|\^/| 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(10.0) * (c(0.1) * c(x) + c(0.2)) * arcsin(sqrt ( c(0.1) * c(x) + c(0.2))) + c(5.0) * sqrt( c(0.1) * c(x) + c(0.2)) * sqrt( c(0.8) - c(0.1) * c(x)) - c(5.0) * arcsin(sqrt( c(0.1) * c(x) + c(0.2)))); > end; exact_soln_y := proc(x) return c(10.0)*(c(0.1)*c(x) + c(0.2))*arcsin(sqrt(c(0.1)*c(x) + c(0.2))) + c(5.0)*sqrt(c(0.1)*c(x) + c(0.2))*sqrt(c(0.8) - c(0.1)*c(x)) - c(5.0)*arcsin(sqrt(c(0.1)*c(x) + c(0.2))) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 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0.001 + 0.003*I, 0. + 0.*I]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > ind_var := array_x[1]; > omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > abserr := float_abs(numeric_val - closed_form_val_y); > if (float_abs(closed_form_val_y) > 0.0) then # if number 3 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 4 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > fi;# end if 4; > else > ; > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 3; > if (glob_good_digits < glob_min_good_digits) then # if number 3 > glob_min_good_digits := glob_good_digits; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,4," "); > omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > #BOTTOM DISPLAY ALOT > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ind_var := array_x[1]; omniout_complex(ALWAYS, "x[1] ", 33, ind_var, 20, " "); term_no := 1; numeric_val := array_y[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_complex(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); abserr := float_abs(numeric_val - closed_form_val_y); if 0. < float_abs(closed_form_val_y) then relerr := abserr/float_abs(closed_form_val_y); if 0. < float_abs(c(relerr)) then glob_good_digits := round(-log10(relerr)) else relerr := 0.; glob_good_digits := Digits - 2 end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 4, " "); omniout_float(ALWAYS, "relative error ", 4, relerr*glob__100, 4, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " ") end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > ; > if (true) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; display_poles() end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre arcsin FULL $eq_no = 1 > array_tmp4[1] := arcsin(array_tmp3[1]); > array_tmp4_a1[1] := cos(array_tmp4[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2; > #emit pre arcsin FULL $eq_no = 1 > temp := att(1,array_tmp4_a1,array_tmp4,2); > array_tmp4[2] := (array_tmp3[2] - temp) / array_tmp4_a1[1]; > temp2 := att(1,array_tmp3,array_tmp4,1); > array_tmp4_a1[2] := neg(temp2); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0; > array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre arcsin FULL $eq_no = 1 > temp := att(2,array_tmp4_a1,array_tmp4,2); > array_tmp4[3] := (array_tmp3[3] - temp) / array_tmp4_a1[1]; > temp2 := att(2,array_tmp3,array_tmp4,1); > array_tmp4_a1[3] := neg(temp2); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0; > array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre arcsin FULL $eq_no = 1 > temp := att(3,array_tmp4_a1,array_tmp4,2); > array_tmp4[4] := (array_tmp3[4] - temp) / array_tmp4_a1[1]; > temp2 := att(3,array_tmp3,array_tmp4,1); > array_tmp4_a1[4] := neg(temp2); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0; > array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre arcsin FULL $eq_no = 1 > temp := att(4,array_tmp4_a1,array_tmp4,2); > array_tmp4[5] := (array_tmp3[5] - temp) / array_tmp4_a1[1]; > temp2 := att(4,array_tmp3,array_tmp4,1); > array_tmp4_a1[5] := neg(temp2); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0; > array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2; > #emit arcsin $eq_no = 1 > temp := att(kkk-1,array_tmp4_a1,array_tmp4,2); > array_tmp4[kkk] := (array_tmp3[kkk] - temp) / array_tmp4_a1[1]; > temp2 := att(kkk-1,array_tmp3,array_tmp4,1); > array_tmp4_a1[kkk] := neg(temp2); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; Warning, `temp` is implicitly declared local to procedure `atomall` Warning, `temp2` is implicitly declared local to procedure `atomall` atomall := proc() local kkk, order_d, adj2, adj3, temporary, term, temp, temp2; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4[1] := arcsin(array_tmp3[1]); array_tmp4_a1[1] := cos(array_tmp4[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2); temp := att(1, array_tmp4_a1, array_tmp4, 2); array_tmp4[2] := (array_tmp3[2] - temp)/array_tmp4_a1[1]; temp2 := att(1, array_tmp3, array_tmp4, 1); array_tmp4_a1[2] := neg(temp2); array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[3] := 0; array_tmp3[3] := neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); temp := att(2, array_tmp4_a1, array_tmp4, 2); array_tmp4[3] := (array_tmp3[3] - temp)/array_tmp4_a1[1]; temp2 := att(2, array_tmp3, array_tmp4, 1); array_tmp4_a1[3] := neg(temp2); array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[4] := 0; array_tmp3[4] := neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); temp := att(3, array_tmp4_a1, array_tmp4, 2); array_tmp4[4] := (array_tmp3[4] - temp)/array_tmp4_a1[1]; temp2 := att(3, array_tmp3, array_tmp4, 1); array_tmp4_a1[4] := neg(temp2); array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[5] := 0; array_tmp3[5] := neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); temp := att(4, array_tmp4_a1, array_tmp4, 2); array_tmp4[5] := (array_tmp3[5] - temp)/array_tmp4_a1[1]; temp2 := att(4, array_tmp3, array_tmp4, 1); array_tmp4_a1[5] := neg(temp2); array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp3[kkk] := 0; array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/( array_tmp3[1]*glob__2); temp := att(kkk - 1, array_tmp4_a1, array_tmp4, 2); array_tmp4[kkk] := (array_tmp3[kkk] - temp)/array_tmp4_a1[1]; temp2 := att(kkk - 1, array_tmp3, array_tmp4, 1); array_tmp4_a1[kkk] := neg(temp2); array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_a1, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #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..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > 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..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4_a1:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_tmp5:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..30+ 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..(30) ,(0..30+ 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 <= 30) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) 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 <= 30) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4_a1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <=30) do # do number 1 > term := 1; > while (term <= 30) 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_a1); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_0D1); > array_const_0D1[1] := c(0.1); > zero_ats_ar(array_const_0D2); > array_const_0D2[1] := c(0.2); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > 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/arcsin_sqrtpostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_h := c( 0.01);"); > 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(-2.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arcsin(sqrt ( c(0.1) * c(x) + c(0.2))) + c(5.0) * sqrt( c(0.1) * c(x) + c(0.2)) * sqrt( c(0.8) - c(0.1) * c(x)) - c(5.0) * arcsin(sqrt( c(0.1) * c(x) + c(0.2))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_h := c( 0.01); > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(-2.0); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(0.5); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=10000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1 > #left paren 0001C > if (true) then # if number 10 > omniout_str(INFO," "); > fi;# end if 10; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > atomall(); > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10 > display_alot(current_iter); > fi;# end if 10; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (true) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2017-11-26T14:34:27-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"arcsin_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; ") > ; > logitem_complex(html_log_file,x_start) > ; > logitem_complex(html_log_file,x_end) > ; > logitem_complex(html_log_file,array_x[1]) > ; > logitem_complex(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > glob_desired_digits_correct := 0.0; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > glob_least_ratio_sing := 0; > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > glob_least_6_sing := 0.0; > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 309 ") > ; > logitem_str(html_log_file,"arcsin_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"arcsin_sqrt maple results") > ; > logitem_str(html_log_file,"Good Accuracy - Wasn't for Real") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_a1, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 32; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); 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 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4_a1 := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_tmp5 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y_higher := Array(0 .. 2, 0 .. 31, []); array_y_higher_work := Array(0 .. 2, 0 .. 31, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y_set_initial := Array(0 .. 2, 0 .. 31, []); 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 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 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 <= 30 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4_a1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 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 <= 30 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 <= 30 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 <= 30 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 <= 30 do term := 1; while term <= 30 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_a1); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_0D1); array_const_0D1[1] := c(0.1); zero_ats_ar(array_const_0D2); array_const_0D2[1] := c(0.2); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; 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/arcsin_sqrtpostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin ( sqrt ( 0\ .1 * x + 0.2 ) ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_h := c( 0.01);"); 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(-2.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arcs\ in(sqrt ( c(0.1) * c(x) + c(0.2))) + c(5.0) * sqrt( c(0.1) * c(x\ ) + c(0.2)) * sqrt( c(0.8) - c(0.1) * c(x)) - c(5.0) * arcsin(sq\ rt( c(0.1) * c(x) + c(0.2))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "next_delta := proc()"); omniout_str(ALWAYS, "global glob_nxt, x_delta;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 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"0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.000 + 0.000 * I ];"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;"); omniout_str(ALWAYS, "it := x_delta[glob_nxt];"); omniout_str(ALWAYS, "return it;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 0.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c(0.01); glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(-2.0); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(0.5); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 10000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius ; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and (glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do omniout_str(INFO, " "); found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); atomall(); if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = arcsin ( sqrt (\ 0.1 * x + 0.2 ) ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2017-11-26T14:34:27-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "arcsin_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ar\ csin ( sqrt ( 0.1 * x + 0.2 ) ) ; "); logitem_complex(html_log_file, x_start); logitem_complex(html_log_file, x_end); logitem_complex(html_log_file, array_x[1]); logitem_complex(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); glob_desired_digits_correct := 0.; logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then glob_least_ratio_sing := 0; logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then glob_least_6_sing := 0.; logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 309 "); logitem_str(html_log_file, "arcsin_sqrt diffeq.mxt"); logitem_str(html_log_file, "arcsin_sqrt maple results"); logitem_str(html_log_file, "Good Accuracy - Wasn't for Real"); 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/arcsin_sqrtpostcpx.cpx################# diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c( 0.01); glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(-2.0); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(0.5); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=10000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arcsin(sqrt ( c(0.1) * c(x) + c(0.2))) + c(5.0) * sqrt( c(0.1) * c(x) + c(0.2)) * sqrt( c(0.8) - c(0.1) * c(x)) - c(5.0) * arcsin(sqrt( c(0.1) * c(x) + c(0.2)))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 0.1 h = 0.0001 0.005 y[1] (numeric) = 0.655429404962 0.0476069564269 y[1] (closed_form) = 0.655429404962 0.0476069564269 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = 0.655414431005 0.0499889657892 y[1] (closed_form) = 0.655414124466 0.0499889773342 absolute error = 3.068e-07 relative error = 4.667e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=29.8MB, alloc=40.3MB, time=0.39 x[1] = 0.1002 0.108 h = 0.001 0.001 y[1] (numeric) = 0.655422472059 0.0514188134279 y[1] (closed_form) = 0.655422533218 0.0514188056948 absolute error = 6.165e-08 relative error = 9.377e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1012 0.109 h = 0.001 0.003 y[1] (numeric) = 0.655885227832 0.0519084436871 y[1] (closed_form) = 0.655885465511 0.0519083651012 absolute error = 2.503e-07 relative error = 3.805e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.104 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = 0.656321297104 0.0533509899372 y[1] (closed_form) = 0.656321169321 0.0533510410348 absolute error = 1.376e-07 relative error = 2.090e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.105 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1023 0.116 h = 0.003 0.006 y[1] (numeric) = 0.656313260081 0.0552583939049 y[1] (closed_form) = 0.656312877314 0.0552582354408 absolute error = 4.143e-07 relative error = 6.290e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.105 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = 0.657655827793 0.0581606439696 y[1] (closed_form) = 0.657655272546 0.0581619234665 absolute error = 1.395e-06 relative error = 0.0002113 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=75.1MB, alloc=52.3MB, time=0.97 x[1] = 0.