1] (numeric) = 0.251021609475 -0.00341758462136 y[1] (closed_form) = 0.251258413866 -0.00321632972864 absolute error = 0.0003108 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.585 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.181 Order of pole (three term test) = 1.437e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7981 1.374 h = 0.0001 0.003 y[1] (numeric) = 0.249007356981 -0.00217263696567 y[1] (closed_form) = 0.249250372699 -0.00196468585989 absolute error = 0.0003198 relative error = 0.1283 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.589 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9537 Order of pole (three term test) = 7.702e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.798 1.377 h = 0.001 0.001 y[1] (numeric) = 0.247820069386 -0.00142135030135 y[1] (closed_form) = 0.248061449943 -0.00121027000478 absolute error = 0.0003207 relative error = 0.1293 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.592 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7498 Order of pole (three term test) = 1.419e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.797 1.378 h = 0.001 0.003 y[1] (numeric) = 0.24765233598 -0.000783873422737 y[1] (closed_form) = 0.247893434202 -0.0005709981873 absolute error = 0.0003216 relative error = 0.1297 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.592 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.56 Order of pole (three term test) = 1.004e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.796 1.381 h = 0.0001 0.004 y[1] (numeric) = 0.246674123316 0.000322284626619 y[1] (closed_form) = 0.246915964074 0.000531532494631 absolute error = 0.0003198 relative error = 0.1295 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.594 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.017 Order of pole (three term test) = 5.332e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7959 1.385 h = 0.003 0.006 y[1] (numeric) = 0.24508609608 0.0012801666358 y[1] (closed_form) = 0.245330888087 0.00148839984326 absolute error = 0.0003214 relative error = 0.131 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.597 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.678 Order of pole (three term test) = 1.013e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7929 1.391 h = 0.0001 0.005 y[1] (numeric) = 0.243363002494 0.00383022537642 y[1] (closed_form) = 0.243597288045 0.00402993120777 absolute error = 0.0003079 relative error = 0.1264 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.601 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.194 Order of pole (three term test) = 2.855e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1145.7MB, alloc=44.3MB, time=14.53 x[1] = -0.7928 1.396 h = 0.0001 0.003 y[1] (numeric) = 0.24138500158 0.00494860011877 y[1] (closed_form) = 0.241624869754 0.00515494578261 absolute error = 0.0003164 relative error = 0.1309 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.605 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9636 Order of pole (three term test) = 9.941e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7927 1.399 h = 0.001 0.001 y[1] (numeric) = 0.240218415975 0.00562478529564 y[1] (closed_form) = 0.240456588461 0.00583402436957 absolute error = 0.000317 relative error = 0.1318 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.608 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7576 Order of pole (three term test) = 1.977e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7917 1.4 h = 0.003 0.006 y[1] (numeric) = 0.240033831993 0.00622987300517 y[1] (closed_form) = 0.240271653953 0.00644080204382 absolute error = 0.0003179 relative error = 0.1323 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.608 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.629 Order of pole (three term test) = 1.924e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7887 1.406 h = 0.0001 0.005 y[1] (numeric) = 0.238284802466 0.00867475089482 y[1] (closed_form) = 0.238517300067 0.00886634595758 absolute error = 0.0003013 relative error = 0.1262 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.612 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.202 Order of pole (three term test) = 3.554e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7886 1.411 h = 0.0001 0.003 y[1] (numeric) = 0.236331122153 0.00970977700383 y[1] (closed_form) = 0.236568791836 0.00990796957662 absolute error = 0.0003095 relative error = 0.1307 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.616 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9702 Order of pole (three term test) = 2.474e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7885 1.414 h = 0.001 0.001 y[1] (numeric) = 0.235178428474 0.0103364982599 y[1] (closed_form) = 0.235414364919 0.0105374295617 absolute error = 0.0003099 relative error = 0.1315 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.619 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7628 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7875 1.415 h = 0.001 0.003 y[1] (numeric) = 0.234982832741 0.010920172001 y[1] (closed_form) = 0.235218374969 0.0111227240496 absolute error = 0.0003107 relative error = 0.1319 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.619 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.621 Order of pole (three term test) = 1.737e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7865 1.418 h = 0.0001 0.004 y[1] (numeric) = 0.234003227742 0.0118905531007 y[1] (closed_form) = 0.234239723576 0.0120898429648 absolute error = 0.0003093 relative error = 0.1319 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.622 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.052 Order of pole (three term test) = 4.611e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7864 1.422 h = 0.003 0.006 y[1] (numeric) = 0.232464744172 0.0126855861472 y[1] (closed_form) = 0.232704016453 0.0128841701374 absolute error = 0.0003109 relative error = 0.1334 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.625 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.724 Order of pole (three term test) = 6.192e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7834 1.428 h = 0.0001 0.005 y[1] (numeric) = 0.230703054831 0.0149565249524 y[1] (closed_form) = 0.230933354126 0.0151465186802 absolute error = 0.0002986 relative error = 0.129 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.629 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.214 Order of pole (three term test) = 1.397e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7833 1.433 h = 0.0001 0.003 y[1] (numeric) = 0.228792073131 0.0158784986881 y[1] (closed_form) = 0.229026984983 0.0160749834686 absolute error = 0.0003063 relative error = 0.1334 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.633 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9802 Order of pole (three term test) = 3.437e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7832 1.436 h = 0.001 0.001 y[1] (numeric) = 0.22766396094 0.0164380600861 y[1] (closed_form) = 0.227897106068 0.0166370664787 absolute error = 0.0003065 relative error = 0.1341 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.636 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7706 Order of pole (three term test) = 1.713e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7822 1.437 h = 0.001 0.003 y[1] (numeric) = 0.227455375203 0.0169908344471 y[1] (closed_form) = 0.227688074149 0.0171913612772 absolute error = 0.0003072 relative error = 0.1345 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.636 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.658 Order of pole (three term test) = 1.073e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7812 1.44 h = 0.0001 0.004 y[1] (numeric) = 0.226480992693 0.0178862860496 y[1] (closed_form) = 0.226714741442 0.018083759775 absolute error = 0.000306 relative error = 0.1345 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.638 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.073 Order of pole (three term test) = 6.437e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1192.0MB, alloc=44.3MB, time=15.12 x[1] = -0.7811 1.444 h = 0.003 0.006 y[1] (numeric) = 0.224976991731 0.0185936996704 y[1] (closed_form) = 0.225213406377 0.018790626476 absolute error = 0.0003077 relative error = 0.1361 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.642 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.752 Order of pole (three term test) = 1.050e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7781 1.45 h = 0.0001 0.005 y[1] (numeric) = 0.223206258404 0.0207090146332 y[1] (closed_form) = 0.223434536469 0.0208973940712 absolute error = 0.000296 relative error = 0.1319 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.646 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.227 Order of pole (three term test) = 6.860e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.778 1.455 h = 0.0001 0.003 y[1] (numeric) = 0.221340795855 0.0215256064593 y[1] (closed_form) = 0.221573166817 0.0217203476153 absolute error = 0.0003032 relative error = 0.1362 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9903 Order of pole (three term test) = 1.285e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7779 1.458 h = 0.001 0.001 y[1] (numeric) = 0.22023897375 0.0220225184758 y[1] (closed_form) = 0.220469557923 0.0222195756478 absolute error = 0.0003033 relative error = 0.1369 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.653 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7786 Order of pole (three term test) = 2.365e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7769 1.459 h = 0.001 0.003 y[1] (numeric) = 0.220019421048 0.0225453969251 y[1] (closed_form) = 0.220249515497 0.0227438776393 absolute error = 0.0003039 relative error = 0.1372 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.653 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.696 Order of pole (three term test) = 7.451e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7759 1.462 h = 0.0001 0.004 y[1] (numeric) = 0.219053292458 0.0233699734591 y[1] (closed_form) = 0.219284516101 0.0235656023841 absolute error = 0.0003029 relative error = 0.1373 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.655 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.094 Order of pole (three term test) = 1.778e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7758 1.466 h = 0.003 0.006 y[1] (numeric) = 0.217585857057 0.0239957500029 y[1] (closed_form) = 0.217819634531 0.0241909754927 absolute error = 0.0003046 relative error = 0.139 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.659 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.781 Order of pole (three term test) = 1.246e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7728 1.472 h = 0.0001 0.005 y[1] (numeric) = 0.215813339697 0.025962973154 y[1] (closed_form) = 0.216039763698 0.0261497348865 absolute error = 0.0002935 relative error = 0.1349 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.663 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.239 Order of pole (three term test) = 9.521e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7727 1.477 h = 0.0001 0.003 y[1] (numeric) = 0.21399564509 0.0266815309108 y[1] (closed_form) = 0.214225680729 0.0268745061735 absolute error = 0.0003003 relative error = 0.1391 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.667 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.001 Order of pole (three term test) = 7.402e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7726 1.48 h = 0.001 0.001 y[1] (numeric) = 0.21292148342 0.0271201172563 y[1] (closed_form) = 0.213149723979 0.0273152144437 absolute error = 0.0003003 relative error = 0.1397 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7866 Order of pole (three term test) = 3.281e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7716 1.481 h = 0.0001 0.004 y[1] (numeric) = 0.212692811389 0.0276141467728 y[1] (closed_form) = 0.2129205263 0.0278105742819 absolute error = 0.0003007 relative error = 0.1401 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.725 Order of pole (three term test) = 1.444e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7715 1.485 h = 0.003 0.006 y[1] (numeric) = 0.211256637051 0.0281774834063 y[1] (closed_form) = 0.211489235208 0.02837084259 absolute error = 0.0003025 relative error = 0.1418 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.673 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.806 Order of pole (three term test) = 1.656e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7685 1.491 h = 0.0001 0.005 y[1] (numeric) = 0.20948940624 0.0300232819601 y[1] (closed_form) = 0.209715281815 0.0302082858157 absolute error = 0.000292 relative error = 0.1378 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.677 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.251 Order of pole (three term test) = 1.545e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7684 1.496 h = 0.0001 0.003 y[1] (numeric) = 0.20771529203 0.0306636806406 y[1] (closed_form) = 0.207944396509 0.0308547529925 absolute error = 0.0002983 relative error = 0.1419 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.682 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.009 Order of pole (three term test) = 8.811e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1238.2MB, alloc=44.3MB, time=15.72 x[1] = -0.7683 1.499 h = 0.001 0.001 y[1] (numeric) = 0.206666432823 0.0310557229382 y[1] (closed_form) = 0.206893745487 0.0312487593314 absolute error = 0.0002982 relative error = 0.1425 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.684 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7936 Order of pole (three term test) = 8.720e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7673 1.5 h = 0.001 0.003 y[1] (numeric) = 0.206431590195 0.0315257001572 y[1] (closed_form) = 0.206658352862 0.031719989399 absolute error = 0.0002986 relative error = 0.1428 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.685 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.767 Order of pole (three term test) = 2.457e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7663 1.503 h = 0.0001 0.004 y[1] (numeric) = 0.205488295143 0.0322290280173 y[1] (closed_form) = 0.205716293453 0.0324208185195 absolute error = 0.0002979 relative error = 0.1431 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.687 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.135 Order of pole (three term test) = 1.511e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7662 1.507 h = 0.003 0.006 y[1] (numeric) = 0.204093802088 0.0327184052957 y[1] (closed_form) = 0.204324143757 0.0329100202984 absolute error = 0.0002996 relative error = 0.1448 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.691 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.834 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7632 1.513 h = 0.0001 0.005 y[1] (numeric) = 0.20233605102 0.0344299296333 y[1] (closed_form) = 0.202560357595 0.0346133324345 absolute error = 0.0002897 relative error = 0.141 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.695 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.263 Order of pole (three term test) = 3.923e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7631 1.518 h = 0.0001 0.003 y[1] (numeric) = 0.200612491567 0.0349850874073 y[1] (closed_form) = 0.200839612977 0.0351743851205 absolute error = 0.0002957 relative error = 0.145 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.699 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.02 Order of pole (three term test) = 8.200e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.763 1.521 h = 0.001 0.001 y[1] (numeric) = 0.199593014882 0.0353263396449 y[1] (closed_form) = 0.199818354047 0.0355174284149 absolute error = 0.0002955 relative error = 0.1456 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.702 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8017 Order of pole (three term test) = 8.538e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.762 1.522 h = 0.001 0.003 y[1] (numeric) = 0.199352044895 0.0357695046118 y[1] (closed_form) = 0.199576810297 0.0359617603631 absolute error = 0.0002958 relative error = 0.1459 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.702 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.806 Order of pole (three term test) = 2.553e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.761 1.525 h = 0.0001 0.004 y[1] (numeric) = 0.198423564169 0.0364130213534 y[1] (closed_form) = 0.198649605441 0.0366029553302 absolute error = 0.0002952 relative error = 0.1462 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.704 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.157 Order of pole (three term test) = 3.211e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7609 1.529 h = 0.003 0.006 y[1] (numeric) = 0.197069284924 0.0368364386563 y[1] (closed_form) = 0.197297558472 0.0370263019039 absolute error = 0.0002969 relative error = 0.1479 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.708 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.863 Order of pole (three term test) = 6.805e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7579 1.535 h = 0.0001 0.005 y[1] (numeric) = 0.195326070972 0.0384208586268 y[1] (closed_form) = 0.195548948322 0.0386026777555 absolute error = 0.0002876 relative error = 0.1443 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.712 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.276 Order of pole (three term test) = 2.429e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7578 1.54 h = 0.0001 0.003 y[1] (numeric) = 0.193654000141 0.0388971509801 y[1] (closed_form) = 0.19387931174 0.0390846818204 absolute error = 0.0002931 relative error = 0.1482 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.716 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.03 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7577 1.543 h = 0.001 0.001 y[1] (numeric) = 0.192664496674 0.0391913718833 y[1] (closed_form) = 0.192888043401 0.0393805317053 absolute error = 0.0002928 relative error = 0.1487 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.719 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8099 Order of pole (three term test) = 4.176e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7567 1.544 h = 0.001 0.003 y[1] (numeric) = 0.192418799875 0.0396088258339 y[1] (closed_form) = 0.19264175466 0.0397990708041 absolute error = 0.0002931 relative error = 0.149 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.719 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.845 Order of pole (three term test) = 1.229e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7557 1.547 h = 0.0001 0.004 y[1] (numeric) = 0.191506820688 0.0401961504679 y[1] (closed_form) = 0.191731080592 0.0403842418828 absolute error = 0.0002927 relative error = 0.1494 % Correct digits = 3 memory used=1284.5MB, alloc=44.3MB, time=16.31 Radius of convergence (given) for eq 1 = 1.722 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.178 Order of pole (three term test) = 7.024e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7556 1.551 h = 0.003 0.006 y[1] (numeric) = 0.190193403305 0.040558562535 y[1] (closed_form) = 0.190419786063 0.0407466763216 absolute error = 0.0002943 relative error = 0.1512 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.725 Order of pole (given) = 4 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) = 8.419e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7526 