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = 0.657626929441 0.0605473488462 y[1] (closed_form) = 0.657626642861 0.0605477278024 absolute error = 4.751e-07 relative error = 7.194e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1055 0.13 h = 0.001 0.001 y[1] (numeric) = 0.657626991865 0.0619795806117 y[1] (closed_form) = 0.657627072455 0.061979938938 absolute error = 3.673e-07 relative error = 5.560e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1065 0.131 h = 0.001 0.003 y[1] (numeric) = 0.658087771122 0.0624725997251 y[1] (closed_form) = 0.658088027747 0.0624728866268 absolute error = 3.849e-07 relative error = 5.823e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.111 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = 0.658516500255 0.0639199458056 y[1] (closed_form) = 0.65851639236 0.0639203635939 absolute error = 4.315e-07 relative error = 6.522e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1076 0.138 h = 0.003 0.006 y[1] (numeric) = 0.658497810307 0.0658304482314 y[1] (closed_form) = 0.658497446966 0.0658306576721 absolute error = 4.194e-07 relative error = 6.337e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=120.6MB, alloc=52.3MB, time=1.52 x[1] = 0.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = 0.659826425035 0.0687449974714 y[1] (closed_form) = 0.659825894785 0.06874664369 absolute error = 1.730e-06 relative error = 0.0002607 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = 0.659784212036 0.0711355306561 y[1] (closed_form) = 0.65978394677 0.0711362764916 absolute error = 7.916e-07 relative error = 0.0001193 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1108 0.152 h = 0.001 0.001 y[1] (numeric) = 0.659776314821 0.0725701732427 y[1] (closed_form) = 0.659776416174 0.0725708971138 absolute error = 7.309e-07 relative error = 0.0001101 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1118 0.153 h = 0.001 0.003 y[1] (numeric) = 0.660235132693 0.0730665842557 y[1] (closed_form) = 0.660235409588 0.0730672361427 absolute error = 7.083e-07 relative error = 0.0001066 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.117 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = 0.660656548866 0.0745187513612 y[1] (closed_form) = 0.660656462197 0.0745195353137 absolute error = 7.887e-07 relative error = 0.0001186 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.119 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=166.0MB, alloc=52.3MB, time=2.08 x[1] = 0.1129 0.16 h = 0.003 0.006 y[1] (numeric) = 0.660627231133 0.0764323878251 y[1] (closed_form) = 0.660626888583 0.076432964646 absolute error = 6.709e-07 relative error = 0.0001009 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.119 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = 0.661941956518 0.0793592721 y[1] (closed_form) = 0.661941452579 0.0793612844181 absolute error = 2.074e-06 relative error = 0.0003112 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.122 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.116 0.171 h = 0.0001 0.003 y[1] (numeric) = 0.661886460384 0.0817536777382 y[1] (closed_form) = 0.661886217768 0.0817547898987 absolute error = 1.138e-06 relative error = 0.0001707 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.123 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1161 0.174 h = 0.001 0.001 y[1] (numeric) = 0.661870622917 0.0831907573388 y[1] (closed_form) = 0.661870746347 0.0831918462179 absolute error = 1.096e-06 relative error = 0.0001643 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.123 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1171 0.175 h = 0.001 0.003 y[1] (numeric) = 0.662327494506 0.0836905629969 y[1] (closed_form) = 0.662327792977 0.0836915793447 absolute error = 1.059e-06 relative error = 0.0001587 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=211.4MB, alloc=52.3MB, time=2.64 x[1] = 0.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = 0.662741625144 0.0851475716975 y[1] (closed_form) = 0.662741561026 0.0851487212653 absolute error = 1.151e-06 relative error = 0.0001723 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.126 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1182 0.182 h = 0.003 0.006 y[1] (numeric) = 0.662701705292 0.0870643771138 y[1] (closed_form) = 0.662701384882 0.0870653207676 absolute error = 9.966e-07 relative error = 0.0001491 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.126 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = 0.664002605296 0.0900036308968 y[1] (closed_form) = 0.664002128962 0.0900060086713 absolute error = 2.425e-06 relative error = 0.0003619 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = 0.663933858185 0.0924019523017 y[1] (closed_form) = 0.663933639537 0.0924034302109 absolute error = 1.494e-06 relative error = 0.0002229 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1214 0.196 h = 0.001 0.001 y[1] (numeric) = 0.663910100232 0.0938414946017 y[1] (closed_form) = 0.663910247036 0.0938429479307 absolute error = 1.461e-06 relative error = 0.0002179 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=256.8MB, alloc=52.3MB, time=3.19 x[1] = 0.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = 0.664365040608 0.094344697354 y[1] (closed_form) = 0.664365361945 0.0943460776169 absolute error = 1.417e-06 relative error = 0.0002112 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1225 0.201 h = 0.003 0.006 y[1] (numeric) = 0.664316464656 0.0962641032653 y[1] (closed_form) = 0.664316042142 0.0962653074703 absolute error = 1.276e-06 relative error = 0.0001901 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = 0.66560536779 0.0992138672121 y[1] (closed_form) = 0.665604794028 0.0992165043421 absolute error = 2.699e-06 relative error = 0.000401 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.136 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = 0.665525193575 0.101615435908 y[1] (closed_form) = 0.665524874386 0.101617173434 absolute error = 1.767e-06 relative error = 0.0002624 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.136 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1257 0.215 h = 0.001 0.001 y[1] (numeric) = 0.665494604297 0.103057024174 y[1] (closed_form) = 0.665494650047 0.103058736009 absolute error = 1.712e-06 relative error = 0.0002543 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.137 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=302.2MB, alloc=52.3MB, time=3.75 x[1] = 0.1267 0.216 h = 0.001 0.003 y[1] (numeric) = 0.665947853886 0.103563130008 y[1] (closed_form) = 0.665948073732 0.10356476832 absolute error = 1.653e-06 relative error = 0.0002453 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = 0.666348443389 0.10502911439 y[1] (closed_form) = 0.666348302488 0.105030888017 absolute error = 1.779e-06 relative error = 0.0002638 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.139 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1278 0.223 h = 0.003 0.006 y[1] (numeric) = 0.666288826801 0.106951781557 y[1] (closed_form) = 0.666288428896 0.106953351533 absolute error = 1.620e-06 relative error = 0.00024 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.139 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = 0.66756402392 0.109913976251 y[1] (closed_form) = 0.667563480126 0.109916977603 absolute error = 3.050e-06 relative error = 0.0004508 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.143 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = 0.667470659711 0.112319539467 y[1] (closed_form) = 0.667470366903 0.112321641629 absolute error = 2.122e-06 relative error = 0.0003136 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.144 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=347.8MB, alloc=52.3MB, time=4.30 x[1] = 0.131 0.237 h = 0.001 0.001 y[1] (numeric) = 0.667432187395 0.113763637106 y[1] (closed_form) = 0.667432258893 0.113765712313 absolute error = 2.076e-06 relative error = 0.0003067 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.144 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.132 0.238 h = 0.001 0.003 y[1] (numeric) = 0.667883533679 0.114273143992 y[1] (closed_form) = 0.667883778754 0.114275145164 absolute error = 2.016e-06 relative error = 0.0002975 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.145 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.133 0.241 h = 0.0001 0.004 y[1] (numeric) = 0.668276917096 0.115744025697 y[1] (closed_form) = 0.668276802441 0.115746163267 absolute error = 2.141e-06 relative error = 0.0003156 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1331 0.245 h = 0.003 0.006 y[1] (numeric) = 0.668206774151 0.117669958287 y[1] (closed_form) = 0.668206402152 0.117671893425 absolute error = 1.971e-06 relative error = 0.0002904 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = 0.669468329944 0.120644614263 y[1] (closed_form) = 0.669467817356 0.120647979138 absolute error = 3.404e-06 relative error = 0.0005004 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=393.1MB, alloc=52.3MB, time=4.86 x[1] = 0.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = 0.669361809621 0.123054212894 y[1] (closed_form) = 0.66936154446 0.123056679056 absolute error = 2.480e-06 relative error = 0.0003645 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1363 0.259 h = 0.001 0.001 y[1] (numeric) = 0.66931547504 0.124500844121 y[1] (closed_form) = 0.669315573534 0.124503282082 absolute error = 2.440e-06 relative error = 0.0003584 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.152 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1373 0.26 h = 0.001 0.003 y[1] (numeric) = 0.669764932962 0.125013753678 y[1] (closed_form) = 0.669765204504 0.125016117105 absolute error = 2.379e-06 relative error = 0.0003492 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.153 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = 0.670151138518 0.126489550865 y[1] (closed_form) = 0.670151051364 0.126492051749 absolute error = 2.502e-06 relative error = 0.0003669 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.154 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1384 0.267 h = 0.003 0.006 y[1] (numeric) = 0.67007049673 0.128418781168 y[1] (closed_form) = 0.670070151917 0.128421080837 absolute error = 2.325e-06 relative error = 0.0003408 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.155 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=438.6MB, alloc=52.3MB, time=5.42 x[1] = 0.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = 0.671318476066 0.131405927597 y[1] (closed_form) = 0.671317995901 0.131409655276 absolute error = 3.758e-06 relative error = 0.0005494 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.159 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = 0.671198834058 0.133819601678 y[1] (closed_form) = 0.671198597791 0.133822431184 absolute error = 2.839e-06 relative error = 0.0004149 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.159 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1416 0.281 h = 0.001 0.001 y[1] (numeric) = 0.671144658306 0.135268790185 y[1] (closed_form) = 0.671144785024 0.135271590264 absolute error = 2.803e-06 relative error = 0.0004094 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1426 0.282 h = 0.001 0.003 y[1] (numeric) = 0.671592242747 0.135785103748 y[1] (closed_form) = 0.67159254198 0.135787828807 absolute error = 2.741e-06 relative error = 0.0004001 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.161 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = 0.671971298836 0.137265833953 y[1] (closed_form) = 0.671971240418 0.137268697503 absolute error = 2.864e-06 relative error = 0.0004176 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.162 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=484.0MB, alloc=52.3MB, time=5.97 x[1] = 0.1437 0.289 h = 0.003 0.006 y[1] (numeric) = 0.671880186146 0.139198393566 y[1] (closed_form) = 0.671879869777 0.139201057117 absolute error = 2.682e-06 relative error = 0.0003909 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.163 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = 0.673114654041 0.142198058261 y[1] (closed_form) = 0.673114207496 0.142202148011 absolute error = 4.114e-06 relative error = 0.000598 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.167 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = 0.6729819253 0.144615846964 y[1] (closed_form) = 0.672981719155 0.144619039141 absolute error = 3.199e-06 relative error = 0.0004647 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.168 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1469 0.303 h = 0.001 0.001 y[1] (numeric) = 0.672919929777 0.146067615917 y[1] (closed_form) = 0.672920085928 0.146070777459 absolute error = 3.165e-06 relative error = 0.0004597 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.168 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = 0.673365655555 0.146587334545 y[1] (closed_form) = 0.673365983683 0.146590420594 absolute error = 3.103e-06 relative error = 0.0004503 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.169 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=529.5MB, alloc=52.3MB, time=6.54 x[1] = 0.148 0.308 h = 0.003 0.006 y[1] (numeric) = 0.67326599545 0.148522623524 y[1] (closed_form) = 0.673265582319 0.148525547509 absolute error = 2.953e-06 relative error = 0.0004283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.151 0.314 h = 0.0001 0.005 y[1] (numeric) = 0.674488735754 0.151532924876 y[1] (closed_form) = 0.674488196874 0.151537273498 absolute error = 4.382e-06 relative error = 0.0006339 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = 0.674344721129 0.1539541307 y[1] (closed_form) = 0.674344419655 0.153957582271 absolute error = 3.465e-06 relative error = 0.0005009 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.175 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1512 0.322 h = 0.001 0.001 y[1] (numeric) = 0.674275980861 0.155408046166 y[1] (closed_form) = 0.674276041091 0.155411466072 absolute error = 3.420e-06 relative error = 0.0004943 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.175 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1522 0.323 h = 0.001 0.003 y[1] (numeric) = 0.674720078003 0.155930674498 y[1] (closed_form) = 0.674720309746 0.155934018505 absolute error = 3.352e-06 relative error = 0.000484 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.176 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=574.9MB, alloc=52.3MB, time=7.09 x[1] = 0.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = 0.675085847439 0.157420544089 y[1] (closed_form) = 0.675085723497 0.157424028456 absolute error = 3.487e-06 relative error = 0.000503 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1533 0.33 h = 0.003 0.006 y[1] (numeric) = 0.674975286071 0.159359256554 y[1] (closed_form) = 0.674974903685 0.159362543175 absolute error = 3.309e-06 relative error = 0.0004771 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = 0.676184635899 0.162382125129 y[1] (closed_form) = 0.676184132819 0.162386834422 absolute error = 4.736e-06 relative error = 0.0006811 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.182 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = 0.676027600445 0.164807516579 y[1] (closed_form) = 0.676027331334 0.164811329532 absolute error = 3.822e-06 relative error = 0.0005493 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1565 0.344 h = 0.001 0.001 y[1] (numeric) = 0.675951080723 0.166264054457 y[1] (closed_form) = 0.675951172593 0.166267834575 absolute error = 3.781e-06 relative error = 0.0005432 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.184 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=620.3MB, alloc=52.3MB, time=7.65 x[1] = 0.1575 0.345 h = 0.001 0.003 y[1] (numeric) = 0.676393346577 0.16679008927 y[1] (closed_form) = 0.676393609413 0.166793793039 absolute error = 3.713e-06 relative error = 0.000533 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.185 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = 0.676752048352 0.168284938971 y[1] (closed_form) = 0.676751956582 0.168288784063 absolute error = 3.846e-06 relative error = 0.0005515 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.186 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1586 0.352 h = 0.003 0.006 y[1] (numeric) = 0.676631097841 0.17022706763 y[1] (closed_form) = 0.676630747403 0.170230716184 absolute error = 3.665e-06 relative error = 0.0005253 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.187 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = 0.677827122464 0.173262527419 y[1] (closed_form) = 0.677826656322 0.173267596603 absolute error = 5.091e-06 relative error = 0.0007276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = 0.677657102504 0.17569214118 y[1] (closed_form) = 0.677656866927 0.175696314791 absolute error = 4.180e-06 relative error = 0.0005971 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.192 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=665.7MB, alloc=52.3MB, time=8.20 x[1] = 0.1618 0.366 h = 0.001 0.001 y[1] (numeric) = 0.677572825522 0.177151323128 y[1] (closed_form) = 0.677572950188 0.177155462754 absolute error = 4.142e-06 relative error = 0.0005913 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.193 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1628 0.367 h = 0.001 0.003 y[1] (numeric) = 0.678013274692 0.177680764707 y[1] (closed_form) = 0.678013569771 0.177684827546 absolute error = 4.074e-06 relative error = 0.0005812 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.194 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = 0.678364937695 0.179180609676 y[1] (closed_form) = 0.678364879258 0.179184814773 absolute error = 4.206e-06 relative error = 0.0005994 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.195 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1639 0.374 h = 0.003 0.006 y[1] (numeric) = 0.678233627448 0.181126183428 y[1] (closed_form) = 0.678233310141 0.181130193194 absolute error = 4.022e-06 relative error = 0.000573 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.196 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = 0.679416392161 0.184174257108 y[1] (closed_form) = 0.679415964074 0.184179685386 absolute error = 5.445e-06 relative error = 0.0007735 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=711.0MB, alloc=52.3MB, time=8.76 x[1] = 0.167 0.385 h = 0.0001 0.003 y[1] (numeric) = 0.679233424446 0.186608128991 y[1] (closed_form) = 0.679233223554 0.186612662519 absolute error = 4.538e-06 relative error = 0.0006442 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.201 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1671 0.388 h = 0.001 0.001 y[1] (numeric) = 0.679141412644 0.188069976138 y[1] (closed_form) = 0.679141571242 0.188074474551 absolute error = 4.501e-06 relative error = 0.0006387 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.202 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1681 0.389 h = 0.001 0.003 y[1] (numeric) = 0.679580059649 0.188602824504 y[1] (closed_form) = 0.679580388102 0.188607245705 absolute error = 4.433e-06 relative error = 0.0006286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.203 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = 0.679924712856 0.190107679289 y[1] (closed_form) = 0.679924688893 0.19011224366 absolute error = 4.564e-06 relative error = 0.0006465 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.204 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1692 0.396 h = 0.003 0.006 y[1] (numeric) = 0.67978307261 0.192056726333 y[1] (closed_form) = 0.679782789598 0.192061096573 absolute error = 4.379e-06 relative error = 0.00062 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.205 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=756.5MB, alloc=52.3MB, time=9.32 x[1] = 0.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = 0.680952642702 0.195117435281 y[1] (closed_form) = 0.680952253764 0.195123221842 absolute error = 5.800e-06 relative error = 0.0008187 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = 0.680756764386 0.197555600221 y[1] (closed_form) = 0.680756599309 0.197560492909 absolute error = 4.895e-06 relative error = 0.0006906 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1724 0.41 h = 0.001 0.001 y[1] (numeric) = 0.680657040438 0.199020133165 y[1] (closed_form) = 0.680657234083 0.199024989628 absolute error = 4.860e-06 relative error = 0.0006854 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.211 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = 0.681093899704 0.199556388085 y[1] (closed_form) = 0.681094262643 0.199561166923 absolute error = 4.793e-06 relative error = 0.0006753 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.212 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1735 0.415 h = 0.003 0.006 y[1] (numeric) = 0.680943828323 0.201508279938 y[1] (closed_form) = 0.680943453712 0.201512910039 absolute error = 4.645e-06 relative error = 0.0006541 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=802.0MB, alloc=52.3MB, time=9.87 x[1] = 0.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = 0.682101942348 0.204579724923 y[1] (closed_form) = 0.682101465961 0.204585769457 absolute error = 6.063e-06 relative error = 0.0008514 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.217 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = 0.681894929369 0.20702145931 y[1] (closed_form) = 0.681894673992 0.207026610728 absolute error = 5.158e-06 relative error = 0.0007238 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.218 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1767 0.429 h = 0.001 0.001 y[1] (numeric) = 0.681788553069 0.208488228692 y[1] (closed_form) = 0.681788655753 0.20849334294 absolute error = 5.115e-06 relative error = 0.0007175 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.219 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1777 0.43 h = 0.001 0.003 y[1] (numeric) = 0.68222384442 0.209027394417 y[1] (closed_form) = 0.682224115916 0.209032430687 absolute error = 5.044e-06 relative error = 0.0007068 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = 0.682555471345 0.210541525278 y[1] (closed_form) = 0.682555392484 0.21054670636 absolute error = 5.182e-06 relative error = 0.0007254 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.221 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=847.5MB, alloc=52.3MB, time=10.44 x[1] = 0.1788 0.437 h = 0.003 0.006 y[1] (numeric) = 0.682394647442 0.212496985747 y[1] (closed_form) = 0.682394309245 0.212501974921 absolute error = 5.001e-06 relative error = 0.0006997 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.222 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = 0.683539687998 0.215581103141 y[1] (closed_form) = 0.683539252751 0.215587504425 absolute error = 6.416e-06 relative error = 0.0008952 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.226 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = 0.683319834153 0.218027193718 y[1] (closed_form) = 0.68331961665 0.218032702861 absolute error = 5.513e-06 relative error = 0.0007687 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.227 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.182 0.451 h = 0.001 0.001 y[1] (numeric) = 0.683205788236 0.219496686095 y[1] (closed_form) = 0.683205927999 0.219502156996 absolute error = 5.473e-06 relative error = 0.0007626 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.228 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.183 0.452 h = 0.001 0.003 y[1] (numeric) = 0.683639318445 0.22003925744 y[1] (closed_form) = 0.683639626453 0.220044649973 absolute error = 5.401e-06 relative error = 0.0007521 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.229 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=893.0MB, alloc=52.3MB, time=11.00 x[1] = 0.184 0.455 h = 0.0001 0.004 y[1] (numeric) = 0.683964018687 0.221558436768 y[1] (closed_form) = 0.683963977462 0.221563974954 absolute error = 5.538e-06 relative error = 0.0007703 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.231 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1841 0.459 h = 0.003 0.006 y[1] (numeric) = 0.683792951196 0.223517447684 y[1] (closed_form) = 0.683792650519 0.223522795148 absolute error = 5.356e-06 relative error = 0.0007445 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.232 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = 0.684924983413 0.226614255222 y[1] (closed_form) = 0.684924590339 0.226621012406 absolute error = 6.769e-06 relative error = 0.0009382 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = 0.684692326888 0.22906473443 y[1] (closed_form) = 0.684692148331 0.229070600499 absolute error = 5.869e-06 relative error = 0.0008129 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.237 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1873 0.473 h = 0.001 0.001 y[1] (numeric) = 0.684570634621 0.230536968891 y[1] (closed_form) = 0.684570812521 0.230542795667 absolute error = 5.829e-06 relative error = 0.000807 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.238 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1883 0.474 h = 0.001 0.003 y[1] (numeric) = 0.685002417833 0.231082944912 y[1] (closed_form) = 0.685002763407 0.231088692943 absolute error = 5.758e-06 relative error = 0.0007965 % Correct digits = 5 memory used=938.6MB, alloc=52.3MB, time=11.57 Radius of convergence (given) for eq 1 = 2.239 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = 0.685320220587 0.232607184956 y[1] (closed_form) = 0.68532021806 0.232613079455 absolute error = 5.894e-06 relative error = 0.0008145 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.241 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1894 0.481 h = 0.003 0.006 y[1] (numeric) = 0.685138940348 0.234569771811 y[1] (closed_form) = 0.685138678274 0.23457547677 absolute error = 5.711e-06 relative error = 0.0007886 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.242 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = 0.686258029238 0.237679285987 y[1] (closed_form) = 0.686257679351 0.23768639821 absolute error = 7.121e-06 relative error = 0.0009805 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.246 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = 0.686012608535 0.240134185398 y[1] (closed_form) = 0.686012469975 0.24014040758 absolute error = 6.224e-06 relative error = 0.0008563 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.247 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1926 0.495 h = 0.001 0.001 y[1] (numeric) = 0.685883293362 0.241609180506 y[1] (closed_form) = 0.685883510439 0.241615362366 absolute error = 6.186e-06 relative error = 0.0008506 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.248 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=984.0MB, alloc=52.3MB, time=12.12 x[1] = 0.1936 0.496 h = 0.001 0.003 y[1] (numeric) = 0.686313343613 0.242158560023 y[1] (closed_form) = 0.68631372779 0.242164662773 absolute error = 6.115e-06 relative error = 0.0008402 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.249 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = 0.686624278097 0.243687872447 y[1] (closed_form) = 0.68662431531 0.243694122454 absolute error = 6.250e-06 relative error = 0.0008578 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.251 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1947 0.503 h = 0.003 0.006 y[1] (numeric) = 0.686432816188 0.245654060038 y[1] (closed_form) = 0.686432593781 0.245660121682 absolute error = 6.066e-06 relative error = 0.000832 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.252 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = 0.687539026625 0.248776296118 y[1] (closed_form) = 0.687538720916 0.248783762508 absolute error = 7.473e-06 relative error = 0.001022 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.256 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = 0.687280880536 0.251235646438 y[1] (closed_form) = 0.687280783004 0.251242223908 absolute error = 6.578e-06 relative error = 0.000899 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.257 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1029.6MB, alloc=52.3MB, time=12.68 x[1] = 0.1979 0.517 h = 0.001 0.001 y[1] (numeric) = 0.687143966068 0.252713420236 y[1] (closed_form) = 0.687144223339 0.252719956375 absolute error = 6.541e-06 relative error = 0.0008934 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.258 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = 0.687572297282 0.253266201835 y[1] (closed_form) = 0.687572721076 0.253272658511 absolute error = 6.471e-06 relative error = 0.0008831 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.259 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.199 0.522 h = 0.003 0.006 y[1] (numeric) = 0.687372526284 0.255235336176 y[1] (closed_form) = 0.68737221722 0.25524165669 absolute error = 6.328e-06 relative error = 0.000863 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.202 0.528 h = 0.0001 0.005 y[1] (numeric) = 0.688467551436 0.258368381791 y[1] (closed_form) = 0.688467162925 0.258376104888 absolute error = 7.733e-06 relative error = 0.001052 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.264 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = 0.688198429526 0.260831436284 y[1] (closed_form) = 0.6881982465 0.260838271426 absolute error = 6.838e-06 relative error = 0.0009291 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.266 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1075.1MB, alloc=52.3MB, time=13.24 x[1] = 0.2022 0.536 h = 0.001 0.001 y[1] (numeric) = 0.688054959479 0.262311525797 y[1] (closed_form) = 0.68805513054 0.262318318747 absolute error = 6.795e-06 relative error = 0.0009228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.266 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2032 0.537 h = 0.001 0.003 y[1] (numeric) = 0.688481781567 0.262867214235 y[1] (closed_form) = 0.688482118657 0.26287392742 absolute error = 6.722e-06 relative error = 0.0009121 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.268 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = 0.688779952863 0.264405913256 y[1] (closed_form) = 0.688779945115 0.264412775118 absolute error = 6.862e-06 relative error = 0.0009301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.269 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2043 0.544 h = 0.003 0.006 y[1] (numeric) = 0.688569585146 0.266378744201 y[1] (closed_form) = 0.688569317681 0.26638541987 absolute error = 6.681e-06 relative error = 0.0009049 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = 0.689651851957 0.269524537695 y[1] (closed_form) = 0.689651509422 0.269532613318 absolute error = 8.083e-06 relative error = 0.001092 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.275 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1120.6MB, alloc=52.3MB, time=13.80 x[1] = 0.