1.557 h = 0.0001 0.005 y[1] (numeric) = 0.188469130874 0.0420228603097 y[1] (closed_form) = 0.188690709764 0.0422031185445 absolute error = 0.0002856 relative error = 0.1477 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.729 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.289 Order of pole (three term test) = 1.008e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7525 1.562 h = 0.0001 0.003 y[1] (numeric) = 0.186849119314 0.0424263224979 y[1] (closed_form) = 0.187072783529 0.0426121021641 absolute error = 0.0002908 relative error = 0.1515 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.734 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.041 Order of pole (three term test) = 1.649e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7524 1.565 h = 0.001 0.001 y[1] (numeric) = 0.185889963848 0.0426770725769 y[1] (closed_form) = 0.186111887213 0.0428643297251 absolute error = 0.0002904 relative error = 0.152 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.736 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8181 Order of pole (three term test) = 3.463e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7514 1.566 h = 0.001 0.003 y[1] (numeric) = 0.185640803676 0.0430699174834 y[1] (closed_form) = 0.185862121894 0.0432581820069 absolute error = 0.0002906 relative error = 0.1523 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.737 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.884 Order of pole (three term test) = 1.627e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7504 1.569 h = 0.0001 0.004 y[1] (numeric) = 0.184746738296 0.0436045315664 y[1] (closed_form) = 0.184969381158 0.043790802016 absolute error = 0.0002903 relative error = 0.1527 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.739 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.201 Order of pole (three term test) = 1.360e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7503 1.573 h = 0.003 0.006 y[1] (numeric) = 0.183474555501 0.0439106254914 y[1] (closed_form) = 0.183699213981 0.0440970006541 absolute error = 0.0002919 relative error = 0.1545 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.743 Order of pole (given) = 4 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) = 5.816e-31 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7473 1.579 h = 0.0001 0.005 y[1] (numeric) = 0.181773032263 0.0452615725369 y[1] (closed_form) = 0.181993434776 0.0454402972124 absolute error = 0.0002838 relative error = 0.1513 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.747 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.302 Order of pole (three term test) = 3.250e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7472 1.584 h = 0.0001 0.003 y[1] (numeric) = 0.180205331632 0.0455979034914 y[1] (closed_form) = 0.180427500377 0.0457819544583 absolute error = 0.0002885 relative error = 0.155 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.751 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.051 Order of pole (three term test) = 1.734e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7471 1.587 h = 0.001 0.001 y[1] (numeric) = 0.179276709035 0.0458085470836 y[1] (closed_form) = 0.179497166562 0.0459939342297 absolute error = 0.000288 relative error = 0.1555 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.754 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8264 Order of pole (three term test) = 5.747e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7461 1.588 h = 0.0001 0.004 y[1] (numeric) = 0.179025221382 0.0461778780954 y[1] (closed_form) = 0.179245064963 0.0463641988897 absolute error = 0.0002882 relative error = 0.1557 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.755 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.964 Order of pole (three term test) = 1.563e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.746 1.592 h = 0.003 0.006 y[1] (numeric) = 0.177786946934 0.0464412758206 y[1] (closed_form) = 0.178011013159 0.0466260268642 absolute error = 0.0002904 relative error = 0.1578 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.758 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.948 Order of pole (three term test) = 2.309e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.743 1.598 h = 0.0001 0.005 y[1] (numeric) = 0.176108882881 0.0477002253783 y[1] (closed_form) = 0.176329128221 0.0478775187938 absolute error = 0.0002827 relative error = 0.1547 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.762 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.314 Order of pole (three term test) = 3.687e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7429 1.603 h = 0.0001 0.003 y[1] (numeric) = 0.174586911019 0.0479837054427 y[1] (closed_form) = 0.17480867279 0.0481661514178 absolute error = 0.0002872 relative error = 0.1584 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.767 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.06 Order of pole (three term test) = 7.682e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1330.9MB, alloc=44.3MB, time=16.89 x[1] = -0.7428 1.606 h = 0.001 0.001 y[1] (numeric) = 0.173685017504 0.0481627371699 y[1] (closed_form) = 0.173905098868 0.0483464059746 absolute error = 0.0002867 relative error = 0.1588 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.769 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8337 Order of pole (three term test) = 1.075e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7418 1.607 h = 0.001 0.003 y[1] (numeric) = 0.173432608069 0.0485126837408 y[1] (closed_form) = 0.173652071854 0.0486972258929 absolute error = 0.0002867 relative error = 0.159 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.958 Order of pole (three term test) = 1.072e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7408 1.61 h = 0.0001 0.004 y[1] (numeric) = 0.172575340133 0.0489582322531 y[1] (closed_form) = 0.172796141231 0.049141054181 absolute error = 0.0002867 relative error = 0.1596 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.772 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.242 Order of pole (three term test) = 2.507e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7407 1.614 h = 0.003 0.006 y[1] (numeric) = 0.171380624457 0.0491715972298 y[1] (closed_form) = 0.171603248135 0.0493546502013 absolute error = 0.0002882 relative error = 0.1614 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.776 Order of pole (given) = 4 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) = 1.067e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7377 1.62 h = 0.0001 0.005 y[1] (numeric) = 0.169730912329 0.0503292092045 y[1] (closed_form) = 0.169950186171 0.0505050307464 absolute error = 0.0002811 relative error = 0.1585 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.327 Order of pole (three term test) = 8.639e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7376 1.625 h = 0.0001 0.003 y[1] (numeric) = 0.168260947788 0.0505552862065 y[1] (closed_form) = 0.168481469655 0.0507360613677 absolute error = 0.0002851 relative error = 0.1621 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.785 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.071 Order of pole (three term test) = 5.901e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7375 1.628 h = 0.001 0.001 y[1] (numeric) = 0.167389470889 0.0506999602718 y[1] (closed_form) = 0.167608349904 0.050881834864 absolute error = 0.0002846 relative error = 0.1625 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.787 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8421 Order of pole (three term test) = 4.107e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7365 1.629 h = 0.001 0.003 y[1] (numeric) = 0.167136527019 0.0510284019408 y[1] (closed_form) = 0.16735478645 0.0512110835725 absolute error = 0.0002846 relative error = 0.1626 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.788 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.998 Order of pole (three term test) = 6.397e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7355 1.632 h = 0.0001 0.004 y[1] (numeric) = 0.166299891299 0.0514304087458 y[1] (closed_form) = 0.166519485887 0.0516115052387 absolute error = 0.0002846 relative error = 0.1633 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.265 Order of pole (three term test) = 1.092e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7354 1.636 h = 0.003 0.006 y[1] (numeric) = 0.165146201508 0.051599422898 y[1] (closed_form) = 0.165367519864 0.0517808066877 absolute error = 0.0002862 relative error = 0.1651 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.794 Order of pole (given) = 4 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) = 1.490e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7324 1.642 h = 0.0001 0.005 y[1] (numeric) = 0.163527227651 0.0526617785779 y[1] (closed_form) = 0.163745629232 0.0528361646172 absolute error = 0.0002795 relative error = 0.1624 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.798 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.34 Order of pole (three term test) = 3.499e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7323 1.647 h = 0.0001 0.003 y[1] (numeric) = 0.162108824375 0.0528352281982 y[1] (closed_form) = 0.162328230269 0.0530143688817 absolute error = 0.0002832 relative error = 0.1659 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.802 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.082 Order of pole (three term test) = 5.713e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7322 1.65 h = 0.001 0.001 y[1] (numeric) = 0.161267532124 0.0529483693167 y[1] (closed_form) = 0.161485335923 0.0531284949891 absolute error = 0.0002826 relative error = 0.1663 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.805 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8505 Order of pole (three term test) = 2.397e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7312 1.651 h = 0.001 0.003 y[1] (numeric) = 0.161014875025 0.0532563489194 y[1] (closed_form) = 0.161232060265 0.0534372191598 absolute error = 0.0002826 relative error = 0.1664 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.806 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.038 Order of pole (three term test) = 6.761e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1377.2MB, alloc=44.3MB, time=17.48 x[1] = -0.7302 1.654 h = 0.0001 0.004 y[1] (numeric) = 0.160199459372 0.0536177293548 y[1] (closed_form) = 0.160417971819 0.0537971414495 absolute error = 0.0002827 relative error = 0.1671 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.808 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.288 Order of pole (three term test) = 1.502e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7301 1.658 h = 0.003 0.006 y[1] (numeric) = 0.159086400336 0.0537460940999 y[1] (closed_form) = 0.159306541125 0.0539258420999 absolute error = 0.0002842 relative error = 0.169 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.812 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.037 Order of pole (three term test) = 2.842e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7271 1.664 h = 0.0001 0.005 y[1] (numeric) = 0.157500142196 0.0547190198071 y[1] (closed_form) = 0.157717763523 0.0548920087727 absolute error = 0.000278 relative error = 0.1665 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.816 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.354 Order of pole (three term test) = 4.812e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.727 1.669 h = 0.0001 0.003 y[1] (numeric) = 0.156132671944 0.0548443154893 y[1] (closed_form) = 0.156351076863 0.0550218613366 absolute error = 0.0002815 relative error = 0.1698 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.093 Order of pole (three term test) = 1.242e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7269 1.672 h = 0.001 0.001 y[1] (numeric) = 0.15532122305 0.0549285714176 y[1] (closed_form) = 0.155538069164 0.0551069963138 absolute error = 0.0002808 relative error = 0.1702 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.823 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.859 Order of pole (three term test) = 1.647e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7259 1.673 h = 0.001 0.003 y[1] (numeric) = 0.155069580105 0.0552171059363 y[1] (closed_form) = 0.155285811314 0.0553962166534 absolute error = 0.0002808 relative error = 0.1703 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.824 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.078 Order of pole (three term test) = 1.095e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7249 1.676 h = 0.0001 0.004 y[1] (numeric) = 0.154275810962 0.0555406286397 y[1] (closed_form) = 0.154493356436 0.0557184003776 absolute error = 0.0002809 relative error = 0.1711 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.826 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.311 Order of pole (three term test) = 1.664e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7248 1.68 h = 0.003 0.006 y[1] (numeric) = 0.153202850618 0.0556318097764 y[1] (closed_form) = 0.153421932545 0.0558099590779 absolute error = 0.0002824 relative error = 0.173 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.068 Order of pole (three term test) = 3.903e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7218 1.686 h = 0.0001 0.005 y[1] (numeric) = 0.151650917688 0.0565208738117 y[1] (closed_form) = 0.151867843918 0.0566925057072 absolute error = 0.0002766 relative error = 0.1706 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.834 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.367 Order of pole (three term test) = 6.608e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7217 1.691 h = 0.0001 0.003 y[1] (numeric) = 0.150333597661 0.0566021984423 y[1] (closed_form) = 0.150551108117 0.0567781917236 absolute error = 0.0002798 relative error = 0.1739 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.104 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7216 1.694 h = 0.001 0.001 y[1] (numeric) = 0.149551557827 0.0566600466719 y[1] (closed_form) = 0.149767554707 0.0568368211069 absolute error = 0.0002791 relative error = 0.1742 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8675 Order of pole (three term test) = 7.532e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7206 1.695 h = 0.0001 0.004 y[1] (numeric) = 0.149301570316 0.0569301243409 y[1] (closed_form) = 0.149516958212 0.0571075294492 absolute error = 0.000279 relative error = 0.1743 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.211 Order of pole (three term test) = 6.636e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7205 1.699 h = 0.003 0.006 y[1] (numeric) = 0.14826097793 0.0569933734556 y[1] (closed_form) = 0.148479849256 0.0571701806999 absolute error = 0.0002814 relative error = 0.1768 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.094 Order of pole (three term test) = 5.137e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7175 1.705 h = 0.0001 0.005 y[1] (numeric) = 0.146740540405 0.0578149425481 y[1] (closed_form) = 0.146957541038 0.0579854451244 absolute error = 0.000276 relative error = 0.1747 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.379 Order of pole (three term test) = 1.195e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1423.4MB, alloc=44.3MB, time=18.08 x[1] = -0.7174 1.71 h = 0.0001 0.003 y[1] (numeric) = 0.145466122646 0.0578621374316 y[1] (closed_form) = 0.145683554077 0.0580368335513 absolute error = 0.0002789 relative error = 0.1779 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.854 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.113 Order of pole (three term test) = 1.003e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7173 1.713 h = 0.001 0.001 y[1] (numeric) = 0.144709266645 0.0578994557511 y[1] (closed_form) = 0.14492522563 0.0580748554155 absolute error = 0.0002782 relative error = 0.1782 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.857 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.875 Order of pole (three term test) = 1.401e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7163 1.714 h = 0.001 0.003 y[1] (numeric) = 0.144461361642 0.0581544427743 y[1] (closed_form) = 0.144676718902 0.0583304285228 absolute error = 0.0002781 relative error = 0.1783 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.858 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.154 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7153 1.717 h = 0.0001 0.004 y[1] (numeric) = 0.14370890889 0.0584146600674 y[1] (closed_form) = 0.14392554427 0.058589508492 absolute error = 0.0002784 relative error = 0.1792 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.354 Order of pole (three term test) = 4.816e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7152 1.721 h = 0.003 0.006 y[1] (numeric) = 0.142709119678 0.0584455655031 y[1] (closed_form) = 0.142927129915 0.0586208517057 absolute error = 0.0002797 relative error = 0.1811 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.864 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.125 Order of pole (three term test) = 1.115e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7122 1.727 h = 0.0001 0.005 y[1] (numeric) = 0.141225091562 0.0591929578895 y[1] (closed_form) = 0.141441538129 0.0593621814439 absolute error = 0.0002747 relative error = 0.1791 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.868 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.393 Order of pole (three term test) = 2.779e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7121 1.732 h = 0.0001 0.003 y[1] (numeric) = 0.139998996875 0.0592032216787 y[1] (closed_form) = 0.140215710447 0.0593764499367 absolute error = 0.0002774 relative error = 0.1822 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.873 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.124 Order of pole (three term test) = 1.399e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.712 1.735 h = 0.001 0.001 y[1] (numeric) = 0.139270518329 0.0592183064782 y[1] (closed_form) = 0.139485806872 0.0593921541615 absolute error = 0.0002767 relative error = 0.1825 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.875 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8836 Order of pole (three term test) = 1.362e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.711 1.736 h = 0.001 0.003 y[1] (numeric) = 0.139025246591 0.0594565973171 y[1] (closed_form) = 0.139239942659 0.0596309822859 absolute error = 0.0002766 relative error = 0.1826 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.876 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.195 Order of pole (three term test) = 9.561e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.71 1.739 h = 0.0001 0.004 y[1] (numeric) = 0.138294899557 0.059686089041 y[1] (closed_form) = 0.138510850373 0.0598594350869 absolute error = 0.0002769 relative error = 0.1835 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.377 Order of pole (three term test) = 1.628e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7099 1.743 h = 0.003 0.006 y[1] (numeric) = 0.137333077578 0.0596884999664 y[1] (closed_form) = 0.137550321941 0.0598623090378 absolute error = 0.0002782 relative error = 0.1855 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.882 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.155 Order of pole (three term test) = 7.105e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7069 1.749 h = 0.0001 0.005 y[1] (numeric) = 0.135886218217 0.0603665470694 y[1] (closed_form) = 