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = 0.689370077202 0.271992098411 y[1] (closed_form) = 0.689369937076 0.271999287286 absolute error = 7.190e-06 relative error = 0.0009702 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.276 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2075 0.558 h = 0.001 0.001 y[1] (numeric) = 0.689219051987 0.273474999087 y[1] (closed_form) = 0.689219265093 0.273482144799 absolute error = 7.149e-06 relative error = 0.0009641 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.277 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2085 0.559 h = 0.001 0.003 y[1] (numeric) = 0.68964418066 0.274034086536 y[1] (closed_form) = 0.689644559215 0.274041152153 absolute error = 7.076e-06 relative error = 0.0009535 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.278 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = 0.689935567161 0.275577888492 y[1] (closed_form) = 0.689935602031 0.275585103506 absolute error = 7.215e-06 relative error = 0.0009712 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2096 0.566 h = 0.003 0.006 y[1] (numeric) = 0.689715107575 0.277554387672 y[1] (closed_form) = 0.689714882713 0.27756141765 absolute error = 7.034e-06 relative error = 0.000946 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.281 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1166.2MB, alloc=52.3MB, time=14.36 x[1] = 0.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = 0.690784680403 0.2807129409 y[1] (closed_form) = 0.690784384774 0.280721368147 absolute error = 8.432e-06 relative error = 0.001131 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.285 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = 0.690490292317 0.283185036092 y[1] (closed_form) = 0.690490196062 0.283192577842 absolute error = 7.542e-06 relative error = 0.001011 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.287 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2128 0.58 h = 0.001 0.001 y[1] (numeric) = 0.690331735952 0.284670764493 y[1] (closed_form) = 0.690331992062 0.28467826213 absolute error = 7.502e-06 relative error = 0.001005 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.288 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2138 0.581 h = 0.001 0.003 y[1] (numeric) = 0.690755184797 0.285233248901 y[1] (closed_form) = 0.690755605775 0.285240666124 absolute error = 7.429e-06 relative error = 0.0009941 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.289 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = 0.691039815694 0.286782163267 y[1] (closed_form) = 0.691039894146 0.286789730583 absolute error = 7.568e-06 relative error = 0.001011 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.291 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1211.8MB, alloc=52.3MB, time=14.91 x[1] = 0.2149 0.588 h = 0.003 0.006 y[1] (numeric) = 0.690809296084 0.288762352823 y[1] (closed_form) = 0.690809114807 0.288769736253 absolute error = 7.386e-06 relative error = 0.0009864 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.292 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = 0.691866239054 0.291933676484 y[1] (closed_form) = 0.691865991241 0.291942454444 absolute error = 8.781e-06 relative error = 0.001169 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.296 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.218 0.599 h = 0.0001 0.003 y[1] (numeric) = 0.691559277362 0.29441033356 y[1] (closed_form) = 0.691559225928 0.294418227315 absolute error = 7.894e-06 relative error = 0.00105 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.297 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2181 0.602 h = 0.001 0.001 y[1] (numeric) = 0.69139321398 0.295898905736 y[1] (closed_form) = 0.691393514036 0.295906754449 absolute error = 7.854e-06 relative error = 0.001044 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.298 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2191 0.603 h = 0.001 0.003 y[1] (numeric) = 0.691814996459 0.296464784838 y[1] (closed_form) = 0.691815460799 0.296472552831 absolute error = 7.782e-06 relative error = 0.001034 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1257.2MB, alloc=52.3MB, time=15.48 x[1] = 0.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = 0.692092900908 0.29801882054 y[1] (closed_form) = 0.692093023884 0.298026739298 absolute error = 7.920e-06 relative error = 0.001051 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.301 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2202 0.61 h = 0.003 0.006 y[1] (numeric) = 0.691852353276 0.300002721936 y[1] (closed_form) = 0.691852216546 0.300010457949 absolute error = 7.737e-06 relative error = 0.001026 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.302 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = 0.692896730264 0.303186825591 y[1] (closed_form) = 0.692896531154 0.303195953343 absolute error = 9.130e-06 relative error = 0.001207 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.307 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = 0.692577234879 0.305668071116 y[1] (closed_form) = 0.692577229196 0.305676315996 absolute error = 8.245e-06 relative error = 0.001089 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.308 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2234 0.624 h = 0.001 0.001 y[1] (numeric) = 0.692403688717 0.307159502611 y[1] (closed_form) = 0.692404033638 0.307167701542 absolute error = 8.206e-06 relative error = 0.001083 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.309 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1302.8MB, alloc=52.3MB, time=16.04 x[1] = 0.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = 0.692823818165 0.307728773933 y[1] (closed_form) = 0.692824326786 0.307736891849 absolute error = 8.134e-06 relative error = 0.001073 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.311 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2245 0.629 h = 0.003 0.006 y[1] (numeric) = 0.69257508756 0.309715710723 y[1] (closed_form) = 0.692574868864 0.309723704247 absolute error = 7.997e-06 relative error = 0.001054 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.312 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = 0.693608546744 0.312910673117 y[1] (closed_form) = 0.69360826922 0.312920055987 absolute error = 9.387e-06 relative error = 0.001234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.316 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = 0.693278239793 0.31539574021 y[1] (closed_form) = 0.693278153172 0.315404241352 absolute error = 8.502e-06 relative error = 0.001116 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.318 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2277 0.643 h = 0.001 0.001 y[1] (numeric) = 0.693098237881 0.316889556235 y[1] (closed_form) = 0.693098501105 0.316898010652 absolute error = 8.459e-06 relative error = 0.00111 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.319 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1348.4MB, alloc=52.3MB, time=16.60 x[1] = 0.2287 0.644 h = 0.001 0.003 y[1] (numeric) = 0.693516914669 0.317461725855 y[1] (closed_form) = 0.693517341092 0.317470099005 absolute error = 8.384e-06 relative error = 0.001099 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = 0.693782318963 0.319025233765 y[1] (closed_form) = 0.693782406186 0.319033758883 absolute error = 8.526e-06 relative error = 0.001116 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.322 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2298 0.651 h = 0.003 0.006 y[1] (numeric) = 0.693523152376 0.32101597831 y[1] (closed_form) = 0.693522979971 0.321024322786 absolute error = 8.346e-06 relative error = 0.001092 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.323 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = 0.694544163617 0.324223736281 y[1] (closed_form) = 0.694543936404 0.324233467221 absolute error = 9.734e-06 relative error = 0.00127 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.327 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = 0.694201397387 0.326713439517 y[1] (closed_form) = 0.694201358201 0.326722290136 absolute error = 8.851e-06 relative error = 0.001154 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.329 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1393.9MB, alloc=52.3MB, time=17.16 x[1] = 0.233 0.665 h = 0.001 0.001 y[1] (numeric) = 0.694013957861 0.328210142741 y[1] (closed_form) = 0.69401426762 0.328218945765 absolute error = 8.808e-06 relative error = 0.001147 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.234 0.666 h = 0.001 0.003 y[1] (numeric) = 0.694431006117 0.328785699601 y[1] (closed_form) = 0.694431478488 0.328794421083 absolute error = 8.734e-06 relative error = 0.001137 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.331 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.235 0.669 h = 0.0001 0.004 y[1] (numeric) = 0.694689766986 0.330354351759 y[1] (closed_form) = 0.694689901327 0.330363225814 absolute error = 8.875e-06 relative error = 0.001154 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.333 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2351 0.673 h = 0.003 0.006 y[1] (numeric) = 0.694420664418 0.332348866239 y[1] (closed_form) = 0.694420539206 0.332357560771 absolute error = 8.695e-06 relative error = 0.001129 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.334 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = 0.695429290781 0.335569426198 y[1] (closed_form) = 0.695429114707 0.335579504266 absolute error = 1.008e-05 relative error = 0.001305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.339 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1439.4MB, alloc=52.3MB, time=17.72 x[1] = 0.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = 0.69507410563 0.338063789775 y[1] (closed_form) = 0.695074114749 0.338072988965 absolute error = 9.199e-06 relative error = 0.00119 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2383 0.687 h = 0.001 0.001 y[1] (numeric) = 0.69487925297 0.339563394317 y[1] (closed_form) = 0.694879610124 0.339572545063 absolute error = 9.158e-06 relative error = 0.001184 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.341 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2393 0.688 h = 0.001 0.003 y[1] (numeric) = 0.69529468565 0.340142335376 y[1] (closed_form) = 0.695295204831 0.340151404317 absolute error = 9.084e-06 relative error = 0.001174 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.343 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = 0.695546832016 0.341716138657 y[1] (closed_form) = 0.695547014339 0.341725360753 absolute error = 9.224e-06 relative error = 0.00119 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.344 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2404 0.695 h = 0.003 0.006 y[1] (numeric) = 0.695267825935 0.343714441974 y[1] (closed_form) = 0.695267748798 0.343723485656 absolute error = 9.044e-06 relative error = 0.001166 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.346 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1485.0MB, alloc=52.3MB, time=18.28 x[1] = 0.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = 0.696264130159 0.34694780927 y[1] (closed_form) = 0.696264006031 0.346958233518 absolute error = 1.042e-05 relative error = 0.00134 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = 0.695896566561 0.349446856572 y[1] (closed_form) = 0.695896624835 0.34945640342 absolute error = 9.547e-06 relative error = 0.001226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.352 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2436 0.709 h = 0.001 0.001 y[1] (numeric) = 0.695694325307 0.350949376061 y[1] (closed_form) = 0.695694730699 0.350958873636 absolute error = 9.506e-06 relative error = 0.00122 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.353 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2446 0.71 h = 0.001 0.003 y[1] (numeric) = 0.696108155233 0.351531698092 y[1] (closed_form) = 0.696108722065 0.351541113611 absolute error = 9.433e-06 relative error = 0.00121 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.354 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = 0.696353715933 0.353110658859 y[1] (closed_form) = 0.696353947081 0.353120228094 absolute error = 9.572e-06 relative error = 0.001226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.356 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1530.5MB, alloc=52.3MB, time=18.83 x[1] = 0.2457 0.717 h = 0.003 0.006 y[1] (numeric) = 0.696064838889 0.355112769265 y[1] (closed_form) = 0.696064810687 0.355122161185 absolute error = 9.392e-06 relative error = 0.001202 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.357 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = 0.697048883374 0.358358948207 y[1] (closed_form) = 0.697048811978 0.35836971768 absolute error = 1.077e-05 relative error = 0.001374 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.362 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = 0.696668981904 0.360862701814 y[1] (closed_form) = 0.696669090163 0.3608725954 absolute error = 9.894e-06 relative error = 0.001261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.364 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2489 0.731 h = 0.001 0.001 y[1] (numeric) = 0.696459376645 0.362368149394 y[1] (closed_form) = 0.696459831098 0.362377992899 absolute error = 9.854e-06 relative error = 0.001255 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.365 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = 0.6968716165 0.362953848987 y[1] (closed_form) = 0.696872231806 0.362963610195 absolute error = 9.781e-06 relative error = 0.001245 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.366 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1576.0MB, alloc=52.3MB, time=19.39 x[1] = 0.25 0.736 h = 0.003 0.006 y[1] (numeric) = 0.696574685144 0.364959070564 y[1] (closed_form) = 0.696574579396 0.364968718315 absolute error = 9.648e-06 relative error = 0.001227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.367 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.253 0.742 h = 0.0001 0.005 y[1] (numeric) = 0.697548073888 0.36821613498 y[1] (closed_form) = 0.697547928194 0.368227157703 absolute error = 1.102e-05 relative error = 0.001398 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.372 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = 0.69715752853 0.37072381078 y[1] (closed_form) = 0.697157560141 0.370733958913 absolute error = 1.015e-05 relative error = 0.001285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.374 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2532 0.75 h = 0.001 0.001 y[1] (numeric) = 0.696941569221 0.372231701605 y[1] (closed_form) = 0.696941946235 0.372241798965 absolute error = 1.010e-05 relative error = 0.001279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.375 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2542 0.751 h = 0.001 0.003 y[1] (numeric) = 0.697352410269 0.372820286886 y[1] (closed_form) = 0.697352947634 0.372830301745 absolute error = 1.003e-05 relative error = 0.001268 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.376 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1621.5MB, alloc=52.3MB, time=19.95 x[1] = 0.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = 0.697585731408 0.374408782114 y[1] (closed_form) = 0.697585935269 0.374418951684 absolute error = 1.017e-05 relative error = 0.001285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.378 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = 0.697278527837 0.376417906345 y[1] (closed_form) = 0.697278472582 0.376427900625 absolute error = 9.994e-06 relative error = 0.001261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.379 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2554 0.762 h = 0.003 0.006 y[1] (numeric) = 0.696969229535 0.378427157865 y[1] (closed_form) = 0.696969174272 0.378437152065 absolute error = 9.994e-06 relative error = 0.00126 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.381 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = 0.697927904687 0.381698807001 y[1] (closed_form) = 0.697927813882 0.381710172684 absolute error = 1.137e-05 relative error = 0.001429 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.385 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = 0.69752280447 0.384211598215 y[1] (closed_form) = 0.697522887783 0.38422209106 absolute error = 1.049e-05 relative error = 0.001318 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.387 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1667.1MB, alloc=52.3MB, time=20.51 x[1] = 0.2586 0.776 h = 0.001 0.001 y[1] (numeric) = 0.697298154362 0.385722681173 y[1] (closed_form) = 0.697298582009 0.385733122307 absolute error = 1.045e-05 relative error = 0.001311 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.388 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2596 0.777 h = 0.001 0.003 y[1] (numeric) = 0.697707034008 0.386315161895 y[1] (closed_form) = 0.697707621326 0.386325520248 absolute error = 1.037e-05 relative error = 0.001301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.389 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = 0.697932537807 0.387909484629 y[1] (closed_form) = 0.697932792981 0.387919998318 absolute error = 1.052e-05 relative error = 0.001317 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.391 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2607 0.784 h = 0.003 0.006 y[1] (numeric) = 0.697613725997 0.389922771335 y[1] (closed_form) = 0.697613722201 0.389933110998 absolute error = 1.034e-05 relative error = 0.001294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.393 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = 0.698560328432 0.39320724202 y[1] (closed_form) = 0.698560292672 0.393218950035 absolute error = 1.171e-05 relative error = 0.001461 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.398 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1712.7MB, alloc=52.3MB, time=21.06 x[1] = 0.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = 0.698143012897 0.395724805203 y[1] (closed_form) = 0.698143148634 0.395735641991 absolute error = 1.084e-05 relative error = 0.00135 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.399 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2639 0.798 h = 0.001 0.001 y[1] (numeric) = 0.69791107303 0.397238854436 y[1] (closed_form) = 0.697911552158 0.397249638765 absolute error = 1.079e-05 relative error = 0.001344 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2649 0.799 h = 0.001 0.003 y[1] (numeric) = 0.698318400411 0.397834701909 y[1] (closed_form) = 0.698319038624 0.39784540325 absolute error = 1.072e-05 relative error = 0.001334 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.402 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = 0.698537433614 0.399434204174 y[1] (closed_form) = 0.698537740859 0.399445061321 absolute error = 1.086e-05 relative error = 0.00135 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.404 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.266 0.806 h = 0.003 0.006 y[1] (numeric) = 0.698208881956 0.401451366756 y[1] (closed_form) = 0.698208930405 0.40146205094 absolute error = 1.068e-05 relative error = 0.001327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.405 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1758.2MB, alloc=52.3MB, time=21.62 x[1] = 0.269 0.812 h = 0.0001 0.005 y[1] (numeric) = 0.699143472598 0.404748659285 y[1] (closed_form) = 0.699143492588 0.404760708657 absolute error = 1.205e-05 relative error = 0.001492 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = 0.69871398259 0.407271013862 y[1] (closed_form) = 0.698714171499 0.407282193648 absolute error = 1.118e-05 relative error = 0.001383 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.412 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2692 0.82 h = 0.001 0.001 y[1] (numeric) = 0.698474777682 0.408788040624 y[1] (closed_form) = 0.698475309034 0.408799167221 absolute error = 1.114e-05 relative error = 0.001376 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.413 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2702 0.821 h = 0.001 0.003 y[1] (numeric) = 0.698880564915 0.409387250745 y[1] (closed_form) = 0.698881254766 0.409398294157 absolute error = 1.106e-05 relative error = 0.001366 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.414 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = 0.699093155825 0.410991936455 y[1] (closed_form) = 0.699093515884 0.411003136122 absolute error = 1.121e-05 relative error = 0.001382 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.416 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1803.8MB, alloc=52.3MB, time=22.18 x[1] = 0.2713 0.828 h = 0.003 0.006 y[1] (numeric) = 0.698754897117 0.41301299001 y[1] (closed_form) = 0.698754998571 0.413024017767 absolute error = 1.103e-05 relative error = 0.001359 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.418 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = 0.699677536478 0.416323103741 y[1] (closed_form) = 0.699677612905 0.41633549349 absolute error = 1.239e-05 relative error = 0.001522 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.422 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = 0.699235912862 0.41885026838 y[1] (closed_form) = 0.699236155674 0.418861790212 absolute error = 1.152e-05 relative error = 0.001414 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.424 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2745 0.842 h = 0.001 0.001 y[1] (numeric) = 0.698989467636 0.420370283464 y[1] (closed_form) = 0.698990051938 0.420381751398 absolute error = 1.148e-05 relative error = 0.001408 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.425 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2755 0.843 h = 0.001 0.003 y[1] (numeric) = 0.699393726691 0.420972851975 y[1] (closed_form) = 0.699394468907 0.420984236537 absolute error = 1.141e-05 relative error = 0.001398 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.427 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1849.3MB, alloc=52.3MB, time=22.74 x[1] = 0.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = 0.699599903478 0.422582724585 y[1] (closed_form) = 0.699600317075 0.42259426583 absolute error = 1.155e-05 relative error = 0.001413 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.429 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2766 0.85 h = 0.003 0.006 y[1] (numeric) = 0.699251970527 0.424607683607 y[1] (closed_form) = 0.699252125725 0.424619053985 absolute error = 1.137e-05 relative error = 0.00139 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = 0.700162718695 0.427930616979 y[1] (closed_form) = 0.700162852226 0.427943346123 absolute error = 1.273e-05 relative error = 0.001551 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.435 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = 0.699709002342 0.430462609598 y[1] (closed_form) = 0.699709299765 0.430474472521 absolute error = 1.187e-05 relative error = 0.001444 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.437 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2798 0.864 h = 0.001 0.001 y[1] (numeric) = 0.699455341515 0.431985623351 y[1] (closed_form) = 0.699455979471 0.431997431686 absolute error = 1.183e-05 relative error = 0.001438 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.438 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1894.9MB, alloc=52.3MB, time=23.30 x[1] = 0.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = 0.699858084215 0.432591545842 y[1] (closed_form) = 0.699858879503 0.432603270626 absolute error = 1.175e-05 relative error = 0.001428 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.439 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2809 0.869 h = 0.003 0.006 y[1] (numeric) = 0.699502257824 0.434619694038 y[1] (closed_form) = 0.699502340584 0.434631317812 absolute error = 1.162e-05 relative error = 0.001411 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.441 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = 0.70040266557 0.437953519513 y[1] (closed_form) = 0.700402729538 0.437966499292 absolute error = 1.298e-05 relative error = 0.001571 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.446 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.284 0.88 h = 0.0001 0.003 y[1] (numeric) = 0.699938515126 0.440489538297 y[1] (closed_form) = 0.699938740854 0.440501653306 absolute error = 1.212e-05 relative error = 0.001465 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.448 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2841 0.883 h = 0.001 0.001 y[1] (numeric) = 0.699678627253 0.4420150556 y[1] (closed_form) = 0.699679192695 0.44202711543 absolute error = 1.207e-05 relative error = 0.001459 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.449 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2851 0.884 h = 0.001 0.003 y[1] (numeric) = 0.700080034205 0.442623843565 y[1] (closed_form) = 0.70008075648 0.442635819694 absolute error = 1.200e-05 relative error = 0.001449 % Correct digits = 5 memory used=1940.5MB, alloc=52.3MB, time=23.85 Radius of convergence (given) for eq 1 = 2.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = 0.700274288432 0.444243299822 y[1] (closed_form) = 0.700274684264 0.444255433392 absolute error = 1.214e-05 relative error = 0.001464 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.452 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2862 0.891 h = 0.003 0.006 y[1] (numeric) = 0.699908394363 0.446275448231 y[1] (closed_form) = 0.699908532201 0.446287412849 absolute error = 1.197e-05 relative error = 0.001441 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.454 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = 0.700797021606 0.449622088774 y[1] (closed_form) = 0.700797143881 0.449635406118 absolute error = 1.332e-05 relative error = 0.001599 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.459 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = 0.70032085425 0.452162967412 y[1] (closed_form) = 0.70032113587 0.452175421731 absolute error = 1.246e-05 relative error = 0.001494 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.461 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2894 0.905 h = 0.001 0.001 y[1] (numeric) = 0.700053796617 0.453691501758 y[1] (closed_form) = 0.700054416987 0.453703900242 absolute error = 1.241e-05 relative error = 0.001488 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.462 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1986.0MB, alloc=52.3MB, time=24.41 x[1] = 0.2904 0.906 h = 0.001 0.003 y[1] (numeric) = 0.700453708881 0.454303635241 y[1] (closed_form) = 0.700454485504 0.454315949866 absolute error = 1.234e-05 relative error = 0.001478 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.463 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = 0.700641628754 0.455928286152 y[1] (closed_form) = 0.700642080103 0.455940758588 absolute error = 1.248e-05 relative error = 0.001493 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.465 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2915 0.913 h = 0.003 0.006 y[1] (numeric) = 0.700266154083 0.457964378621 y[1] (closed_form) = 0.700266347682 0.457976683119 absolute error = 1.231e-05 relative error = 0.001471 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.467 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = 0.701143059654 0.461323830154 y[1] (closed_form) = 0.701143240848 0.461337484073 absolute error = 1.366e-05 relative error = 0.001627 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.472 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = 0.700654916204 0.463869584483 y[1] (closed_form) = 0.700655254372 0.463882377143 absolute error = 1.280e-05 relative error = 0.001523 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.474 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2031.5MB, alloc=52.3MB, time=24.97 x[1] = 0.2947 0.927 h = 0.001 0.001 y[1] (numeric) = 0.700380713475 0.46540114497 y[1] (closed_form) = 0.700381389426 0.46541388116 absolute error = 1.275e-05 relative error = 0.001517 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.475 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2957 0.928 h = 0.001 0.003 y[1] (numeric) = 0.700779142455 0.466016619148 y[1] (closed_form) = 0.70077997408 0.46602927133 absolute error = 1.268e-05 relative error = 0.001507 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.476 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = 0.700960755575 0.467646466475 y[1] (closed_form) = 0.700961263092 0.467659276819 absolute error = 1.282e-05 relative error = 0.001521 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.478 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2968 0.935 h = 0.003 0.006 y[1] (numeric) = 0.700575733039 0.469686515245 y[1] (closed_form) = 0.700575983065 0.469699158654 absolute error = 1.265e-05 relative error = 0.001499 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = 0.701440975308 0.473058772851 y[1] (closed_form) = 0.701441216016 0.473072762353 absolute error = 1.399e-05 relative error = 0.001654 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.485 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2077.0MB, alloc=52.3MB, time=25.53 x[1] = 0.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = 0.700940896539 0.475609417998 y[1] (closed_form) = 0.700941291891 0.475622548032 absolute error = 1.314e-05 relative error = 0.001551 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.487 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3 0.949 h = 0.001 0.001 y[1] (numeric) = 0.700659573343 0.477144013301 y[1] (closed_form) = 0.700660305509 0.477157086245 absolute error = 1.309e-05 relative error = 0.001545 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.488 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.301 0.95 h = 0.001 0.003 y[1] (numeric) = 0.701056530295 0.477762823218 y[1] (closed_form) = 0.701057417558 0.477775812014 absolute error = 1.302e-05 relative error = 0.001535 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.489 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.302 0.953 h = 0.0001 0.004 y[1] (numeric) = 0.701231864102 0.479397868307 y[1] (closed_form) = 0.701232428419 0.479411015597 absolute error = 1.316e-05 relative error = 0.001549 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.491 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3021 0.957 h = 0.003 0.006 y[1] (numeric) = 0.700837326395 0.481441885057 y[1] (closed_form) = 0.700837633492 0.481454866404 absolute error = 1.298e-05 relative error = 0.001527 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.493 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2122.4MB, alloc=52.3MB, time=26.08 x[1] = 0.