0.136102178361 0.0605345338674 absolute error = 0.0002736 relative error = 0.1837 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.886 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.406 Order of pole (three term test) = 5.430e-31 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7068 1.754 h = 0.0001 0.003 y[1] (numeric) = 0.13470735284 0.0603432997049 y[1] (closed_form) = 0.134923433262 0.0605151067419 absolute error = 0.0002761 relative error = 0.1867 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.891 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.135 Order of pole (three term test) = 1.876e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7067 1.757 h = 0.001 0.001 y[1] (numeric) = 0.134006628984 0.0603381806893 y[1] (closed_form) = 0.134221332416 0.0605105297942 absolute error = 0.0002753 relative error = 0.187 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.894 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8922 Order of pole (three term test) = 3.705e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7057 1.758 h = 0.001 0.003 y[1] (numeric) = 0.133764424551 0.060560670123 y[1] (closed_form) = 0.13397854617 0.0607335109058 absolute error = 0.0002752 relative error = 0.1871 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.894 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.236 Order of pole (three term test) = 9.421e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1469.8MB, alloc=44.3MB, time=18.66 x[1] = -0.7047 1.761 h = 0.0001 0.004 y[1] (numeric) = 0.133056146924 0.0607616636439 y[1] (closed_form) = 0.133271497347 0.0609335572815 absolute error = 0.0002755 relative error = 0.188 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.897 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.4 Order of pole (three term test) = 6.963e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7046 1.765 h = 0.003 0.006 y[1] (numeric) = 0.13213141265 0.0607382266347 y[1] (closed_form) = 0.132347979002 0.0609106038545 absolute error = 0.0002768 relative error = 0.19 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.186 Order of pole (three term test) = 1.868e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7016 1.771 h = 0.0001 0.005 y[1] (numeric) = 0.130722244058 0.0613515108296 y[1] (closed_form) = 0.130937780005 0.0615183033438 absolute error = 0.0002725 relative error = 0.1884 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.905 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.42 Order of pole (three term test) = 8.156e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7015 1.776 h = 0.0001 0.003 y[1] (numeric) = 0.129589441603 0.0612979310257 y[1] (closed_form) = 0.129804966816 0.0614683641779 absolute error = 0.0002748 relative error = 0.1913 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.146 Order of pole (three term test) = 2.573e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7014 1.779 h = 0.001 0.001 y[1] (numeric) = 0.128915805177 0.0612744961165 y[1] (closed_form) = 0.129130001711 0.061445400316 absolute error = 0.000274 relative error = 0.1916 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.901 Order of pole (three term test) = 9.112e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7004 1.78 h = 0.001 0.003 y[1] (numeric) = 0.128677041661 0.0614820445046 y[1] (closed_form) = 0.128890668218 0.0616533978157 absolute error = 0.0002739 relative error = 0.1917 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.913 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.277 Order of pole (three term test) = 1.611e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6994 1.783 h = 0.0001 0.004 y[1] (numeric) = 0.127990711169 0.0616566372311 y[1] (closed_form) = 0.128205538489 0.0618271288784 absolute error = 0.0002743 relative error = 0.1927 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.915 Order of pole (given) = 4 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) = 2.687e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6993 1.787 h = 0.003 0.006 y[1] (numeric) = 0.127102131515 0.061609811643 y[1] (closed_form) = 0.127318100807 0.0617808032212 absolute error = 0.0002755 relative error = 0.1947 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.919 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.217 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6963 1.793 h = 0.0001 0.005 y[1] (numeric) = 0.125730965719 0.0621626721059 y[1] (closed_form) = 0.125946134625 0.0623283127658 absolute error = 0.0002715 relative error = 0.1932 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.923 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.434 Order of pole (three term test) = 1.011e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6962 1.798 h = 0.0001 0.003 y[1] (numeric) = 0.124643003013 0.0620817102395 y[1] (closed_form) = 0.124858044619 0.0622508171824 absolute error = 0.0002736 relative error = 0.1961 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.928 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.157 Order of pole (three term test) = 2.093e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6961 1.801 h = 0.001 0.001 y[1] (numeric) = 0.123995751674 0.0620417130522 y[1] (closed_form) = 0.124209512876 0.062211225947 absolute error = 0.0002728 relative error = 0.1964 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.931 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9097 Order of pole (three term test) = 1.379e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6951 1.802 h = 0.0001 0.004 y[1] (numeric) = 0.123760747862 0.0622351459021 y[1] (closed_form) = 0.123973951884 0.0624050682332 absolute error = 0.0002726 relative error = 0.1964 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.931 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.465 Order of pole (three term test) = 8.582e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.695 1.806 h = 0.003 0.006 y[1] (numeric) = 0.122901045371 0.0621709500007 y[1] (closed_form) = 0.123117036818 0.0623408693659 absolute error = 0.0002748 relative error = 0.1991 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.935 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.244 Order of pole (three term test) = 3.706e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.692 1.812 h = 0.0001 0.005 y[1] (numeric) = 0.121563352901 0.0626755480621 y[1] (closed_form) = 0.121778721536 0.0628403164854 absolute error = 0.0002712 relative error = 0.1979 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.446 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1516.1MB, alloc=44.3MB, time=19.27 x[1] = -0.6919 1.817 h = 0.0001 0.003 y[1] (numeric) = 0.120513256602 0.0625737277627 y[1] (closed_form) = 0.120728410239 0.0627418156368 absolute error = 0.000273 relative error = 0.2007 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.944 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.167 Order of pole (three term test) = 9.119e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6918 1.82 h = 0.001 0.001 y[1] (numeric) = 0.119888304821 0.0625210838891 y[1] (closed_form) = 0.120102220073 0.0626895266959 absolute error = 0.0002723 relative error = 0.201 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9173 Order of pole (three term test) = 7.739e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6908 1.821 h = 0.001 0.003 y[1] (numeric) = 0.119656909909 0.062703049932 y[1] (closed_form) = 0.119870280044 0.0628718703888 absolute error = 0.0002721 relative error = 0.201 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.948 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.355 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6898 1.824 h = 0.0001 0.004 y[1] (numeric) = 0.119011106943 0.0628339290916 y[1] (closed_form) = 0.119225620632 0.06300203093 absolute error = 0.0002725 relative error = 0.2021 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.467 Order of pole (three term test) = 1.690e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6897 1.828 h = 0.003 0.006 y[1] (numeric) = 0.118187402265 0.0627499319177 y[1] (closed_form) = 0.118402929746 0.0629185536213 absolute error = 0.0002737 relative error = 0.2041 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.954 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.276 Order of pole (three term test) = 4.507e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6867 1.834 h = 0.0001 0.005 y[1] (numeric) = 0.116887772948 0.0632015559518 y[1] (closed_form) = 0.117102868021 0.0633652511996 absolute error = 0.0002703 relative error = 0.203 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.958 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.46 Order of pole (three term test) = 1.048e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6866 1.839 h = 0.0001 0.003 y[1] (numeric) = 0.115880106534 0.0630772636266 y[1] (closed_form) = 0.116094893734 0.0632441145778 absolute error = 0.000272 relative error = 0.2057 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.963 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.178 Order of pole (three term test) = 8.761e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6865 1.842 h = 0.001 0.001 y[1] (numeric) = 0.115280149837 0.063010979292 y[1] (closed_form) = 0.11549374615 0.063178130061 absolute error = 0.0002712 relative error = 0.206 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.966 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9262 Order of pole (three term test) = 6.110e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6855 1.843 h = 0.001 0.003 y[1] (numeric) = 0.11505297057 0.063180275408 y[1] (closed_form) = 0.115266035825 0.06334776914 absolute error = 0.000271 relative error = 0.2061 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.966 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.397 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6845 1.846 h = 0.0001 0.004 y[1] (numeric) = 0.114428369518 0.0632900762935 y[1] (closed_form) = 0.114642546513 0.0634569206559 absolute error = 0.0002715 relative error = 0.2072 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.969 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.491 Order of pole (three term test) = 8.278e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6844 1.85 h = 0.003 0.006 y[1] (numeric) = 0.113637933441 0.0631887697472 y[1] (closed_form) = 0.113853060406 0.0633561406547 absolute error = 0.0002726 relative error = 0.2092 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.973 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.307 Order of pole (three term test) = 3.059e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6814 1.856 h = 0.0001 0.005 y[1] (numeric) = 0.112376211427 0.0635911015732 y[1] (closed_form) = 0.112591077369 0.0637537648254 absolute error = 0.0002695 relative error = 0.2083 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.977 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.474 Order of pole (three term test) = 2.439e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6813 1.861 h = 0.0001 0.003 y[1] (numeric) = 0.111409662995 0.0634467034301 y[1] (closed_form) = 0.111624139419 0.0636123644912 absolute error = 0.000271 relative error = 0.2109 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.982 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.189 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6812 1.864 h = 0.001 0.001 y[1] (numeric) = 0.110833942532 0.0633681881642 y[1] (closed_form) = 0.111047274901 0.0635340987672 absolute error = 0.0002703 relative error = 0.2112 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.985 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.935 Order of pole (three term test) = 8.286e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1562.5MB, alloc=44.3MB, time=19.86 x[1] = -0.6802 1.865 h = 0.001 0.003 y[1] (numeric) = 0.110611168662 0.0635255399427 y[1] (closed_form) = 0.1108239845 0.0636917612881 absolute error = 0.00027 relative error = 0.2113 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.985 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.439 Order of pole (three term test) = 1.169e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6792 1.868 h = 0.0001 0.004 y[1] (numeric) = 0.110007416087 0.0636159045587 y[1] (closed_form) = 0.110221311129 0.0637815407236 absolute error = 0.0002705 relative error = 0.2124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.988 Order of pole (given) = 4 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) = 1.341e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6791 1.872 h = 0.003 0.006 y[1] (numeric) = 0.109249211083 0.0634991182305 y[1] (closed_form) = 0.109463995621 0.063665284931 absolute error = 0.0002716 relative error = 0.2144 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.991 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.339 Order of pole (three term test) = 8.304e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6761 1.878 h = 0.0001 0.005 y[1] (numeric) = 0.10802511493 0.063855626428 y[1] (closed_form) = 0.108239792298 0.0640172981601 absolute error = 0.0002687 relative error = 0.2137 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.996 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.488 Order of pole (three term test) = 9.915e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.676 1.883 h = 0.0001 0.003 y[1] (numeric) = 0.107098360782 0.0636933078264 y[1] (closed_form) = 0.107312577237 0.0638578254121 absolute error = 0.0002701 relative error = 0.2163 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.001 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.201 Order of pole (three term test) = 1.138e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6759 1.886 h = 0.001 0.001 y[1] (numeric) = 0.106546109432 0.063603864495 y[1] (closed_form) = 0.106759227838 0.0637685858413 absolute error = 0.0002694 relative error = 0.2166 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.003 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9439 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6749 1.887 h = 0.001 0.003 y[1] (numeric) = 0.106327893869 0.0637499636071 y[1] (closed_form) = 0.106540510609 0.0639149658001 absolute error = 0.0002691 relative error = 0.2166 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.004 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.481 Order of pole (three term test) = 3.166e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6739 1.89 h = 0.0001 0.004 y[1] (numeric) = 0.105744597008 0.0638224289051 y[1] (closed_form) = 0.105958259947 0.0639869053476 absolute error = 0.0002696 relative error = 0.2178 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.007 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.539 Order of pole (three term test) = 2.108e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6738 1.894 h = 0.003 0.006 y[1] (numeric) = 0.105017578083 0.0636918523528 y[1] (closed_form) = 0.105232073291 0.0638568609471 absolute error = 0.0002706 relative error = 0.2199 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.01 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.37 Order of pole (three term test) = 1.742e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6708 1.9 h = 0.0001 0.005 y[1] (numeric) = 0.103830717883 0.0640058009608 y[1] (closed_form) = 0.104045243635 0.0641665208339 absolute error = 0.0002681 relative error = 0.2193 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.015 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.502 Order of pole (three term test) = 4.999e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6707 1.905 h = 0.0001 0.003 y[1] (numeric) = 0.102942430798 0.0638275777452 y[1] (closed_form) = 0.103156433581 0.06399099749 absolute error = 0.0002693 relative error = 0.2218 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.02 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.212 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6706 1.908 h = 0.001 0.001 y[1] (numeric) = 0.102412878123 0.0637284091654 y[1] (closed_form) = 0.102625827904 0.0638919910579 absolute error = 0.0002685 relative error = 0.2221 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.022 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9528 Order of pole (three term test) = 7.583e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6696 1.909 h = 0.0001 0.004 y[1] (numeric) = 0.102199340737 0.0638639140529 y[1] (closed_form) = 0.10241180394 0.0640277490839 absolute error = 0.0002683 relative error = 0.2221 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.023 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.724 Order of pole (three term test) = 4.010e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6695 1.913 h = 0.003 0.006 y[1] (numeric) = 0.101497067322 0.0637232692683 y[1] (closed_form) = 0.101711715922 0.0638874406663 absolute error = 0.0002702 relative error = 0.225 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.027 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.398 Order of pole (three term test) = 7.324e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6665 1.919 h = 0.0001 0.005 y[1] (numeric) = 0.100342332646 0.064003483623 y[1] (closed_form) = 0.100557116063 0.064163539894 absolute error = 0.0002679 relative error = 0.2246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.031 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.514 Order of pole (three term test) = 5.921e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1609.0MB, alloc=44.3MB, time=20.46 x[1] = -0.6664 1.924 h = 0.0001 0.003 y[1] (numeric) = 0.0994862562311 0.063813499853 y[1] (closed_form) = 0.0997004717339 0.063976134512 absolute error = 0.000269 relative error = 0.227 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.036 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.222 Order of pole (three term test) = 5.993e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6663 1.927 h = 0.001 0.001 y[1] (numeric) = 0.0989757235887 0.0637071095045 y[1] (closed_form) = 0.0991889244529 0.0638698741136 absolute error = 0.0002682 relative error = 0.2274 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.039 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9606 Order of pole (three term test) = 3.936e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6653 1.928 h = 0.001 0.003 y[1] (numeric) = 0.0987664024921 0.0638340548483 y[1] (closed_form) = 0.0989791301583 0.0639970505773 absolute error = 0.000268 relative error = 0.2274 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.561 Order of pole (three term test) = 1.111e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6643 1.931 h = 0.0001 0.004 y[1] (numeric) = 0.0982201916313 0.0638771974757 y[1] (closed_form) = 0.0984339030001 0.0640397659633 absolute error = 0.0002685 relative error = 0.2287 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.042 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.584 Order of pole (three term test) = 2.090e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6642 1.935 h = 0.003 0.006 y[1] (numeric) = 0.0975485439703 0.0637253563247 y[1] (closed_form) = 0.0977629893935 0.0638884540171 absolute error = 0.0002694 relative error = 0.2307 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.046 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.43 Order of pole (three term test) = 1.966e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6612 1.941 h = 0.0001 0.005 y[1] (numeric) = 0.0964300492366 0.0639685636814 y[1] (closed_form) = 0.0966447406629 0.0641277397828 absolute error = 0.0002673 relative error = 0.2304 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.051 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.529 Order of pole (three term test) = 3.915e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6611 1.946 h = 0.0001 0.003 y[1] (numeric) = 0.095609964781 0.0637659964475 y[1] (closed_form) = 0.0958240413389 0.0639276161016 absolute error = 0.0002682 relative error = 0.2329 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.055 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.234 Order of pole (three term test) = 6.021e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.661 1.949 h = 0.001 0.001 y[1] (numeric) = 0.0951206907732 0.06365186521 y[1] (closed_form) = 0.0953337956548 0.0638135801375 absolute error = 0.0002675 relative error = 0.2332 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.058 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9696 Order of pole (three term test) = 2.652e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.66 1.95 h = 0.001 0.003 y[1] (numeric) = 0.0949161877609 0.0637693566126 y[1] (closed_form) = 0.0951288346567 0.0639312786731 absolute error = 0.0002673 relative error = 0.2332 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.603 Order of pole (three term test) = 7.110e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.659 1.953 h = 0.0001 0.004 y[1] (numeric) = 0.094389135945 0.0637984574187 y[1] (closed_form) = 0.0946027333899 0.0639599996205 absolute error = 0.0002678 relative error = 0.2345 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.061 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.608 Order of pole (three term test) = 2.226e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6589 1.957 h = 0.003 0.006 y[1] (numeric) = 0.0937456807501 0.0636369512775 y[1] (closed_form) = 0.0939599636746 0.0637990190339 absolute error = 0.0002687 relative error = 0.2366 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.065 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.462 Order of pole (three term test) = 1.350e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6559 1.963 h = 0.0001 0.005 y[1] (numeric) = 0.092662807908 0.0638458788206 y[1] (closed_form) = 0.0928774354021 0.0640042116143 absolute error = 0.0002667 relative error = 0.2365 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.543 Order of pole (three term test) = 4.217e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6558 1.968 h = 0.0001 0.003 y[1] (numeric) = 0.0918774156684 0.0636323176387 y[1] (closed_form) = 0.0920913884234 0.0637929649897 absolute error = 0.0002676 relative error = 0.2388 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.245 Order of pole (three term test) = 1.097e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6557 1.971 h = 0.001 0.001 y[1] (numeric) = 0.0914086429149 0.0635113963681 y[1] (closed_form) = 0.0916216857552 0.0636721076495 absolute error = 0.0002669 relative error = 0.2392 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9787 Order of pole (three term test) = 1.035e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1655.4MB, alloc=44.3MB, time=21.06 x[1] = -0.6547 1.972 h = 0.001 0.003 y[1] (numeric) = 0.0912090019789 0.0636200017598 y[1] (closed_form) = 0.09142160201 0.0637808980086 absolute error = 0.0002666 relative error = 0.2392 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.078 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.646 Order of pole (three term test) = 5.871e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6537 1.975 h = 0.0001 0.004 y[1] (numeric) = 0.0907006238858 0.0636362402598 y[1] (closed_form) = 0.0909141415557 0.0637968003327 absolute error = 0.0002672 relative error = 0.2405 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.632 Order of pole (three term test) = 1.894e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6536 1.979 h = 0.003 0.006 y[1] (numeric) = 0.0900843398016 0.0634662976385 y[1] (closed_form) = 0.0902984971574 0.0636273782065 absolute error = 0.000268 relative error = 0.2426 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.084 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.494 Order of pole (three term test) = 9.587e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6506 1.985 h = 0.0001 0.005 y[1] (numeric) = 0.0890364137265 0.0636435023623 y[1] (closed_form) = 0.0892510026699 0.0638010276433 absolute error = 0.0002662 relative error = 0.2426 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.089 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.557 Order of pole (three term test) = 5.669e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6505 1.99 h = 0.0001 0.003 y[1] (numeric) = 0.0882844325678 0.0634204065982 y[1] (closed_form) = 0.0884983333099 0.0635801231797 absolute error = 0.000267 relative error = 0.245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.257 Order of pole (three term test) = 4.869e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6504 1.993 h = 0.001 0.001 y[1] (numeric) = 0.0878354136969 0.0632935691311 y[1] (closed_form) = 0.0880484250346 0.0634533213755 absolute error = 0.0002663 relative error = 0.2453 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.096 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9877 Order of pole (three term test) = 1.170e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6494 1.994 h = 0.001 0.003 y[1] (numeric) = 0.0876406576909 0.0633938268559 y[1] (closed_form) = 0.0878532412933 0.0635537436064 absolute error = 0.000266 relative error = 0.2453 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.097 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.689 Order of pole (three term test) = 1.483e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6484 1.997 h = 0.0001 0.004 y[1] (numeric) = 0.087150455663 0.0633983020707 y[1] (closed_form) = 0.0873639243624 0.063557922873 absolute error = 0.0002665 relative error = 0.2467 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.657 Order of pole (three term test) = 1.272e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6483 2.001 h = 0.003 0.006 y[1] (numeric) = 0.0865603367721 0.0632210508211 y[1] (closed_form) = 0.0867744020215 0.0633811858447 absolute error = 0.0002673 relative error = 0.2488 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.526 Order of pole (three term test) = 5.344e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6453 2.007 h = 0.0001 0.005 y[1] (numeric) = 0.0855466353998 0.0633689281764 y[1] (closed_form) = 0.0857612087015 0.0635256806402 absolute error = 0.0002657 relative error = 0.249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.108 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.572 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6452 2.012 h = 0.0001 0.003 y[1] (numeric) = 0.0848268065484 0.0631376360249 y[1] (closed_form) = 0.0850406639737 0.0632964621484 absolute error = 0.0002664 relative error = 0.2513 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.113 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.268 Order of pole (three term test) = 1.460e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6451 2.015 h = 0.001 0.001 y[1] (numeric) = 0.084396806477 0.0630056844428 y[1] (closed_form) = 0.0846098137207 0.0631645207962 absolute error = 0.0002657 relative error = 0.2516 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9968 Order of pole (three term test) = 6.457e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6441 2.016 h = 0.0001 0.004 y[1] (numeric) = 0.0842069395743 0.0630981043352 y[1] (closed_form) = 0.0844195339966 0.0632570863257 absolute error = 0.0002655 relative error = 0.2516 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.988 Order of pole (three term test) = 8.009e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.644 2.02 h = 0.003 0.006 y[1] (numeric) = 0.0836374937066 0.0629156869116 y[1] (closed_form) = 0.0838517776497 0.0630751787117 absolute error = 0.0002671 relative error = 0.2546 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.12 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.555 Order of pole (three term test) = 8.715e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1701.7MB, alloc=44.3MB, time=21.64 x[1] = -0.641 2.026 h = 0.0001 0.005 y[1] (numeric) = 0.0826529578018 0.063040516632 y[1] (closed_form) = 0.0828678059256 0.0631967697775 absolute error = 0.0002657 relative error = 0.2549 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.125 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.584 Order of pole (three term test) = 2.452e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6409 2.031 h = 0.0001 0.003 y[1] (numeric) = 0.0819598939949 0.0628035177123 y[1] (closed_form) = 0.0821740079299 0.0629617474 absolute error = 0.0002662 relative error = 0.2572 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.278 Order of pole (three term test) = 8.414e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6408 2.034 h = 0.001 0.001 y[1] (numeric) = 0.0815457359771 0.0626679701468 y[1] (closed_form) = 0.0817590327041 0.0628261907154 absolute error = 0.0002656 relative error = 0.2576 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.133 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.005 Order of pole (three term test) = 8.276e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6398 2.035 h = 0.001 0.003 y[1] (numeric) = 0.0813601537907 0.0627540888032 y[1] (closed_form) = 0.081573050569 0.0629124401355 absolute error = 0.0002653 relative error = 0.2576 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.133 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.77 Order of pole (three term test) = 2.612e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6388 2.038 h = 0.0001 0.004 y[1] (numeric) = 0.0809025346349 0.0627395460504 y[1] (closed_form) = 0.0811162568952 0.0628976675064 absolute error = 0.0002659 relative error = 0.259 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.136 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.702 Order of pole (three term test) = 2.083e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6387 2.042 h = 0.003 0.006 y[1] (numeric) = 0.0803585495811 0.0625516651866 y[1] (closed_form) = 0.0805727948824 0.0627102861021 absolute error = 0.0002666 relative error = 0.2611 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.587 Order of pole (three term test) = 1.237e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6357 2.048 h = 0.0001 0.005 y[1] (numeric) = 0.0794067756612 0.062651214234 y[1] (closed_form) = 0.0796216444568 0.0628067563423 absolute error = 0.0002653 relative error = 0.2616 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.144 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.599 Order of pole (three term test) = 9.839e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6356 2.053 h = 0.0001 0.003 y[1] (numeric) = 0.0787435786639 0.0624082009892 y[1] (closed_form) = 0.0789576948155 0.0625656121188 absolute error = 0.0002658 relative error = 0.2638 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.149 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.29 Order of pole (three term test) = 1.125e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6355 2.056 h = 0.001 0.001 y[1] (numeric) = 0.0783471027964 0.0622688493456 y[1] (closed_form) = 0.0785604384855 0.0624262305924 absolute error = 0.0002651 relative error = 0.2642 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.152 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.014 Order of pole (three term test) = 1.106e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6345 2.057 h = 0.001 0.003 y[1] (numeric) = 0.0781663699414 0.0623480063872 y[1] (closed_form) = 0.0783793201586 0.062505502211 absolute error = 0.0002649 relative error = 0.2642 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.153 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.813 Order of pole (three term test) = 7.806e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6335 2.06 h = 0.0001 0.004 y[1] (numeric) = 0.0777254570497 0.0623244345462 y[1] (closed_form) = 0.0779392018202 0.0624817320854 absolute error = 0.0002654 relative error = 0.2657 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.155 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.727 Order of pole (three term test) = 5.314e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6334 2.064 h = 0.003 0.006 y[1] (numeric) = 0.0772048578803 0.0621319652336 y[1] (closed_form) = 0.0774190894965 0.0622897534226 absolute error = 0.0002661 relative error = 0.2678 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.159 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.62 Order of pole (three term test) = 5.535e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6304 2.07 h = 0.0001 0.005 y[1] (numeric) = 0.0762850376907 0.0622082125729 y[1] (closed_form) = 0.0764999440235 0.0623630750844 absolute error = 0.0002649 relative error = 0.2684 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.164 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.613 Order of pole (three term test) = 7.007e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6303 2.075 h = 0.0001 0.003 y[1] (numeric) = 0.075650529018 0.0619602221737 y[1] (closed_form) = 0.0758646685272 0.0621168513611 absolute error = 0.0002653 relative error = 0.2706 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.169 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.302 Order of pole (three term test) = 6.006e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6302 2.078 h = 0.001 0.001 y[1] (numeric) = 0.0752710453423 0.0618176900295 y[1] (closed_form) = 0.0754844398101 0.0619742707989 absolute error = 0.0002647 relative error = 0.271 % Correct digits = 3 memory used=1748.2MB, alloc=44.3MB, time=22.23 Radius of convergence (given) for eq 1 = 2.171 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.023 Order of pole (three term test) = 1.483e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6292 2.079 h = 0.001 0.003 y[1] (numeric) = 0.0750951244972 0.0618903197224 y[1] (closed_form) = 0.0753081476923 0.0620470001859 absolute error = 0.0002644 relative error = 0.271 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.172 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.857 Order of pole (three term test) = 7.511e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6282 2.082 h = 0.0001 0.004 y[1] (numeric) = 0.0746704051448 0.061858549018 y[1] (closed_form) = 0.0748841926503 0.0620150601638 absolute error = 0.000265 relative error = 0.2725 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.175 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.752 Order of pole (three term test) = 1.669e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6281 2.086 h = 0.003 0.006 y[1] (numeric) = 0.0741722685764 0.0616622926877 y[1] (closed_form) = 0.0743865089258 0.0618192850436 absolute error = 0.0002656 relative error = 0.2746 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.179 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.652 Order of pole (three term test) = 2.938e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6251 2.092 h = 0.0001 0.005 y[1] (numeric) = 0.0732835764558 0.0617170871098 y[1] (closed_form) = 0.0734985353915 0.0618713003312 absolute error = 0.0002646 relative error = 0.2754 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.628 Order of pole (three term test) = 1.174e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.625 2.097 h = 0.0001 0.003 y[1] (numeric) = 0.072676608911 0.0614650657452 y[1] (closed_form) = 0.0728907906725 0.0616209483021 absolute error = 0.0002649 relative error = 0.2775 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.188 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.313 Order of pole (three term test) = 8.947e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6249 2.1 h = 0.001 0.001 y[1] (numeric) = 0.0723134452515 0.0613199226547 y[1] (closed_form) = 0.0725269160725 0.061475740303 absolute error = 0.0002643 relative error = 0.278 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.032 Order of pole (three term test) = 4.396e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6239 2.101 h = 0.001 0.003 y[1] (numeric) = 0.0721422879473 0.061386435077 y[1] (closed_form) = 0.0723554013887 0.0615423387499 absolute error = 0.0002641 relative error = 0.278 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.192 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.901 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6229 2.104 h = 0.0001 0.004 y[1] (numeric) = 0.0717332515722 0.0613472361382 y[1] (closed_form) = 0.0719470998162 0.0615029970216 absolute error = 0.0002646 relative error = 0.2795 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.194 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.776 Order of pole (three term test) = 7.697e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6228 2.108 h = 0.003 0.006 y[1] (numeric) = 0.0712566791921 0.0611479238903 y[1] (closed_form) = 0.0714709483582 0.0613041560292 absolute error = 0.0002652 relative error = 0.2816 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.198 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.685 Order of pole (three term test) = 1.252e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6198 2.114 h = 0.0001 0.005 y[1] (numeric) = 0.0703982777086 0.0611829914483 y[1] (closed_form) = 0.0706133026591 0.06133658456 absolute error = 0.0002642 relative error = 0.2825 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.203 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.642 Order of pole (three term test) = 4.662e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6197 2.119 h = 0.0001 0.003 y[1] (numeric) = 0.0698177366144 0.0609278010317 y[1] (closed_form) = 0.0700319774613 0.0610829709674 absolute error = 0.0002645 relative error = 0.2847 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.208 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.325 Order of pole (three term test) = 1.357e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6196 2.122 h = 0.001 0.001 y[1] (numeric) = 0.0694702393578 0.0607805664722 y[1] (closed_form) = 0.0696838020554 0.0609356568823 absolute error = 0.0002639 relative error = 0.2851 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.211 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.042 Order of pole (three term test) = 9.427e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6186 2.123 h = 0.0001 0.004 y[1] (numeric) = 0.0693037875024 0.0608413486172 y[1] (closed_form) = 0.069517006385 0.0609965125109 absolute error = 0.0002637 relative error = 0.2851 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.211 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.256 Order of pole (three term test) = 1.630e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6185 2.127 h = 0.003 0.006 y[1] (numeric) = 0.0688442046493 0.0606400664709 y[1] (closed_form) = 0.0690587168801 0.060795810199 absolute error = 0.0002651 relative error = 0.2881 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.215 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.714 Order of pole (three term test) = 1.251e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1794.5MB, alloc=44.3MB, time=22.82 x[1] = -0.6155 2.133 h = 0.0001 0.005 y[1] (numeric) = 0.0680114095663 0.0606597946531 y[1] (closed_form) = 0.0682267031711 0.0608130152737 absolute error = 0.0002642 relative error = 