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = 0.70169096326 0.484826942999 y[1] (closed_form) = 0.701691264058 0.484841267089 absolute error = 1.433e-05 relative error = 0.00168 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.498 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = 0.701178989891 0.487382493397 y[1] (closed_form) = 0.701179443044 0.487395959831 absolute error = 1.347e-05 relative error = 0.001578 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3053 0.971 h = 0.001 0.001 y[1] (numeric) = 0.700890570817 0.488920131772 y[1] (closed_form) = 0.700891359812 0.488933540517 absolute error = 1.343e-05 relative error = 0.001572 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.501 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = 0.701286066847 0.489542272342 y[1] (closed_form) = 0.701287010364 0.489555596808 absolute error = 1.336e-05 relative error = 0.001562 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.503 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3064 0.976 h = 0.003 0.006 y[1] (numeric) = 0.700883765581 0.491589527579 y[1] (closed_form) = 0.700884004022 0.491602760084 absolute error = 1.323e-05 relative error = 0.001546 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.504 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2168.1MB, alloc=52.3MB, time=26.64 x[1] = 0.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = 0.701727306533 0.494985461106 y[1] (closed_form) = 0.701727541259 0.495000033488 absolute error = 1.457e-05 relative error = 0.001697 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = 0.70120506859 0.497545103785 y[1] (closed_form) = 0.701205453713 0.497558820061 absolute error = 1.372e-05 relative error = 0.001596 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.512 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3096 0.99 h = 0.001 0.001 y[1] (numeric) = 0.700910524898 0.499085283706 y[1] (closed_form) = 0.700911245032 0.49909894178 absolute error = 1.368e-05 relative error = 0.00159 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.513 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3106 0.991 h = 0.001 0.003 y[1] (numeric) = 0.701304732607 0.499710269796 y[1] (closed_form) = 0.70130560677 0.499723843479 absolute error = 1.360e-05 relative error = 0.00158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.514 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = 0.701468392597 0.501354914863 y[1] (closed_form) = 0.701468945967 0.50136864762 absolute error = 1.374e-05 relative error = 0.001594 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.516 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2213.7MB, alloc=52.3MB, time=27.20 x[1] = 0.3117 0.998 h = 0.003 0.006 y[1] (numeric) = 0.701056188638 0.503406231868 y[1] (closed_form) = 0.701056485314 0.503419800504 absolute error = 1.357e-05 relative error = 0.001572 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.518 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = 0.701888230742 0.506814953622 y[1] (closed_form) = 0.701888526594 0.506829858747 absolute error = 1.491e-05 relative error = 0.001722 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.523 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = 0.701354173623 0.509379527076 y[1] (closed_form) = 0.701354617661 0.509393577943 absolute error = 1.406e-05 relative error = 0.001622 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.525 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3149 1.012 h = 0.001 0.001 y[1] (numeric) = 0.701052579586 0.51092276464 y[1] (closed_form) = 0.701053357659 0.510936756738 absolute error = 1.401e-05 relative error = 0.001615 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.526 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3159 1.013 h = 0.001 0.003 y[1] (numeric) = 0.701445346709 0.511551071715 y[1] (closed_form) = 0.701446278239 0.51156497931 absolute error = 1.394e-05 relative error = 0.001606 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.528 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2259.3MB, alloc=52.3MB, time=27.76 x[1] = 0.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = 0.701602804945 0.513200916493 y[1] (closed_form) = 0.701603416837 0.513214983439 absolute error = 1.408e-05 relative error = 0.00162 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.53 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.317 1.02 h = 0.003 0.006 y[1] (numeric) = 0.701181178907 0.515256232252 y[1] (closed_form) = 0.701181534411 0.515270136039 absolute error = 1.391e-05 relative error = 0.001598 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.532 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.32 1.026 h = 0.0001 0.005 y[1] (numeric) = 0.702001778691 0.518677734259 y[1] (closed_form) = 0.702002136195 0.518692971128 absolute error = 1.524e-05 relative error = 0.001746 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.537 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = 0.7014559429 0.521247250989 y[1] (closed_form) = 0.70145644642 0.521261635469 absolute error = 1.439e-05 relative error = 0.001647 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.539 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3202 1.034 h = 0.001 0.001 y[1] (numeric) = 0.701147322956 0.522793553296 y[1] (closed_form) = 0.701148159534 0.522807878458 absolute error = 1.435e-05 relative error = 0.001641 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2305.0MB, alloc=52.3MB, time=28.32 x[1] = 0.3212 1.035 h = 0.001 0.003 y[1] (numeric) = 0.701538660176 0.523425175921 y[1] (closed_form) = 0.701539649642 0.523439416476 absolute error = 1.427e-05 relative error = 0.001631 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.541 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = 0.701689943434 0.525080220229 y[1] (closed_form) = 0.701690614412 0.525094620394 absolute error = 1.442e-05 relative error = 0.001645 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.544 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3223 1.042 h = 0.003 0.006 y[1] (numeric) = 0.701258927768 0.527139544334 y[1] (closed_form) = 0.701259342674 0.527153782291 absolute error = 1.424e-05 relative error = 0.001624 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.545 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = 0.702068141265 0.530573817877 y[1] (closed_form) = 0.702068560928 0.530589385493 absolute error = 1.557e-05 relative error = 0.00177 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.551 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = 0.701510567209 0.53314828973 y[1] (closed_form) = 0.701511130758 0.533163006843 absolute error = 1.473e-05 relative error = 0.001671 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.553 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2350.4MB, alloc=52.3MB, time=28.88 x[1] = 0.3255 1.056 h = 0.001 0.001 y[1] (numeric) = 0.701194945732 0.534697663492 y[1] (closed_form) = 0.701195841361 0.534712320756 absolute error = 1.468e-05 relative error = 0.001665 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.554 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3265 1.057 h = 0.001 0.003 y[1] (numeric) = 0.701584863584 0.535332596119 y[1] (closed_form) = 0.701585911534 0.535347168679 absolute error = 1.461e-05 relative error = 0.001656 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.555 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = 0.701729998456 0.536992839401 y[1] (closed_form) = 0.701730729064 0.537007571814 absolute error = 1.475e-05 relative error = 0.001669 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.558 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3276 1.064 h = 0.003 0.006 y[1] (numeric) = 0.701289625526 0.539056180926 y[1] (closed_form) = 0.701290100391 0.539070752071 absolute error = 1.458e-05 relative error = 0.001648 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.559 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = 0.70208750827 0.542503216565 y[1] (closed_form) = 0.702087990583 0.54251911393 absolute error = 1.590e-05 relative error = 0.001793 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.564 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2396.0MB, alloc=52.3MB, time=29.44 x[1] = 0.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = 0.701518236248 0.545082654746 y[1] (closed_form) = 0.701518860359 0.545097703512 absolute error = 1.506e-05 relative error = 0.001695 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.567 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3308 1.078 h = 0.001 0.001 y[1] (numeric) = 0.701195637541 0.546635106291 y[1] (closed_form) = 0.701196592753 0.546650094693 absolute error = 1.502e-05 relative error = 0.001689 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.568 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = 0.701584146413 0.547273343263 y[1] (closed_form) = 0.701585253381 0.547288246873 absolute error = 1.494e-05 relative error = 0.00168 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.569 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3319 1.083 h = 0.003 0.006 y[1] (numeric) = 0.701136138718 0.549339962049 y[1] (closed_form) = 0.701136548422 0.549354781933 absolute error = 1.483e-05 relative error = 0.001664 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.571 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = 0.701924160557 0.552797840695 y[1] (closed_form) = 0.701924580016 0.55281398386 absolute error = 1.615e-05 relative error = 0.001807 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.576 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2441.6MB, alloc=52.3MB, time=30.00 x[1] = 0.335 1.094 h = 0.0001 0.003 y[1] (numeric) = 0.701344792171 0.555381423525 y[1] (closed_form) = 0.701345351638 0.555396719716 absolute error = 1.531e-05 relative error = 0.001711 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.579 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3351 1.097 h = 0.001 0.001 y[1] (numeric) = 0.701016170342 0.55693644638 y[1] (closed_form) = 0.701017060072 0.556951681767 absolute error = 1.526e-05 relative error = 0.001705 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3361 1.098 h = 0.001 0.003 y[1] (numeric) = 0.701403435348 0.557577506394 y[1] (closed_form) = 0.701404476352 0.557592656914 absolute error = 1.519e-05 relative error = 0.001695 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.581 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = 0.701537137746 0.55924734853 y[1] (closed_form) = 0.701537863526 0.55926265932 absolute error = 1.533e-05 relative error = 0.001708 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.583 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3372 1.105 h = 0.003 0.006 y[1] (numeric) = 0.701079390867 0.561318077391 y[1] (closed_form) = 0.701079861533 0.561333228638 absolute error = 1.516e-05 relative error = 0.001688 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.585 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2487.3MB, alloc=52.3MB, time=30.56 x[1] = 0.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = 0.701856184078 0.564788699354 y[1] (closed_form) = 0.701856667068 0.564805170417 absolute error = 1.648e-05 relative error = 0.001829 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.591 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = 0.701265192286 0.567377268171 y[1] (closed_form) = 0.701265813268 0.567392894194 absolute error = 1.564e-05 relative error = 0.001734 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.593 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3404 1.119 h = 0.001 0.001 y[1] (numeric) = 0.700929638178 0.568935379872 y[1] (closed_form) = 0.700930588444 0.568950944607 absolute error = 1.559e-05 relative error = 0.001727 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.594 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3414 1.12 h = 0.001 0.003 y[1] (numeric) = 0.701315513209 0.569579733549 y[1] (closed_form) = 0.70131661419 0.569595213345 absolute error = 1.552e-05 relative error = 0.001718 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.595 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = 0.701443142276 0.571254771392 y[1] (closed_form) = 0.701443929166 0.571270411651 absolute error = 1.566e-05 relative error = 0.001731 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.598 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2532.9MB, alloc=52.3MB, time=31.11 x[1] = 0.3425 1.127 h = 0.003 0.006 y[1] (numeric) = 0.700976130105 0.57332954123 y[1] (closed_form) = 0.700976662239 0.573345022856 absolute error = 1.549e-05 relative error = 0.001711 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.6 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = 0.701741748779 0.576812895098 y[1] (closed_form) = 0.701742295743 0.576829693064 absolute error = 1.681e-05 relative error = 0.00185 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.605 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = 0.701139173534 0.579406459334 y[1] (closed_form) = 0.701139856516 0.579422414206 absolute error = 1.597e-05 relative error = 0.001756 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.607 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3457 1.141 h = 0.001 0.001 y[1] (numeric) = 0.700796711223 0.580967665147 y[1] (closed_form) = 0.700797722509 0.580983558264 absolute error = 1.593e-05 relative error = 0.001749 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.608 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3467 1.142 h = 0.001 0.003 y[1] (numeric) = 0.701181206248 0.581615306539 y[1] (closed_form) = 0.701182367692 0.581631114653 absolute error = 1.585e-05 relative error = 0.00174 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2578.4MB, alloc=52.3MB, time=31.67 x[1] = 0.