0.2891 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.655 Order of pole (three term test) = 1.989e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6154 2.138 h = 0.0001 0.003 y[1] (numeric) = 0.0674527735871 0.0604028042555 y[1] (closed_form) = 0.0676672806048 0.0605575257652 absolute error = 0.0002645 relative error = 0.2913 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.225 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.335 Order of pole (three term test) = 3.666e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6153 2.141 h = 0.001 0.001 y[1] (numeric) = 0.0671182700014 0.060254326288 y[1] (closed_form) = 0.0673321262061 0.0604089574388 absolute error = 0.0002639 relative error = 0.2917 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.228 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 1.705e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6143 2.142 h = 0.001 0.003 y[1] (numeric) = 0.0669558779839 0.0603105240268 y[1] (closed_form) = 0.0671694019048 0.0604652188648 absolute error = 0.0002637 relative error = 0.2918 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.228 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.983 Order of pole (three term test) = 4.247e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6133 2.145 h = 0.0001 0.004 y[1] (numeric) = 0.0665747496828 0.0602595379574 y[1] (closed_form) = 0.0667889553245 0.0604141331398 absolute error = 0.0002642 relative error = 0.2933 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.231 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.823 Order of pole (three term test) = 8.773e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6132 2.149 h = 0.003 0.006 y[1] (numeric) = 0.0661360195805 0.0600564984982 y[1] (closed_form) = 0.0663505920359 0.0602115450591 absolute error = 0.0002647 relative error = 0.2955 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.235 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.747 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6102 2.155 h = 0.0001 0.005 y[1] (numeric) = 0.0653319245905 0.0600593990536 y[1] (closed_form) = 0.0655473049084 0.0602120510298 absolute error = 0.000264 relative error = 0.2966 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.24 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.67 Order of pole (three term test) = 1.345e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6101 2.16 h = 0.0001 0.003 y[1] (numeric) = 0.0647977220782 0.0598006280172 y[1] (closed_form) = 0.0650123142261 0.0599546969082 absolute error = 0.0002642 relative error = 0.2987 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.245 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.347 Order of pole (three term test) = 4.862e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.61 2.163 h = 0.001 0.001 y[1] (numeric) = 0.0644777149489 0.0596508971835 y[1] (closed_form) = 0.0646916866683 0.0598048641565 absolute error = 0.0002636 relative error = 0.2992 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.247 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.059 Order of pole (three term test) = 4.432e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.609 2.164 h = 0.001 0.003 y[1] (numeric) = 0.0643198952704 0.0597020261083 y[1] (closed_form) = 0.0645335476027 0.0598560461137 absolute error = 0.0002634 relative error = 0.2992 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.248 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.027 Order of pole (three term test) = 2.377e-31 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.608 2.167 h = 0.0001 0.004 y[1] (numeric) = 0.0639530103079 0.0596455141884 y[1] (closed_form) = 0.0641673171594 0.0597994550294 absolute error = 0.0002639 relative error = 0.3008 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.251 Order of pole (given) = 4 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) = 8.945e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6079 2.171 h = 0.003 0.006 y[1] (numeric) = 0.0635334122139 0.0594411573371 y[1] (closed_form) = 0.0637480593158 0.0595955386787 absolute error = 0.0002644 relative error = 0.303 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.255 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.78 Order of pole (three term test) = 4.400e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6049 2.177 h = 0.0001 0.005 y[1] (numeric) = 0.0627571726422 0.0594286435771 y[1] (closed_form) = 0.0629726490866 0.0595807529352 absolute error = 0.0002638 relative error = 0.3042 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.259 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.684 Order of pole (three term test) = 8.736e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6048 2.182 h = 0.0001 0.003 y[1] (numeric) = 0.0622463865923 0.0591687464624 y[1] (closed_form) = 0.0624610757259 0.0593221930695 absolute error = 0.0002639 relative error = 0.3063 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.264 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.359 Order of pole (three term test) = 6.435e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1840.7MB, alloc=44.3MB, time=23.42 x[1] = -0.6047 2.185 h = 0.001 0.001 y[1] (numeric) = 0.0619402784141 0.0590181588518 y[1] (closed_form) = 0.0621543762557 0.059171493432 absolute error = 0.0002633 relative error = 0.3069 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.267 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.068 Order of pole (three term test) = 6.032e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6037 2.186 h = 0.001 0.003 y[1] (numeric) = 0.061786952819 0.0590645457622 y[1] (closed_form) = 0.0620007438014 0.0592179236327 absolute error = 0.0002631 relative error = 0.3069 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.268 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.071 Order of pole (three term test) = 9.933e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6027 2.189 h = 0.0001 0.004 y[1] (numeric) = 0.0614338252357 0.0590030821315 y[1] (closed_form) = 0.0616482443696 0.0591563995078 absolute error = 0.0002636 relative error = 0.3085 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.27 Order of pole (given) = 4 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) = 1.585e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6026 2.193 h = 0.003 0.006 y[1] (numeric) = 0.0610325635462 0.0587979135728 y[1] (closed_form) = 0.0612472980431 0.0589516603929 absolute error = 0.0002641 relative error = 0.3107 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.274 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.813 Order of pole (three term test) = 1.455e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5996 2.199 h = 0.0001 0.005 y[1] (numeric) = 0.0602833387529 0.0587713019559 y[1] (closed_form) = 0.0604989195575 0.0589228936665 absolute error = 0.0002635 relative error = 0.3121 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.279 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.699 Order of pole (three term test) = 7.305e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5995 2.204 h = 0.0001 0.003 y[1] (numeric) = 0.0597949864961 0.0585108711411 y[1] (closed_form) = 0.0600097830054 0.0586637245627 absolute error = 0.0002636 relative error = 0.3141 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.284 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.371 Order of pole (three term test) = 3.158e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5994 2.207 h = 0.001 0.001 y[1] (numeric) = 0.0595021995721 0.0583597857872 y[1] (closed_form) = 0.0597164327061 0.0585125183965 absolute error = 0.0002631 relative error = 0.3147 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.287 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.077 Order of pole (three term test) = 8.663e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5984 2.208 h = 0.001 0.003 y[1] (numeric) = 0.0593532847608 0.0584017384607 y[1] (closed_form) = 0.0595672231879 0.0585545054637 absolute error = 0.0002629 relative error = 0.3147 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.288 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.115 Order of pole (three term test) = 5.468e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5974 2.211 h = 0.0001 0.004 y[1] (numeric) = 0.0590134377297 0.0583358541569 y[1] (closed_form) = 0.0592279787827 0.0584885776512 absolute error = 0.0002633 relative error = 0.3164 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.29 Order of pole (given) = 4 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) = 1.693e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5973 2.215 h = 0.003 0.006 y[1] (numeric) = 0.0586297438441 0.0581303315094 y[1] (closed_form) = 0.0588445769537 0.0582834732762 absolute error = 0.0002638 relative error = 0.3185 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.294 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.846 Order of pole (three term test) = 1.153e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5943 2.221 h = 0.0001 0.005 y[1] (numeric) = 0.0579067001002 0.0580908475833 y[1] (closed_form) = 0.0581223924202 0.0582419455856 absolute error = 0.0002634 relative error = 0.3201 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.299 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.714 Order of pole (three term test) = 1.364e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5942 2.226 h = 0.0001 0.003 y[1] (numeric) = 0.0574398332309 0.0578304180882 y[1] (closed_form) = 0.0576547461681 0.0579827062135 absolute error = 0.0002634 relative error = 0.3221 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.304 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.383 Order of pole (three term test) = 1.042e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5941 2.229 h = 0.001 0.001 y[1] (numeric) = 0.0571598096699 0.0576791598182 y[1] (closed_form) = 0.0573741859595 0.0578313195515 absolute error = 0.0002629 relative error = 0.3227 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.307 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.087 Order of pole (three term test) = 1.192e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5931 2.23 h = 0.0001 0.004 y[1] (numeric) = 0.0570152182064 0.0577169679862 y[1] (closed_form) = 0.0572293115614 0.0578691540002 absolute error = 0.0002627 relative error = 0.3227 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.308 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.529 Order of pole (three term test) = 9.009e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.593 2.234 h = 0.003 0.006 y[1] (numeric) = 0.056645339099 0.0575114904991 y[1] (closed_form) = 0.056860415484 0.0576642647294 absolute error = 0.0002638 relative error = 0.3258 % Correct digits = 2 memory used=1887.2MB, alloc=44.3MB, time=24.00 Radius of convergence (given) for eq 1 = 2.311 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.875 Order of pole (three term test) = 1.092e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.59 2.24 h = 0.0001 0.005 y[1] (numeric) = 0.0559443056533 0.0574621411831 y[1] (closed_form) = 0.056160248179 0.057612963313 absolute error = 0.0002634 relative error = 0.3274 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.316 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.727 Order of pole (three term test) = 8.661e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5899 2.245 h = 0.0001 0.003 y[1] (numeric) = 0.0554951915114 0.0572023419695 y[1] (closed_form) = 0.0557103610134 0.0573542957157 absolute error = 0.0002634 relative error = 0.3294 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.321 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.393 Order of pole (three term test) = 3.969e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5898 2.248 h = 0.001 0.001 y[1] (numeric) = 0.0552257199093 0.0570513141743 y[1] (closed_form) = 0.0554403749159 0.0572031341863 absolute error = 0.0002629 relative error = 0.33 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.324 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.095 Order of pole (three term test) = 7.784e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5888 2.249 h = 0.001 0.003 y[1] (numeric) = 0.0550848222547 0.0570858238368 y[1] (closed_form) = 0.055299204239 0.0572376638631 absolute error = 0.0002627 relative error = 0.3301 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.325 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.198 Order of pole (three term test) = 6.602e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5878 2.252 h = 0.0001 0.004 y[1] (numeric) = 0.0547684922918 0.0570131365308 y[1] (closed_form) = 0.0549834314924 0.0571649603184 absolute error = 0.0002632 relative error = 0.3318 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.327 Order of pole (given) = 4 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) = 1.002e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5877 2.256 h = 0.003 0.006 y[1] (numeric) = 0.0544155277105 0.0568082125858 y[1] (closed_form) = 0.0546307196347 0.056960433505 absolute error = 0.0002636 relative error = 0.334 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.331 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.908 Order of pole (three term test) = 7.494e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5847 2.262 h = 0.0001 0.005 y[1] (numeric) = 0.0537391382037 0.0567480389301 y[1] (closed_form) = 0.0539552027493 0.0568984093057 absolute error = 0.0002632 relative error = 0.3357 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.336 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.742 Order of pole (three term test) = 5.097e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5846 2.267 h = 0.0001 0.003 y[1] (numeric) = 0.0533098299936 0.0564890887365 y[1] (closed_form) = 0.053525129305 0.0566405260422 absolute error = 0.0002632 relative error = 0.3378 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.341 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.405 Order of pole (three term test) = 8.871e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5845 2.27 h = 0.001 0.001 y[1] (numeric) = 0.0530521329109 0.0563384042737 y[1] (closed_form) = 0.05326694232 0.0564897022138 absolute error = 0.0002627 relative error = 0.3384 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.344 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.104 Order of pole (three term test) = 1.740e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5835 2.271 h = 0.001 0.003 y[1] (numeric) = 0.052915384623 0.0563692626042 y[1] (closed_form) = 0.0531299320638 0.056520573747 absolute error = 0.0002625 relative error = 0.3384 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.345 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.243 Order of pole (three term test) = 9.630e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5825 2.274 h = 0.0001 0.004 y[1] (numeric) = 0.0526110234543 0.0562934555096 y[1] (closed_form) = 0.0528261050113 0.0564447632617 absolute error = 0.000263 relative error = 0.3402 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.347 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.97 Order of pole (three term test) = 1.279e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5824 2.278 h = 0.003 0.006 y[1] (numeric) = 0.0522735718708 0.0560892453925 y[1] (closed_form) = 0.0524888868816 0.0562409390813 absolute error = 0.0002634 relative error = 0.3424 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.351 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.942 Order of pole (three term test) = 8.443e-31 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5794 2.284 h = 0.0001 0.005 y[1] (numeric) = 0.0516210255973 0.0560192431822 y[1] (closed_form) = 0.0518372167405 0.0561691829372 absolute error = 0.0002631 relative error = 0.3442 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.356 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.757 Order of pole (three term test) = 7.807e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5793 2.289 h = 0.0001 0.003 y[1] (numeric) = 0.0512106716597 0.0557615370925 y[1] (closed_form) = 0.0514261066402 0.0559124825471 absolute error = 0.0002631 relative error = 0.3463 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.361 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.417 Order of pole (three term test) = 7.223e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1933.5MB, alloc=44.3MB, time=24.60 x[1] = -0.5792 2.292 h = 0.001 0.001 y[1] (numeric) = 0.0509642473084 0.0556114372026 y[1] (closed_form) = 0.0511792158899 0.0557622385783 absolute error = 0.0002626 relative error = 0.3469 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.364 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.114 Order of pole (three term test) = 7.080e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5782 2.293 h = 0.001 0.003 y[1] (numeric) = 0.0508315534804 0.0556388873715 y[1] (closed_form) = 0.0510462707686 0.0557896957654 absolute error = 0.0002624 relative error = 0.347 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.365 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.288 Order of pole (three term test) = 6.320e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5772 2.296 h = 0.0001 0.004 y[1] (numeric) = 0.0505387263176 0.0555603507225 y[1] (closed_form) = 0.0507539554505 0.0557111673338 absolute error = 0.0002628 relative error = 0.3487 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.367 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.996 Order of pole (three term test) = 3.352e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5771 2.3 h = 0.003 0.006 y[1] (numeric) = 0.0502161219003 0.0553571595385 y[1] (closed_form) = 0.050431566471 0.0555083509579 absolute error = 0.0002632 relative error = 0.351 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.371 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.976 Order of pole (three term test) = 1.772e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5741 2.306 h = 0.0001 0.005 y[1] (numeric) = 0.0495866326288 0.0552782538438 y[1] (closed_form) = 0.049802954194 0.0554277831924 absolute error = 0.000263 relative error = 0.3529 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.376 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.772 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.574 2.311 h = 0.0001 0.003 y[1] (numeric) = 0.0491944138923 0.0550221452617 y[1] (closed_form) = 0.0494099894712 0.0551726223715 absolute error = 0.0002629 relative error = 0.355 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.381 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.429 Order of pole (three term test) = 2.994e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5739 2.314 h = 0.001 0.001 y[1] (numeric) = 0.0489587794284 0.0548728462496 y[1] (closed_form) = 0.0491739110582 0.0550231753996 absolute error = 0.0002625 relative error = 0.3557 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.384 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.123 Order of pole (three term test) = 6.560e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5729 2.315 h = 0.001 0.003 y[1] (numeric) = 0.0488300436799 0.0548971168311 y[1] (closed_form) = 0.0490449343155 0.0550474473941 absolute error = 0.0002623 relative error = 0.3557 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.385 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.333 Order of pole (three term test) = 4.141e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5719 2.318 h = 0.0001 0.004 y[1] (numeric) = 0.048548327524 0.0548162102131 y[1] (closed_form) = 0.0487637085501 0.0549665594581 absolute error = 0.0002627 relative error = 0.3575 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.388 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.021 Order of pole (three term test) = 1.103e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5718 2.322 h = 0.003 0.006 y[1] (numeric) = 0.0482399299591 0.0546143108422 y[1] (closed_form) = 0.0484555095858 0.0547650238662 absolute error = 0.000263 relative error = 0.3597 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.391 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.009 Order of pole (three term test) = 2.901e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5688 2.328 h = 0.0001 0.005 y[1] (numeric) = 0.0476327271865 0.0545273605655 y[1] (closed_form) = 0.0478491823145 0.0546764988328 absolute error = 0.0002629 relative error = 0.3618 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.396 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.787 Order of pole (three term test) = 3.218e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5687 2.333 h = 0.0001 0.003 y[1] (numeric) = 0.0472578564999 0.0542731645986 y[1] (closed_form) = 0.0474735767623 0.0544231958224 absolute error = 0.0002628 relative error = 0.3638 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.401 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.441 Order of pole (three term test) = 8.760e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5686 2.336 h = 0.001 0.001 y[1] (numeric) = 0.0470325476565 0.0541248598385 y[1] (closed_form) = 0.0472478454031 0.0542747399748 absolute error = 0.0002623 relative error = 0.3646 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.404 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.133 Order of pole (three term test) = 3.838e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5676 2.337 h = 0.0001 0.004 y[1] (numeric) = 0.0469076726472 0.0541461656144 y[1] (closed_form) = 0.047122739328 0.0542960420936 absolute error = 0.0002621 relative error = 0.3646 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.405 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.804 Order of pole (three term test) = 3.383e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1979.8MB, alloc=44.3MB, time=25.19 x[1] = -0.5675 2.341 h = 0.003 0.006 y[1] (numeric) = 0.0466104329578 0.0539455255539 y[1] (closed_form) = 0.0468262427553 0.0540959640336 absolute error = 0.0002631 relative error = 0.3677 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.409 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.038 Order of pole (three term test) = 3.660e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5645 2.347 h = 0.0001 0.005 y[1] (numeric) = 0.0460218924797 0.0538525444986 y[1] (closed_form) = 0.0462385738418 0.0540014798333 absolute error = 0.0002629 relative error = 0.3698 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.414 Order of pole (given) = 4 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) = 1.478e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5644 2.352 h = 0.0001 0.003 y[1] (numeric) = 0.0456613206778 0.0536004147236 y[1] (closed_form) = 0.0458772779971 0.0537501983778 absolute error = 0.0002628 relative error = 0.3719 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.419 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.452 Order of pole (three term test) = 2.964e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5643 2.355 h = 0.001 0.001 y[1] (numeric) = 0.045444527308 0.0534532203065 y[1] (closed_form) = 0.045660079801 0.0536028509686 absolute error = 0.0002624 relative error = 0.3726 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.422 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.141 Order of pole (three term test) = 9.676e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5633 2.356 h = 0.001 0.003 y[1] (numeric) = 0.0453229292266 0.0534721805055 y[1] (closed_form) = 0.04553825896 0.0536218036553 absolute error = 0.0002622 relative error = 0.3727 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.422 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.417 Order of pole (three term test) = 1.366e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5623 2.359 h = 0.0001 0.004 y[1] (numeric) = 0.0450608228585 0.0533878457716 y[1] (closed_form) = 0.0452766050893 0.0535375041024 absolute error = 0.0002626 relative error = 0.3745 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.425 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.068 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5622 2.363 h = 0.003 0.006 y[1] (numeric) = 0.0447772201137 0.0531891291966 y[1] (closed_form) = 0.0449931726398 0.0533391309722 absolute error = 0.0002629 relative error = 0.3768 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.429 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.072 Order of pole (three term test) = 7.556e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5592 2.369 h = 0.0001 0.005 y[1] (numeric) = 0.0442095690441 0.0530895314827 y[1] (closed_form) = 0.0444263880006 0.053238109456 absolute error = 0.0002628 relative error = 0.3791 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.434 Order of pole (given) = 4 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) = 1.902e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5591 2.374 h = 0.0001 0.003 y[1] (numeric) = 0.0438649601627 0.0528398008039 y[1] (closed_form) = 0.0440810675481 0.0529891777262 absolute error = 0.0002627 relative error = 0.3811 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.439 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.464 Order of pole (three term test) = 6.444e-31 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.559 2.377 h = 0.001 0.001 y[1] (numeric) = 0.0436576747967 0.0526939006751 y[1] (closed_form) = 0.0438733969883 0.0528431226801 absolute error = 0.0002623 relative error = 0.3819 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.442 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.15 Order of pole (three term test) = 6.310e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.558 2.378 h = 0.001 0.003 y[1] (numeric) = 0.0435397530809 0.0527102604545 y[1] (closed_form) = 0.0437552617626 0.0528594707603 absolute error = 0.0002621 relative error = 0.382 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.443 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.462 Order of pole (three term test) = 9.081e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.557 2.381 h = 0.0001 0.004 y[1] (numeric) = 0.0432876110682 0.0526244290943 y[1] (closed_form) = 0.0435035530568 0.052773682259 absolute error = 0.0002625 relative error = 0.3838 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.445 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.094 Order of pole (three term test) = 6.675e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5569 2.385 h = 0.003 0.006 y[1] (numeric) = 0.0430165171214 0.0524276229769 y[1] (closed_form) = 0.0432326155592 0.0525772089961 absolute error = 0.0002628 relative error = 0.3861 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.449 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.106 Order of pole (three term test) = 6.964e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5539 2.391 h = 0.0001 0.005 y[1] (numeric) = 0.0424690355195 0.0523221012764 y[1] (closed_form) = 0.0426859935985 0.0524703388345 absolute error = 0.0002628 relative error = 0.3885 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.454 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.83 Order of pole (three term test) = 1.654e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2026.1MB, alloc=44.3MB, time=25.78 x[1] = -0.5538 2.396 h = 0.0001 0.003 y[1] (numeric) = 0.0421396898226 0.052074992149 y[1] (closed_form) = 0.0423559493726 0.0522239819933 absolute error = 0.0002626 relative error = 0.3906 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.459 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.476 Order of pole (three term test) = 7.385e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5537 2.399 h = 0.001 0.001 y[1] (numeric) = 0.0419414991756 0.051930524102 y[1] (closed_form) = 0.0421573922533 0.0520793576659 absolute error = 0.0002622 relative error = 0.3914 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.462 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.16 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5527 2.4 h = 0.001 0.003 y[1] (numeric) = 0.041827156197 0.0519444629084 y[1] (closed_form) = 0.042042844664 0.0520932810104 absolute error = 0.000262 relative error = 0.3914 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.463 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.507 Order of pole (three term test) = 1.174e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5517 2.403 h = 0.0001 0.004 y[1] (numeric) = 0.0415846026282 0.0518573950969 y[1] (closed_form) = 0.0418007059637 0.052006262905 absolute error = 0.0002624 relative error = 0.3933 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.466 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.12 Order of pole (three term test) = 1.267e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5516 2.407 h = 0.003 0.006 y[1] (numeric) = 0.0413254704987 0.0516626710593 y[1] (closed_form) = 0.041541717362 0.0518118613187 absolute error = 0.0002627 relative error = 0.3956 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.469 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.14 Order of pole (three term test) = 5.731e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5486 2.413 h = 0.0001 0.005 y[1] (numeric) = 0.0407974569828 0.0515518671034 y[1] (closed_form) = 0.0410145552473 0.0516997804224 absolute error = 0.0002627 relative error = 0.3981 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.475 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.845 Order of pole (three term test) = 1.604e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5485 2.418 h = 0.0001 0.003 y[1] (numeric) = 0.0404827035263 0.0513075745735 y[1] (closed_form) = 0.0406991167677 0.051456196086 absolute error = 0.0002625 relative error = 0.4002 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.479 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.488 Order of pole (three term test) = 1.091e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5484 2.421 h = 0.001 0.001 y[1] (numeric) = 0.0402932111334 0.05116465993 y[1] (closed_form) = 0.0405092757495 0.0513131243043 absolute error = 0.0002622 relative error = 0.401 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.482 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.17 Order of pole (three term test) = 1.068e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5474 2.422 h = 0.001 0.003 y[1] (numeric) = 0.040182349764 0.0511763461902 y[1] (closed_form) = 0.0403982183257 0.0513247917306 absolute error = 0.000262 relative error = 0.4011 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.483 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.552 Order of pole (three term test) = 1.537e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5464 2.425 h = 0.0001 0.004 y[1] (numeric) = 0.0399490208453 0.0510882805916 y[1] (closed_form) = 0.0401652865694 0.0512367819227 absolute error = 0.0002623 relative error = 0.403 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.486 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.145 Order of pole (three term test) = 5.646e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5463 2.429 h = 0.003 0.006 y[1] (numeric) = 0.0397013260522 0.0508957890564 y[1] (closed_form) = 0.0399177232504 0.0510446026368 absolute error = 0.0002626 relative error = 0.4053 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.49 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.174 Order of pole (three term test) = 1.177e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5433 2.435 h = 0.0001 0.005 y[1] (numeric) = 0.039192098146 0.0507802970228 y[1] (closed_form) = 0.0394093372399 0.050927901539 absolute error = 0.0002626 relative error = 0.4079 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.495 Order of pole (given) = 4 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) = 5.891e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5432 2.44 h = 0.0001 0.003 y[1] (numeric) = 0.0388912938983 0.0505389910575 y[1] (closed_form) = 0.0391078618436 0.0506872621127 absolute error = 0.0002625 relative error = 0.41 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 7.083e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5431 2.443 h = 0.001 0.001 y[1] (numeric) = 0.0387101196145 0.050397736052 y[1] (closed_form) = 0.0389263559421 0.0505458495645 absolute error = 0.0002621 relative error = 0.4108 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.503 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.179 Order of pole (three term test) = 1.402e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5421 2.444 h = 0.0001 0.004 y[1] (numeric) = 0.0386026434971 0.0504073278073 y[1] (closed_form) = 0.0388186919927 0.0505554194734 absolute error = 0.0002619 relative error = 0.4109 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.503 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.083 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2072.5MB, alloc=44.3MB, time=26.38 x[1] = -0.542 2.448 h = 0.003 0.006 y[1] (numeric) = 0.0383639242196 0.0502167769935 y[1] (closed_form) = 0.038580531954 0.0503653868514 absolute error = 0.0002627 relative error = 0.414 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.507 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.204 Order of pole (three term test) = 1.475e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.539 2.454 h = 0.0001 0.005 y[1] (numeric) = 0.0378703814666 0.0500979045262 y[1] (closed_form) = 0.0380878212776 0.0502453608264 absolute error = 0.0002627 relative error = 0.4167 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.512 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.873 Order of pole (three term test) = 5.217e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5389 2.459 h = 0.0001 0.003 y[1] (numeric) = 0.0375810520577 0.0498594440843 y[1] (closed_form) = 0.0377978333513 0.0500075330939 absolute error = 0.0002625 relative error = 0.4188 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.517 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.511 Order of pole (three term test) = 1.774e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5388 2.462 h = 0.001 0.001 y[1] (numeric) = 0.0374067241641 0.0497197853524 y[1] (closed_form) = 0.0376231878325 0.0498677169874 absolute error = 0.0002622 relative error = 0.4197 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.52 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.187 Order of pole (three term test) = 1.811e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5378 2.463 h = 0.001 0.003 y[1] (numeric) = 0.0373021081294 0.049727732079 y[1] (closed_form) = 0.0375183908137 0.0498756396331 absolute error = 0.000262 relative error = 0.4198 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.521 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.637 Order of pole (three term test) = 8.828e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5368 2.466 h = 0.0001 0.004 y[1] (numeric) = 0.0370850230205 0.0496384779187 y[1] (closed_form) = 0.0373016717448 0.0497864505742 absolute error = 0.0002624 relative error = 0.4217 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.524 Order of pole (given) = 4 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) = 9.170e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5367 2.47 h = 0.003 0.006 y[1] (numeric) = 0.0368572587373 0.049450598187 y[1] (closed_form) = 0.0370740187479 0.0495988645624 absolute error = 0.0002626 relative error = 0.4241 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.528 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.238 Order of pole (three term test) = 8.545e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5337 2.476 h = 0.0001 0.005 y[1] (numeric) = 0.0363812767693 0.049328019861 y[1] (closed_form) = 0.0365988574703 0.0494751942112 absolute error = 0.0002627 relative error = 0.4268 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.533 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.888 Order of pole (three term test) = 1.351e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5336 2.481 h = 0.0001 0.003 y[1] (numeric) = 0.0361047698412 0.0490927958434 y[1] (closed_form) = 0.0363217063393 0.049240565455 absolute error = 0.0002625 relative error = 0.429 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.538 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.523 Order of pole (three term test) = 8.278e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5335 2.484 h = 0.001 0.001 y[1] (numeric) = 0.0359380934792 0.0489549544938 y[1] (closed_form) = 0.036154727886 0.0491025670373 absolute error = 0.0002621 relative error = 0.4299 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.541 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.197 Order of pole (three term test) = 1.004e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5325 2.485 h = 0.001 0.003 y[1] (numeric) = 0.0358366846091 0.0489610740735 y[1] (closed_form) = 0.0360531456539 0.0491086601135 absolute error = 0.000262 relative error = 0.43 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.541 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.683 Order of pole (three term test) = 3.168e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5315 2.488 h = 0.0001 0.004 y[1] (numeric) = 0.0356278471752 0.0488713956005 y[1] (closed_form) = 0.0358446585404 0.0490190509813 absolute error = 0.0002623 relative error = 0.432 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.544 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.219 Order of pole (three term test) = 1.840e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5314 2.492 h = 0.003 0.006 y[1] (numeric) = 0.035410136731 0.0486860717654 y[1] (closed_form) = 0.0356270495198 0.0488340113072 absolute error = 0.0002626 relative error = 0.4344 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.548 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.272 Order of pole (three term test) = 1.105e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5284 2.498 h = 0.0001 0.005 y[1] (numeric) = 0.0349510884516 0.0485602628467 y[1] (closed_form) = 0.0351688097174 0.0487071687243 absolute error = 0.0002626 relative error = 0.4372 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.553 Order of pole (given) = 4 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) = 8.734e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2118.8MB, alloc=44.3MB, time=26.97 x[1] = -0.5283 2.503 h = 0.0001 0.003 y[1] (numeric) = 0.0346868360819 0.0483283851126 y[1] (closed_form) = 0.0349039276086 0.0484758508934 absolute error = 0.0002624 relative error = 0.4393 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.558 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.535 Order of pole (three term test) = 4.195e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5282 2.506 h = 0.001 0.001 y[1] (numeric) = 0.0345274750894 0.0481924311389 y[1] (closed_form) = 0.0347442793175 0.0483397404864 absolute error = 0.0002621 relative error = 0.4403 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.561 