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = 0.701302787844 0.583295538168 y[1] (closed_form) = 0.701303636325 0.583311506921 absolute error = 1.599e-05 relative error = 0.001753 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.612 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3478 1.149 h = 0.003 0.006 y[1] (numeric) = 0.700826542361 0.585374356141 y[1] (closed_form) = 0.700827136454 0.585390167159 absolute error = 1.582e-05 relative error = 0.001733 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.614 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = 0.701581040074 0.58887042985 y[1] (closed_form) = 0.701581651442 0.588887553723 absolute error = 1.713e-05 relative error = 0.001871 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.619 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = 0.700966921193 0.591468998339 y[1] (closed_form) = 0.700967666641 0.591485281078 absolute error = 1.630e-05 relative error = 0.001777 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.622 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.351 1.163 h = 0.001 0.001 y[1] (numeric) = 0.700617574667 0.593033303174 y[1] (closed_form) = 0.700618647439 0.593049523707 absolute error = 1.626e-05 relative error = 0.001771 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.623 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2623.8MB, alloc=52.3MB, time=32.23 x[1] = 0.352 1.164 h = 0.001 0.003 y[1] (numeric) = 0.701000699507 0.593684226238 y[1] (closed_form) = 0.701001921883 0.593700361712 absolute error = 1.618e-05 relative error = 0.001762 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.624 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.353 1.167 h = 0.0001 0.004 y[1] (numeric) = 0.701116259295 0.5953696494 y[1] (closed_form) = 0.701117169832 0.595385945672 absolute error = 1.632e-05 relative error = 0.001774 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.626 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3531 1.171 h = 0.003 0.006 y[1] (numeric) = 0.700630812364 0.59745252219 y[1] (closed_form) = 0.70063146889 0.597468661616 absolute error = 1.615e-05 relative error = 0.001754 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.628 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = 0.701374242178 0.600961303044 y[1] (closed_form) = 0.701374918359 0.600978751829 absolute error = 1.746e-05 relative error = 0.001891 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.634 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = 0.70074861933 0.603564884032 y[1] (closed_form) = 0.700749427694 0.603581493656 absolute error = 1.663e-05 relative error = 0.001798 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.636 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2669.3MB, alloc=52.3MB, time=32.78 x[1] = 0.3563 1.185 h = 0.001 0.001 y[1] (numeric) = 0.700392412482 0.605132292449 y[1] (closed_form) = 0.700393547191 0.605148839432 absolute error = 1.659e-05 relative error = 0.001792 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.637 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = 0.700774176815 0.605786491054 y[1] (closed_form) = 0.700775460577 0.605802952929 absolute error = 1.651e-05 relative error = 0.001783 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.639 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3574 1.19 h = 0.003 0.006 y[1] (numeric) = 0.700281222098 0.607872670187 y[1] (closed_form) = 0.700281816679 0.607889055787 absolute error = 1.640e-05 relative error = 0.001768 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.641 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = 0.701015015978 0.611392247302 y[1] (closed_form) = 0.701015632257 0.611409939273 absolute error = 1.770e-05 relative error = 0.001903 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.646 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = 0.700379462717 0.61400001265 y[1] (closed_form) = 0.700380209552 0.614016867146 absolute error = 1.687e-05 relative error = 0.001811 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.648 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2714.8MB, alloc=52.3MB, time=33.35 x[1] = 0.3606 1.204 h = 0.001 0.001 y[1] (numeric) = 0.700017332753 0.615570014581 y[1] (closed_form) = 0.700018405097 0.615586806063 absolute error = 1.683e-05 relative error = 0.001805 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.65 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3616 1.205 h = 0.001 0.003 y[1] (numeric) = 0.70039789473 0.616227011635 y[1] (closed_form) = 0.700399115654 0.616243717966 absolute error = 1.675e-05 relative error = 0.001796 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.651 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = 0.700502255192 0.617922016902 y[1] (closed_form) = 0.700503166351 0.617938884302 absolute error = 1.689e-05 relative error = 0.001808 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.654 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3627 1.212 h = 0.003 0.006 y[1] (numeric) = 0.699999722428 0.620012342245 y[1] (closed_form) = 0.700000380293 0.620029054425 absolute error = 1.673e-05 relative error = 0.001789 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.655 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = 0.700722545932 0.623544601873 y[1] (closed_form) = 0.700723227762 0.623562616914 absolute error = 1.803e-05 relative error = 0.001922 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.661 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = 0.700075562026 0.62615739401 y[1] (closed_form) = 0.700076372585 0.626174573569 absolute error = 1.720e-05 relative error = 0.001831 % Correct digits = 5 memory used=2760.4MB, alloc=52.3MB, time=33.90 Radius of convergence (given) for eq 1 = 2.663 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3659 1.226 h = 0.001 0.001 y[1] (numeric) = 0.699706615893 0.62773050738 y[1] (closed_form) = 0.699707750982 0.627747623519 absolute error = 1.715e-05 relative error = 0.001825 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.665 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3669 1.227 h = 0.001 0.003 y[1] (numeric) = 0.700085835061 0.628390768449 y[1] (closed_form) = 0.700087118187 0.628407799404 absolute error = 1.708e-05 relative error = 0.001815 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.666 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = 0.700184246062 0.630090957334 y[1] (closed_form) = 0.70018522053 0.630108149472 absolute error = 1.722e-05 relative error = 0.001828 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.668 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.368 1.234 h = 0.003 0.006 y[1] (numeric) = 0.699672602248 0.632185354448 y[1] (closed_form) = 0.699673323825 0.632202392225 absolute error = 1.705e-05 relative error = 0.001808 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.371 1.24 h = 0.0001 0.005 y[1] (numeric) = 0.700384506959 0.635730282173 y[1] (closed_form) = 0.700385254708 0.635748619294 absolute error = 1.835e-05 relative error = 0.00194 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.676 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2805.9MB, alloc=52.3MB, time=34.46 x[1] = 0.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = 0.69972613163 0.638348107726 y[1] (closed_form) = 0.699727006319 0.63836561137 absolute error = 1.753e-05 relative error = 0.00185 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.678 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3712 1.248 h = 0.001 0.001 y[1] (numeric) = 0.699350392934 0.63992433613 y[1] (closed_form) = 0.699351591178 0.639941775963 absolute error = 1.748e-05 relative error = 0.001844 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3722 1.249 h = 0.001 0.003 y[1] (numeric) = 0.699728278564 0.640587854844 y[1] (closed_form) = 0.699729624301 0.640605209464 absolute error = 1.741e-05 relative error = 0.001835 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.681 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = 0.699820764988 0.64229322388 y[1] (closed_form) = 0.699821803169 0.642310739785 absolute error = 1.755e-05 relative error = 0.001847 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.683 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3733 1.256 h = 0.003 0.006 y[1] (numeric) = 0.699300041494 0.644391697703 y[1] (closed_form) = 0.699300827195 0.644409060092 absolute error = 1.738e-05 relative error = 0.001828 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.685 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2851.4MB, alloc=52.3MB, time=35.02 x[1] = 0.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = 0.700001078472 0.647949278542 y[1] (closed_form) = 0.700001892493 0.647967936753 absolute error = 1.868e-05 relative error = 0.001958 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.691 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = 0.699331350772 0.650572143594 y[1] (closed_form) = 0.69933228998 0.650589970345 absolute error = 1.785e-05 relative error = 0.001869 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.693 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3765 1.27 h = 0.001 0.001 y[1] (numeric) = 0.698948843014 0.652151490302 y[1] (closed_form) = 0.698950104802 0.652169252865 absolute error = 1.781e-05 relative error = 0.001863 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.695 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3775 1.271 h = 0.001 0.003 y[1] (numeric) = 0.699325404231 0.652818260213 y[1] (closed_form) = 0.699326812974 0.652835937543 absolute error = 1.773e-05 relative error = 0.001854 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.696 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = 0.69941199076 0.654528805641 y[1] (closed_form) = 0.699413093043 0.654546644342 absolute error = 1.787e-05 relative error = 0.001866 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.698 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2897.0MB, alloc=52.3MB, time=35.58 x[1] = 0.3786 1.278 h = 0.003 0.006 y[1] (numeric) = 0.698882218812 0.656631360677 y[1] (closed_form) = 0.698883069034 0.656649046697 absolute error = 1.771e-05 relative error = 0.001846 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = 0.699572438595 0.660201579097 y[1] (closed_form) = 0.699573319228 0.660220557414 absolute error = 1.900e-05 relative error = 0.001975 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.706 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = 0.6988913974 0.662829489201 y[1] (closed_form) = 0.698892401504 0.662847638081 absolute error = 1.818e-05 relative error = 0.001887 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.708 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3818 1.292 h = 0.001 0.001 y[1] (numeric) = 0.698502143968 0.664411957165 y[1] (closed_form) = 0.698503469678 0.664430041496 absolute error = 1.813e-05 relative error = 0.001881 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = 0.69887738976 0.665081971753 y[1] (closed_form) = 0.698878861888 0.665099970837 absolute error = 1.806e-05 relative error = 0.001872 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.711 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2942.7MB, alloc=52.3MB, time=36.14 x[1] = 0.3829 1.297 h = 0.003 0.006 y[1] (numeric) = 0.698340234621 0.667187853369 y[1] (closed_form) = 0.698341025844 0.667205782885 absolute error = 1.795e-05 relative error = 0.001858 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.713 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = 0.69902103312 0.670768808908 y[1] (closed_form) = 0.699021856549 0.670788027706 absolute error = 1.924e-05 relative error = 0.001986 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.719 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.386 1.308 h = 0.0001 0.003 y[1] (numeric) = 0.69833022446 0.673400931532 y[1] (closed_form) = 0.698331169887 0.673419322621 absolute error = 1.842e-05 relative error = 0.001898 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.721 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3861 1.311 h = 0.001 0.001 y[1] (numeric) = 0.697935145996 0.674986008319 y[1] (closed_form) = 0.697936412198 0.675004334549 absolute error = 1.837e-05 relative error = 0.001892 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.723 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3871 1.312 h = 0.001 0.003 y[1] (numeric) = 0.69830922806 0.675658795015 y[1] (closed_form) = 0.698310640221 0.675677035985 absolute error = 1.830e-05 relative error = 0.001883 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.724 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2988.2MB, alloc=52.3MB, time=36.70 x[1] = 0.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = 0.698384839693 0.677378891925 y[1] (closed_form) = 0.698385947418 0.677397294401 absolute error = 1.844e-05 relative error = 0.001895 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.726 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3882 1.319 h = 0.003 0.006 y[1] (numeric) = 0.697838264573 0.679488944786 y[1] (closed_form) = 0.697839121029 0.679507196113 absolute error = 1.827e-05 relative error = 0.001876 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.728 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = 0.698508338731 0.683082508183 y[1] (closed_form) = 0.698509229376 0.683102045261 absolute error = 1.956e-05 relative error = 0.002002 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.734 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = 0.697806288376 0.685719685266 y[1] (closed_form) = 0.69780729937 0.685738396674 absolute error = 1.874e-05 relative error = 0.001915 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.736 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3914 1.333 h = 0.001 0.001 y[1] (numeric) = 0.697404507427 0.687307888258 y[1] (closed_form) = 0.697405838226 0.687326534471 absolute error = 1.869e-05 relative error = 0.001909 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.738 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3033.7MB, alloc=52.3MB, time=37.26 x[1] = 0.3924 1.334 h = 0.001 0.003 y[1] (numeric) = 0.697777290497 0.687983907416 y[1] (closed_form) = 0.697778766725 0.68800246837 absolute error = 1.862e-05 relative error = 0.0019 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.739 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = 0.697847071747 0.689709168693 y[1] (closed_form) = 0.697848244618 0.689727891199 absolute error = 1.876e-05 relative error = 0.001912 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.742 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3935 1.341 h = 0.003 0.006 y[1] (numeric) = 0.697291536654 0.691823313723 y[1] (closed_form) = 0.697292458696 0.691841885885 absolute error = 1.860e-05 relative error = 0.001893 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.744 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = 0.697950935524 0.695429467957 y[1] (closed_form) = 0.697951893684 0.695449322335 absolute error = 1.988e-05 relative error = 0.002017 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.749 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = 0.697237681824 0.698071703585 y[1] (closed_form) = 0.69723875872 0.69809073434 absolute error = 1.906e-05 relative error = 0.001932 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.752 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3079.3MB, alloc=52.3MB, time=37.82 x[1] = 0.3967 1.355 h = 0.001 0.001 y[1] (numeric) = 0.696829221449 0.69966303486 y[1] (closed_form) = 0.69683061718 0.6996820001 absolute error = 1.902e-05 relative error = 0.001926 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.753 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3977 1.356 h = 0.001 0.003 y[1] (numeric) = 0.697200714117 0.700342279768 y[1] (closed_form) = 0.697202254752 0.700361159753 absolute error = 1.894e-05 relative error = 0.001917 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.755 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = 0.697264688863 0.702072700585 y[1] (closed_form) = 0.697265927213 0.702091742154 absolute error = 1.908e-05 relative error = 0.001928 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.757 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3988 1.363 h = 0.003 0.006 y[1] (numeric) = 0.696700224447 0.704190940708 y[1] (closed_form) = 0.696701212415 0.704209832728 absolute error = 1.892e-05 relative error = 0.00191 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.759 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = 0.697348996562 0.707809668268 y[1] (closed_form) = 0.697350022522 0.70782983897 absolute error = 2.020e-05 relative error = 0.002033 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.765 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3124.8MB, alloc=52.3MB, time=38.38 x[1] = 0.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = 0.696624577675 0.710456966035 y[1] (closed_form) = 0.696625720791 0.710476315167 absolute error = 1.938e-05 relative error = 0.001948 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.767 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.402 1.377 h = 0.001 0.001 y[1] (numeric) = 0.69620946081 0.712051427382 y[1] (closed_form) = 0.696210921797 0.712070710691 absolute error = 1.934e-05 relative error = 0.001942 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.769 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.403 1.378 h = 0.001 0.003 y[1] (numeric) = 0.696579671533 0.712733891263 y[1] (closed_form) = 0.6965812769 0.712753089329 absolute error = 1.927e-05 relative error = 0.001933 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.77 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.404 1.381 h = 0.0001 0.004 y[1] (numeric) = 0.696637863443 0.714469466536 y[1] (closed_form) = 0.696639167591 0.714488826206 absolute error = 1.940e-05 relative error = 0.001944 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.772 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4041 1.385 h = 0.003 0.006 y[1] (numeric) = 0.696064500194 0.716591804286 y[1] (closed_form) = 0.696065554416 0.716611015192 absolute error = 1.924e-05 relative error = 0.001926 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.775 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3170.4MB, alloc=52.3MB, time=38.94 x[1] = 0.