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.207 Order of pole (three term test) = 6.485e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5272 2.507 h = 0.001 0.003 y[1] (numeric) = 0.0344291805153 0.0481968551354 y[1] (closed_form) = 0.0346458186965 0.0483441358395 absolute error = 0.000262 relative error = 0.4404 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.562 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.728 Order of pole (three term test) = 4.093e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5262 2.51 h = 0.0001 0.004 y[1] (numeric) = 0.0342282726599 0.0481069216668 y[1] (closed_form) = 0.0344452460915 0.0482542754048 absolute error = 0.0002623 relative error = 0.4424 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.565 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.245 Order of pole (three term test) = 4.334e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5261 2.514 h = 0.003 0.006 y[1] (numeric) = 0.0340201720361 0.0479242382499 y[1] (closed_form) = 0.034237237704 0.0480718668247 absolute error = 0.0002625 relative error = 0.4448 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.568 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.306 Order of pole (three term test) = 2.854e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5231 2.52 h = 0.0001 0.005 y[1] (numeric) = 0.0335774495119 0.0477956376801 y[1] (closed_form) = 0.0337953107424 0.0479422879335 absolute error = 0.0002626 relative error = 0.4477 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.574 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.919 Order of pole (three term test) = 3.382e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.523 2.525 h = 0.0001 0.003 y[1] (numeric) = 0.0333249081941 0.0475671984465 y[1] (closed_form) = 0.0335421542378 0.047714375224 absolute error = 0.0002624 relative error = 0.4499 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.579 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.548 Order of pole (three term test) = 5.413e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5229 2.528 h = 0.001 0.001 y[1] (numeric) = 0.033172540725 0.047433191182 y[1] (closed_form) = 0.0333895135536 0.0475802124524 absolute error = 0.0002621 relative error = 0.4509 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.582 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.216 Order of pole (three term test) = 1.496e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5219 2.529 h = 0.001 0.003 y[1] (numeric) = 0.0330772690763 0.0474360429296 y[1] (closed_form) = 0.0332940828761 0.0475830336758 absolute error = 0.0002619 relative error = 0.451 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.582 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.774 Order of pole (three term test) = 1.056e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5209 2.532 h = 0.0001 0.004 y[1] (numeric) = 0.032883983996 0.0473460088528 y[1] (closed_form) = 0.0331011186042 0.0474930758262 absolute error = 0.0002623 relative error = 0.453 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.585 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.271 Order of pole (three term test) = 5.588e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5208 2.536 h = 0.003 0.006 y[1] (numeric) = 0.032685068237 0.0471660367239 y[1] (closed_form) = 0.0329022865266 0.0473133694487 absolute error = 0.0002625 relative error = 0.4554 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.589 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.34 Order of pole (three term test) = 1.839e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5178 2.542 h = 0.0001 0.005 y[1] (numeric) = 0.0322580825678 0.0470350495978 y[1] (closed_form) = 0.0324760829189 0.0471814564733 absolute error = 0.0002626 relative error = 0.4585 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.594 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.934 Order of pole (three term test) = 1.460e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5177 2.547 h = 0.0001 0.003 y[1] (numeric) = 0.0320167323189 0.0468101250212 y[1] (closed_form) = 0.0322341320694 0.0469570269148 absolute error = 0.0002624 relative error = 0.4607 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.599 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.56 Order of pole (three term test) = 4.931e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5176 2.55 h = 0.001 0.001 y[1] (numeric) = 0.0318710503283 0.0466781140814 y[1] (closed_form) = 0.0320881902698 0.046824861652 absolute error = 0.0002621 relative error = 0.4617 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.602 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.226 Order of pole (three term test) = 1.077e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2165.2MB, alloc=44.3MB, time=27.57 x[1] = -0.5166 2.551 h = 0.0001 0.004 y[1] (numeric) = 0.0317787118576 0.0466795091719 y[1] (closed_form) = 0.0319956995007 0.0468262245753 absolute error = 0.0002619 relative error = 0.4619 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.603 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.364 Order of pole (three term test) = 1.699e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5165 2.555 h = 0.003 0.006 y[1] (numeric) = 0.0315870004352 0.0465018117957 y[1] (closed_form) = 0.0318044071962 0.0466489943568 absolute error = 0.0002625 relative error = 0.465 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.607 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.37 Order of pole (three term test) = 1.224e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5135 2.561 h = 0.0001 0.005 y[1] (numeric) = 0.0311731257899 0.0463692489216 y[1] (closed_form) = 0.0313913020188 0.0465155484403 absolute error = 0.0002627 relative error = 0.4681 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.612 Order of pole (given) = 4 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) = 1.817e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5134 2.566 h = 0.0001 0.003 y[1] (numeric) = 0.0309409665316 0.0461475247409 y[1] (closed_form) = 0.0311585550526 0.0462942937548 absolute error = 0.0002625 relative error = 0.4703 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.617 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.571 Order of pole (three term test) = 1.226e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5133 2.569 h = 0.001 0.001 y[1] (numeric) = 0.0308007782463 0.0460173400152 y[1] (closed_form) = 0.0310181179606 0.0461639560577 absolute error = 0.0002622 relative error = 0.4714 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.62 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.234 Order of pole (three term test) = 1.340e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5123 2.57 h = 0.001 0.003 y[1] (numeric) = 0.0307109096188 0.0460176017722 y[1] (closed_form) = 0.0309281026215 0.0461641844839 absolute error = 0.000262 relative error = 0.4716 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.621 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.86 Order of pole (three term test) = 8.453e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5113 2.573 h = 0.0001 0.004 y[1] (numeric) = 0.0305310273179 0.045927827467 y[1] (closed_form) = 0.0307485158264 0.0460744910061 absolute error = 0.0002623 relative error = 0.4736 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.623 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.319 Order of pole (three term test) = 5.728e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5112 2.577 h = 0.003 0.006 y[1] (numeric) = 0.0303481000699 0.0457531455982 y[1] (closed_form) = 0.0305656579899 0.0459000585418 absolute error = 0.0002625 relative error = 0.476 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.627 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.405 Order of pole (three term test) = 1.316e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5082 2.583 h = 0.0001 0.005 y[1] (numeric) = 0.0299489124548 0.0456188612169 y[1] (closed_form) = 0.0301672255458 0.0457649386158 absolute error = 0.0002627 relative error = 0.4792 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.633 Order of pole (given) = 4 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) = 3.453e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5081 2.588 h = 0.0001 0.003 y[1] (numeric) = 0.0297270357732 0.045400749989 y[1] (closed_form) = 0.0299447756633 0.0455472685973 absolute error = 0.0002624 relative error = 0.4815 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.637 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.583 Order of pole (three term test) = 1.761e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.508 2.591 h = 0.001 0.001 y[1] (numeric) = 0.0295929944044 0.0452726276709 y[1] (closed_form) = 0.0298104977105 0.0454189948853 absolute error = 0.0002622 relative error = 0.4826 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.64 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.244 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.507 2.592 h = 0.001 0.003 y[1] (numeric) = 0.0295058954349 0.0452716277928 y[1] (closed_form) = 0.0297232582486 0.0454179604205 absolute error = 0.000262 relative error = 0.4827 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.641 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.906 Order of pole (three term test) = 5.427e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.506 2.595 h = 0.0001 0.004 y[1] (numeric) = 0.0293328170152 0.0451821184013 y[1] (closed_form) = 0.0295504625738 0.0453285338518 absolute error = 0.0002623 relative error = 0.4848 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.644 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.345 Order of pole (three term test) = 4.060e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5059 2.599 h = 0.003 0.006 y[1] (numeric) = 0.0291579575901 0.0450102813564 y[1] (closed_form) = 0.0293756655972 0.0451569378264 absolute error = 0.0002625 relative error = 0.4873 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.648 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.439 Order of pole (three term test) = 4.609e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5029 2.605 h = 0.0001 0.005 y[1] (numeric) = 0.0287729216337 0.0448745962592 y[1] (closed_form) = 0.0289913701945 0.0450204622014 absolute error = 0.0002627 relative error = 0.4905 % Correct digits = 2 memory used=2211.4MB, alloc=44.3MB, time=28.16 Radius of convergence (given) for eq 1 = 2.653 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.978 Order of pole (three term test) = 6.115e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5028 2.61 h = 0.0001 0.003 y[1] (numeric) = 0.0285608701561 0.0446601361008 y[1] (closed_form) = 0.0287787599356 0.0448064165642 absolute error = 0.0002624 relative error = 0.4928 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.658 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.595 Order of pole (three term test) = 1.030e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5027 2.613 h = 0.001 0.001 y[1] (numeric) = 0.0284327044396 0.0445341027244 y[1] (closed_form) = 0.0286503692648 0.0446802335489 absolute error = 0.0002622 relative error = 0.4939 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.661 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.254 Order of pole (three term test) = 9.863e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5017 2.614 h = 0.001 0.003 y[1] (numeric) = 0.028348290605 0.0445319371328 y[1] (closed_form) = 0.0285658208973 0.0446780322995 absolute error = 0.000262 relative error = 0.4941 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.662 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.952 Order of pole (three term test) = 1.872e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5007 2.617 h = 0.0001 0.004 y[1] (numeric) = 0.0281817505862 0.0444427991852 y[1] (closed_form) = 0.028399551407 0.044588978818 absolute error = 0.0002623 relative error = 0.4962 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.664 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.371 Order of pole (three term test) = 3.680e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5006 2.621 h = 0.003 0.006 y[1] (numeric) = 0.0280146012623 0.0442738359609 y[1] (closed_form) = 0.0282324580585 0.0444202484708 absolute error = 0.0002625 relative error = 0.4987 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.668 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.474 Order of pole (three term test) = 4.839e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4976 2.627 h = 0.0001 0.005 y[1] (numeric) = 0.027643199596 0.0441370452513 y[1] (closed_form) = 0.0278617820835 0.0442827098943 absolute error = 0.0002627 relative error = 0.5021 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.674 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.993 Order of pole (three term test) = 1.151e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4975 2.632 h = 0.0001 0.003 y[1] (numeric) = 0.0274405361389 0.04392626323 y[1] (closed_form) = 0.0276585741449 0.0440723172159 absolute error = 0.0002624 relative error = 0.5044 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.679 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.608 Order of pole (three term test) = 1.350e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4974 2.635 h = 0.001 0.001 y[1] (numeric) = 0.027317986683 0.0438023386053 y[1] (closed_form) = 0.0275358107984 0.0439482448618 absolute error = 0.0002622 relative error = 0.5055 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.682 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.263 Order of pole (three term test) = 2.525e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4964 2.636 h = 0.001 0.003 y[1] (numeric) = 0.027236175379 0.0437990971208 y[1] (closed_form) = 0.0274538706709 0.0439449668173 absolute error = 0.000262 relative error = 0.5057 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.682 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.998 Order of pole (three term test) = 1.782e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4954 2.639 h = 0.0001 0.004 y[1] (numeric) = 0.0270759182645 0.0437104268939 y[1] (closed_form) = 0.0272938723924 0.0438563823794 absolute error = 0.0002623 relative error = 0.5078 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.685 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.397 Order of pole (three term test) = 1.053e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4953 2.643 h = 0.003 0.006 y[1] (numeric) = 0.0269161370783 0.0435443579324 y[1] (closed_form) = 0.0271341411666 0.0436905383933 absolute error = 0.0002625 relative error = 0.5104 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.689 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.508 Order of pole (three term test) = 6.191e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4923 2.649 h = 0.0001 0.005 y[1] (numeric) = 0.0265578699821 0.0434067328168 y[1] (closed_form) = 0.0267765847224 0.0435522058351 absolute error = 0.0002627 relative error = 0.5138 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.694 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.009 Order of pole (three term test) = 9.874e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4922 2.654 h = 0.0001 0.003 y[1] (numeric) = 0.0263641767367 0.0431996460098 y[1] (closed_form) = 0.0265823611465 0.0433454846202 absolute error = 0.0002624 relative error = 0.5161 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.699 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 3.307e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4921 2.657 h = 0.001 0.001 y[1] (numeric) = 0.0262469955493 0.0430778438567 y[1] (closed_form) = 0.0264649765928 0.0432235367801 absolute error = 0.0002622 relative error = 0.5173 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.702 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.273 Order of pole (three term test) = 1.614e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2257.7MB, alloc=44.3MB, time=28.76 x[1] = -0.4911 2.658 h = 0.0001 0.004 y[1] (numeric) = 0.0261677061305 0.0430736105672 y[1] (closed_form) = 0.0263855638191 0.0432192661825 absolute error = 0.0002621 relative error = 0.5175 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.703 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.648 Order of pole (three term test) = 4.267e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.491 2.662 h = 0.003 0.006 y[1] (numeric) = 0.0260137027254 0.0429099291578 y[1] (closed_form) = 0.0262318731605 0.0430559997558 absolute error = 0.0002626 relative error = 0.5208 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.707 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.538 Order of pole (three term test) = 1.083e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.488 2.668 h = 0.0001 0.005 y[1] (numeric) = 0.0256663604187 0.0427719346564 y[1] (closed_form) = 0.025885228018 0.0429173307226 absolute error = 0.0002628 relative error = 0.5243 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.712 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.022 Order of pole (three term test) = 1.350e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4879 2.673 h = 0.0001 0.003 y[1] (numeric) = 0.0254800239435 0.0425681357583 y[1] (closed_form) = 0.025698373516 0.0427138782213 absolute error = 0.0002625 relative error = 0.5266 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.717 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.631 Order of pole (three term test) = 2.061e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4878 2.676 h = 0.001 0.001 y[1] (numeric) = 0.0253672479579 0.0424482274551 y[1] (closed_form) = 0.0255854027844 0.0425938261982 absolute error = 0.0002623 relative error = 0.5279 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.72 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.282 Order of pole (three term test) = 2.082e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4868 2.677 h = 0.001 0.003 y[1] (numeric) = 0.0252900767836 0.0424432324377 y[1] (closed_form) = 0.0255081127832 0.0425887934031 absolute error = 0.0002622 relative error = 0.5281 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.721 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.084 Order of pole (three term test) = 6.040e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4858 2.68 h = 0.0001 0.004 y[1] (numeric) = 0.0251408558075 0.0423557249526 y[1] (closed_form) = 0.0253591302033 0.0425013732877 absolute error = 0.0002624 relative error = 0.5302 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.724 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.446 Order of pole (three term test) = 1.052e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4857 2.684 h = 0.003 0.006 y[1] (numeric) = 0.0249938914895 0.0421951488545 y[1] (closed_form) = 0.0252122058588 0.0423410080355 absolute error = 0.0002626 relative error = 0.5328 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.728 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.573 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4827 2.69 h = 0.0001 0.005 y[1] (numeric) = 0.0246587969132 0.0420567611704 y[1] (closed_form) = 0.0248777932583 0.0422019823804 absolute error = 0.0002628 relative error = 0.5364 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.733 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.037 Order of pole (three term test) = 7.698e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4826 2.695 h = 0.0001 0.003 y[1] (numeric) = 0.0244807021031 0.0418566614818 y[1] (closed_form) = 0.0246991942176 0.0420022077855 absolute error = 0.0002625 relative error = 0.5388 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.738 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.643 Order of pole (three term test) = 7.855e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4825 2.698 h = 0.001 0.001 y[1] (numeric) = 0.0243728616824 0.0417388842787 y[1] (closed_form) = 0.0245911686369 0.0418842890969 absolute error = 0.0002623 relative error = 0.54 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.741 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.291 Order of pole (three term test) = 9.164e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4815 2.699 h = 0.001 0.003 y[1] (numeric) = 0.0242980667786 0.0417330389361 y[1] (closed_form) = 0.0245162599494 0.0418784054771 absolute error = 0.0002622 relative error = 0.5403 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.742 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.13 Order of pole (three term test) = 7.172e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4805 2.702 h = 0.0001 0.004 y[1] (numeric) = 0.0241544495133 0.0416462220288 y[1] (closed_form) = 0.0243728707787 0.0417916765037 absolute error = 0.0002624 relative error = 0.5424 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.744 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.472 Order of pole (three term test) = 9.476e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4804 2.706 h = 0.003 0.006 y[1] (numeric) = 0.0240139564867 0.0414885549935 y[1] (closed_form) = 0.02423241286 0.0416342130926 absolute error = 0.0002626 relative error = 0.545 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.748 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.608 Order of pole (three term test) = 1.760e-29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2304.1MB, alloc=44.3MB, time=29.34 x[1] = -0.4774 2.712 h = 0.0001 0.005 y[1] (numeric) = 0.023690658468 0.0413499860297 y[1] (closed_form) = 0.0239097816073 0.041495040794 absolute error = 0.0002628 relative error = 0.5487 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.754 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.053 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4773 2.717 h = 0.0001 0.003 y[1] (numeric) = 0.0235204387191 0.0411535793588 y[1] (closed_form) = 0.023739071214 0.0412989391269 absolute error = 0.0002625 relative error = 0.5512 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.759 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.656 Order of pole (three term test) = 3.317e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4772 2.72 h = 0.001 0.001 y[1] (numeric) = 0.0234173160309 0.041037932734 y[1] (closed_form) = 0.0236357724823 0.0411831533338 absolute error = 0.0002623 relative error = 0.5524 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.762 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.301 Order of pole (three term test) = 1.730e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4762 2.721 h = 0.001 0.003 y[1] (numeric) = 0.0233448225335 0.041031306627 y[1] (closed_form) = 0.0235631700294 0.0411764885682 absolute error = 0.0002622 relative error = 0.5527 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.762 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.177 Order of pole (three term test) = 4.564e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4752 2.724 h = 0.0001 0.004 y[1] (numeric) = 0.023206589368 0.0409452439047 y[1] (closed_form) = 0.0234251551051 0.0410905141235 absolute error = 0.0002624 relative error = 0.5549 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.765 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.499 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4751 2.728 h = 0.003 0.006 y[1] (numeric) = 0.0230722807568 0.0407904806196 y[1] (closed_form) = 0.0232908770893 0.0409359474697 absolute error = 0.0002626 relative error = 0.5575 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.769 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.642 Order of pole (three term test) = 1.705e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4721 2.734 h = 0.0001 0.005 y[1] (numeric) = 0.0227603441905 0.0406519242491 y[1] (closed_form) = 0.0229795921009 0.0407968205758 absolute error = 0.0002628 relative error = 0.5613 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.774 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.068 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.472 2.739 h = 0.0001 0.003 y[1] (numeric) = 0.0225976493268 0.0404591977485 y[1] (closed_form) = 0.0228164199537 0.0406043801349 absolute error = 0.0002626 relative error = 0.5637 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.779 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.668 Order of pole (three term test) = 1.265e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4719 2.742 h = 0.001 0.001 y[1] (numeric) = 0.0224990362238 0.0403456770896 y[1] (closed_form) = 0.0227176394766 0.0404907226931 absolute error = 0.0002623 relative error = 0.5651 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.782 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.311 Order of pole (three term test) = 6.167e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4709 2.743 h = 0.001 0.003 y[1] (numeric) = 0.0224287712793 0.040338335279 y[1] (closed_form) = 0.0226472701982 0.0404833419498 absolute error = 0.0002622 relative error = 0.5653 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.783 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.223 Order of pole (three term test) = 5.829e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4699 2.746 h = 0.0001 0.004 y[1] (numeric) = 0.0222957111552 0.0402530833867 y[1] (closed_form) = 0.0225144188914 0.0403981784794 absolute error = 0.0002625 relative error = 0.5675 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.786 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.525 Order of pole (three term test) = 3.064e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4698 2.75 h = 0.003 0.006 y[1] (numeric) = 0.0221673129068 0.0401012133835 y[1] (closed_form) = 0.0223860470556 0.0402464983396 absolute error = 0.0002626 relative error = 0.5702 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.79 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.677 Order of pole (three term test) = 2.011e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4668 2.756 h = 0.0001 0.005 y[1] (numeric) = 0.021866318319 0.039962846733 y[1] (closed_form) = 0.0220856889183 0.0401075922464 absolute error = 0.0002628 relative error = 0.574 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.795 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.084 Order of pole (three term test) = 3.167e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4667 2.761 h = 0.0001 0.003 y[1] (numeric) = 0.0217108138903 0.0397737816 y[1] (closed_form) = 0.0219297203282 0.0399187953109 absolute error = 0.0002626 relative error = 0.5765 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.681 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4666 2.764 h = 0.001 0.001 y[1] (numeric) = 0.0216165114999 0.0396623786251 y[1] (closed_form) = 0.0218352588076 0.0398072579937 absolute error = 0.0002624 relative error = 0.5779 % Correct digits = 2 memory used=2350.6MB, alloc=44.3MB, time=29.93 Radius of convergence (given) for eq 1 = 2.803 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.321 Order of pole (three term test) = 5.321e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4656 2.765 h = 0.0001 0.004 y[1] (numeric) = 0.0215484042598 0.0396543819471 y[1] (closed_form) = 0.0217670516569 0.0397992222063 absolute error = 0.0002623 relative error = 0.5782 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.804 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.933 Order of pole (three term test) = 1.896e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4655 2.769 h = 0.003 0.006 y[1] (numeric) = 0.0214246401162 0.0395048757802 y[1] (closed_form) = 0.0216435197118 0.0396500810845 absolute error = 0.0002627 relative error = 0.5815 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.808 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.707 Order of pole (three term test) = 5.525e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4625 2.775 h = 0.0001 0.005 y[1] (numeric) = 0.0211327348832 0.0393669261931 y[1] (closed_form) = 0.0213522376384 0.0395116173121 absolute error = 0.0002629 relative error = 0.5854 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.813 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.097 Order of pole (three term test) = 7.012e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4624 2.78 h = 0.0001 0.003 y[1] (numeric) = 0.0209831202176 0.0391810740239 y[1] (closed_form) = 0.0212021701036 0.039326018938 absolute error = 0.0002627 relative error = 0.5879 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.818 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.692 Order of pole (three term test) = 1.470e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4623 2.783 h = 0.001 0.001 y[1] (numeric) = 0.0208923508518 0.0390715330226 y[1] (closed_form) = 0.0211112483488 0.0392163458219 absolute error = 0.0002625 relative error = 0.5893 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.821 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.329 Order of pole (three term test) = 5.765e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4613 2.784 h = 0.001 0.003 y[1] (numeric) = 0.0208260525681 0.0390630429293 y[1] (closed_form) = 0.0210448538101 0.0392078165875 absolute error = 0.0002624 relative error = 0.5896 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.822 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.31 Order of pole (three term test) = 9.435e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4603 2.787 h = 0.0001 0.004 y[1] (numeric) = 0.0207020736547 0.0389794850194 y[1] (closed_form) = 0.0209210672645 0.0391243468017 absolute error = 0.0002626 relative error = 0.5918 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.825 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.574 Order of pole (three term test) = 3.375e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4602 2.791 h = 0.003 0.006 y[1] (numeric) = 0.0205839514988 0.0388330187037 y[1] (closed_form) = 0.0208029646173 0.0389780582979 absolute error = 0.0002627 relative error = 0.5946 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.829 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.742 Order of pole (three term test) = 4.427e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4572 2.797 h = 0.0001 0.005 y[1] (numeric) = 0.020302246098 0.0386955433191 y[1] (closed_form) = 0.0205218674661 0.0388400968258 absolute error = 0.0002629 relative error = 0.5985 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.834 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.113 Order of pole (three term test) = 7.789e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4571 2.802 h = 0.0001 0.003 y[1] (numeric) = 0.0201592394417 0.0385133002663 y[1] (closed_form) = 0.0203784205805 0.0386580915581 absolute error = 0.0002627 relative error = 0.6011 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.839 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.704 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.457 2.805 h = 0.001 0.001 y[1] (numeric) = 0.0200724342559 0.0384058509446 y[1] (closed_form) = 0.0202914705112 0.0385505126296 absolute error = 0.0002625 relative error = 0.6025 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.842 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.339 Order of pole (three term test) = 8.269e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.456 2.806 h = 0.001 0.003 y[1] (numeric) = 0.0200081665161 0.0383968080293 y[1] (closed_form) = 0.0202271105911 0.0385414305515 absolute error = 0.0002624 relative error = 0.6028 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.843 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.357 Order of pole (three term test) = 1.144e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.455 2.809 h = 0.0001 0.004 y[1] (numeric) = 0.0198888010676 0.0383141870567 y[1] (closed_form) = 0.0201079292213 0.0384588973835 absolute error = 0.0002626 relative error = 0.6051 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.846 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.601 Order of pole (three term test) = 9.059e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4549 2.813 h = 0.003 0.006 y[1] (numeric) = 0.0197758715489 0.0381705574742 y[1] (closed_form) = 0.0199950158544 0.0383154394662 absolute error = 0.0002627 relative error = 0.6079 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.85 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.777 Order of pole (three term test) = 3.960e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2397.0MB, alloc=44.3MB, time=30.52 x[1] = -0.4519 2.819 h = 0.0001 0.005 y[1] (numeric) = 0.0195039889323 0.0380336920175 y[1] (closed_form) = 0.019723726723 0.038178114535 absolute error = 0.0002629 relative error = 0.6119 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.855 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.128 Order of pole (three term test) = 1.123e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4518 2.824 h = 0.0001 0.003 y[1] (numeric) = 0.0193672972024 0.0378550257681 y[1] (closed_form) = 0.0195866071402 0.0379996709784 absolute error = 0.0002627 relative error = 0.6145 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.86 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.717 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4517 2.827 h = 0.001 0.001 y[1] (numeric) = 0.0192842817455 0.0377496514668 y[1] (closed_form) = 0.0195034539362 0.0378941696028 absolute error = 0.0002625 relative error = 0.616 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.863 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.349 Order of pole (three term test) = 1.070e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4507 2.828 h = 0.001 0.003 y[1] (numeric) = 0.0192219793908 0.0377401058814 y[1] (closed_form) = 0.0194410633003 0.0378845849059 absolute error = 0.0002624 relative error = 0.6163 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.864 Order of pole (given) = 4 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) = 1.445e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4497 2.831 h = 0.0001 0.004 y[1] (numeric) = 0.0191070467444 0.0376584564628 y[1] (closed_form) = 0.0193263068072 0.0378030228398 absolute error = 0.0002626 relative error = 0.6186 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.866 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.627 Order of pole (three term test) = 1.207e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4496 2.835 h = 0.003 0.006 y[1] (numeric) = 0.0189990803802 0.0375176380655 y[1] (closed_form) = 0.0192183534913 0.0376623701673 absolute error = 0.0002627 relative error = 0.6214 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.87 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.812 Order of pole (three term test) = 5.002e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4466 2.841 h = 0.0001 0.005 y[1] (numeric) = 0.0187366574048 0.0373815057046 y[1] (closed_form) = 0.0189565094057 0.0375258035378 absolute error = 0.000263 relative error = 0.6255 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.876 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.144 Order of pole (three term test) = 3.934e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4465 2.846 h = 0.0001 0.003 y[1] (numeric) = 0.0186060007493 0.0372063801791 y[1] (closed_form) = 0.0188254370047 0.0373508864791 absolute error = 0.0002627 relative error = 0.6282 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.881 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.729 Order of pole (three term test) = 1.878e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4464 2.849 h = 0.001 0.001 y[1] (numeric) = 0.0185266083873 0.0371030618881 y[1] (closed_form) = 0.018745913681 0.0372474436621 absolute error = 0.0002626 relative error = 0.6297 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.884 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.359 Order of pole (three term test) = 1.035e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4454 2.85 h = 0.001 0.003 y[1] (numeric) = 0.0184662081862 0.0370930604774 y[1] (closed_form) = 0.0186854289291 0.0372374032571 absolute error = 0.0002625 relative error = 0.63 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.885 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.45 Order of pole (three term test) = 1.064e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4444 2.853 h = 0.0001 0.004 y[1] (numeric) = 0.0183555348603 0.037012412565 y[1] (closed_form) = 0.0185749241798 0.0371568421263 absolute error = 0.0002627 relative error = 0.6323 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.887 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.653 Order of pole (three term test) = 1.444e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4443 2.857 h = 0.003 0.006 y[1] (numeric) = 0.0182523124985 0.036874376887 y[1] (closed_form) = 0.0184717119992 0.0370189664338 absolute error = 0.0002628 relative error = 0.6351 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.891 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.847 Order of pole (three term test) = 6.310e-31 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4413 2.863 h = 0.0001 0.005 y[1] (numeric) = 0.017998999485 0.0367390891455 y[1] (closed_form) = 0.0182189634688 0.0368832682962 absolute error = 0.000263 relative error = 0.6393 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.897 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.16 Order of pole (three term test) = 7.015e-30 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4412 2.868 h = 0.0001 0.003 y[1] (numeric) = 0.0178741106963 0.0365674649551 y[1] (closed_form) = 0.018093670769 0.0367118391643 absolute error = 0.0002628 relative error = 0.642 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.902 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.742 Order of pole (three term test) = 9.760e-30 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=2443.4MB, alloc=44.3MB, time=31.11 x[1] = -0.4411 2.871 h = 0.001 0.001 y[1] (numeric) = 0.017798182269 0.0364661815891 y[1] (closed_form) = 0.0180176178314 0.0366104338284 absolute error = 0.0002626 relative error = 0.6436 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.905 Order of pole (given) = 4 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.369 Order of pole (three term test) = 1.990e-29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4401 2.872 h = 0.001 0.003 y[1] (numeric) = 0.0177396228871 0.0364557680952 y[1] (closed_form) = 0.0179589774679 0.0365999815166 absolute error = 0.0002625 relative error = 0.6439 % Correct digits = 2 Radius of convergence (given) for eq 1 = 2.906 Order of pole (given) = 4 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) = 6.898e-30 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; Iterations = 754 Total Elapsed Time = 31 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 31 Seconds > quit memory used=2451.4MB, alloc=44.3MB, time=31.21