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = 0.69670269357 0.720223087189 y[1] (closed_form) = 0.696703787601 0.720243573242 absolute error = 2.052e-05 relative error = 0.002047 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = 0.695967147453 0.72287545021 y[1] (closed_form) = 0.695968357097 0.722895116751 absolute error = 1.970e-05 relative error = 0.001964 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.783 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4073 1.399 h = 0.001 0.001 y[1] (numeric) = 0.695545396912 0.724473043129 y[1] (closed_form) = 0.695546923464 0.724492643554 absolute error = 1.966e-05 relative error = 0.001958 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.784 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4083 1.4 h = 0.003 0.006 y[1] (numeric) = 0.695914334012 0.72515871915 y[1] (closed_form) = 0.695916004423 0.72517823435 absolute error = 1.959e-05 relative error = 0.001949 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.786 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = 0.696546659651 0.728798510616 y[1] (closed_form) = 0.696547305081 0.728819680974 absolute error = 2.118e-05 relative error = 0.002101 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.791 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3215.9MB, alloc=52.3MB, time=39.50 x[1] = 0.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = 0.695803608855 0.731454638696 y[1] (closed_form) = 0.695804368908 0.731474990998 absolute error = 2.037e-05 relative error = 0.002017 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.794 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4115 1.414 h = 0.001 0.001 y[1] (numeric) = 0.69537738719 0.733054552938 y[1] (closed_form) = 0.695378463482 0.733074838955 absolute error = 2.031e-05 relative error = 0.002011 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.795 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4125 1.415 h = 0.001 0.003 y[1] (numeric) = 0.69574553365 0.733742466393 y[1] (closed_form) = 0.695746753448 0.733762667213 absolute error = 2.024e-05 relative error = 0.002001 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.797 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = 0.69579414743 0.735486873965 y[1] (closed_form) = 0.695795067792 0.735507236366 absolute error = 2.038e-05 relative error = 0.002013 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.799 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4136 1.422 h = 0.003 0.006 y[1] (numeric) = 0.69520593599 0.737616355246 y[1] (closed_form) = 0.695206607228 0.737636570172 absolute error = 2.023e-05 relative error = 0.001995 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.801 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3261.5MB, alloc=52.3MB, time=40.06 x[1] = 0.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = 0.695826696361 0.741269051974 y[1] (closed_form) = 0.695827410269 0.74129053604 absolute error = 2.150e-05 relative error = 0.002114 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.807 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = 0.695072582 0.743930248557 y[1] (closed_form) = 0.695073409043 0.743950916634 absolute error = 2.068e-05 relative error = 0.002032 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4168 1.436 h = 0.001 0.001 y[1] (numeric) = 0.694639764902 0.745533295707 y[1] (closed_form) = 0.694640907226 0.745553897227 absolute error = 2.063e-05 relative error = 0.002025 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.811 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4178 1.437 h = 0.001 0.003 y[1] (numeric) = 0.695006651309 0.746224409442 y[1] (closed_form) = 0.695007936624 0.746244925793 absolute error = 2.056e-05 relative error = 0.002016 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.813 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = 0.695049544681 0.747973955999 y[1] (closed_form) = 0.69505053161 0.747994633917 absolute error = 2.070e-05 relative error = 0.002027 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.815 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3307.1MB, alloc=52.3MB, time=40.62 x[1] = 0.4189 1.444 h = 0.003 0.006 y[1] (numeric) = 0.694452515587 0.750107539107 y[1] (closed_form) = 0.694453253863 0.750128070307 absolute error = 2.054e-05 relative error = 0.00201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.817 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = 0.69506282323 0.753772739441 y[1] (closed_form) = 0.695063605853 0.753794536251 absolute error = 2.181e-05 relative error = 0.002127 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.823 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.422 1.455 h = 0.0001 0.003 y[1] (numeric) = 0.694297682702 0.756439006406 y[1] (closed_form) = 0.694298577006 0.756459989297 absolute error = 2.100e-05 relative error = 0.002045 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.825 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4221 1.458 h = 0.001 0.001 y[1] (numeric) = 0.693858292636 0.758045187232 y[1] (closed_form) = 0.693859501265 0.758066103308 absolute error = 2.095e-05 relative error = 0.002039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.827 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4231 1.459 h = 0.001 0.003 y[1] (numeric) = 0.694223926954 0.758739494274 y[1] (closed_form) = 0.694225278065 0.758760325214 absolute error = 2.087e-05 relative error = 0.00203 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.828 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3352.8MB, alloc=52.3MB, time=41.18 x[1] = 0.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = 0.694261122807 0.760494173845 y[1] (closed_form) = 0.694262176572 0.760515166326 absolute error = 2.102e-05 relative error = 0.002041 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.831 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4242 1.466 h = 0.003 0.006 y[1] (numeric) = 0.69365530593 0.76263185996 y[1] (closed_form) = 0.693656111519 0.76265270647 absolute error = 2.086e-05 relative error = 0.002024 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.833 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = 0.694255206952 0.76630954431 y[1] (closed_form) = 0.694256058515 0.766331652901 absolute error = 2.212e-05 relative error = 0.00214 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.839 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = 0.693479077444 0.768980883093 y[1] (closed_form) = 0.693480039267 0.769002179841 absolute error = 2.132e-05 relative error = 0.002059 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.841 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4274 1.48 h = 0.001 0.001 y[1] (numeric) = 0.693033136744 0.770590198099 y[1] (closed_form) = 0.69303441194 0.770611427785 absolute error = 2.127e-05 relative error = 0.002052 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.843 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3398.4MB, alloc=52.3MB, time=41.74 x[1] = 0.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = 0.693397526811 0.771287691426 y[1] (closed_form) = 0.693398943982 0.771308836015 absolute error = 2.119e-05 relative error = 0.002043 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.844 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4285 1.485 h = 0.003 0.006 y[1] (numeric) = 0.692784538869 0.77342871993 y[1] (closed_form) = 0.692785290006 0.773449805009 absolute error = 2.110e-05 relative error = 0.002032 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.847 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = 0.693375370366 0.77711701088 y[1] (closed_form) = 0.693376168879 0.777139355026 absolute error = 2.236e-05 relative error = 0.002147 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.852 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = 0.692589751099 0.779792585834 y[1] (closed_form) = 0.69259065865 0.779814119909 absolute error = 2.155e-05 relative error = 0.002067 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.855 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4317 1.499 h = 0.001 0.001 y[1] (numeric) = 0.692138152278 0.781404521173 y[1] (closed_form) = 0.692139372387 0.781425987972 absolute error = 2.150e-05 relative error = 0.00206 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.857 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3444.0MB, alloc=52.3MB, time=42.30 x[1] = 0.4327 1.5 h = 0.001 0.003 y[1] (numeric) = 0.692501439672 0.782104736794 y[1] (closed_form) = 0.692502801321 0.782126118529 absolute error = 2.143e-05 relative error = 0.002051 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.858 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = 0.692528032999 0.783868883812 y[1] (closed_form) = 0.692529099224 0.78389042702 absolute error = 2.157e-05 relative error = 0.002062 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.86 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4338 1.507 h = 0.003 0.006 y[1] (numeric) = 0.691905894132 0.786014102764 y[1] (closed_form) = 0.691906713074 0.786035501369 absolute error = 2.141e-05 relative error = 0.002045 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.863 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = 0.692486403693 0.789714840741 y[1] (closed_form) = 0.692487271545 0.789737494892 absolute error = 2.267e-05 relative error = 0.002158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.868 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = 0.691689864075 0.792395489478 y[1] (closed_form) = 0.691690839603 0.792417335639 absolute error = 2.187e-05 relative error = 0.002079 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.871 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3489.4MB, alloc=52.3MB, time=42.85 x[1] = 0.437 1.521 h = 0.001 0.001 y[1] (numeric) = 0.691231755829 0.794010559518 y[1] (closed_form) = 0.691233042968 0.794032338179 absolute error = 2.182e-05 relative error = 0.002072 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.873 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.438 1.522 h = 0.001 0.003 y[1] (numeric) = 0.691593813297 0.794713948328 y[1] (closed_form) = 0.691595241477 0.794735641974 absolute error = 2.174e-05 relative error = 0.002064 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.874 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.439 1.525 h = 0.0001 0.004 y[1] (numeric) = 0.6916147735 0.796483210318 y[1] (closed_form) = 0.691615907278 0.796505065379 absolute error = 2.188e-05 relative error = 0.002075 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.877 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4391 1.529 h = 0.003 0.006 y[1] (numeric) = 0.690983931353 0.798632534095 y[1] (closed_form) = 0.69098481834 0.798654245271 absolute error = 2.173e-05 relative error = 0.002058 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.879 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = 0.691554163641 0.802345698375 y[1] (closed_form) = 0.691555101024 0.80236866158 absolute error = 2.298e-05 relative error = 0.00217 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.884 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3535.0MB, alloc=52.3MB, time=43.41 x[1] = 0.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = 0.690746740251 0.805031421117 y[1] (closed_form) = 0.69074778398 0.805053578415 absolute error = 2.218e-05 relative error = 0.002091 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.887 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4423 1.543 h = 0.001 0.001 y[1] (numeric) = 0.690282144536 0.80664962564 y[1] (closed_form) = 0.690283498933 0.806671715227 absolute error = 2.213e-05 relative error = 0.002084 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.889 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4433 1.544 h = 0.001 0.003 y[1] (numeric) = 0.690642979555 0.807356180493 y[1] (closed_form) = 0.690644474495 0.807378185119 absolute error = 2.206e-05 relative error = 0.002076 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.89 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = 0.690658328713 0.809130550643 y[1] (closed_form) = 0.690659530267 0.809152716614 absolute error = 2.220e-05 relative error = 0.002087 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.893 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4444 1.551 h = 0.003 0.006 y[1] (numeric) = 0.69001881249 0.811283979115 y[1] (closed_form) = 0.690019767751 0.81130600191 absolute error = 2.204e-05 relative error = 0.00207 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.895 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = 0.690578811667 0.815009548607 y[1] (closed_form) = 0.690579818761 0.815032819918 absolute error = 2.329e-05 relative error = 0.00218 % Correct digits = 5 memory used=3580.6MB, alloc=52.3MB, time=43.97 Radius of convergence (given) for eq 1 = 2.901 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = 0.689760540867 0.817700345171 y[1] (closed_form) = 0.689761653008 0.817722812661 absolute error = 2.249e-05 relative error = 0.002103 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.903 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4476 1.565 h = 0.001 0.001 y[1] (numeric) = 0.689289479506 0.819321683719 y[1] (closed_form) = 0.689290901373 0.819344083298 absolute error = 2.244e-05 relative error = 0.002096 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.905 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4486 1.566 h = 0.001 0.003 y[1] (numeric) = 0.689649099424 0.820031397428 y[1] (closed_form) = 0.689650661343 0.820053712105 absolute error = 2.237e-05 relative error = 0.002088 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.907 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = 0.689658859411 0.821810868727 y[1] (closed_form) = 0.689660128951 0.821833344668 absolute error = 2.251e-05 relative error = 0.002098 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.909 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4497 1.573 h = 0.003 0.006 y[1] (numeric) = 0.689010698139 0.823968401444 y[1] (closed_form) = 0.689011721889 0.823990734908 absolute error = 2.236e-05 relative error = 0.002081 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.911 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3626.2MB, alloc=52.3MB, time=44.52 x[1] = 0.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = 0.68956050787 0.827706354699 y[1] (closed_form) = 0.689561584844 0.827729933172 absolute error = 2.360e-05 relative error = 0.002191 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.917 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = 0.688731425801 0.830402224505 y[1] (closed_form) = 0.688732606552 0.830425001244 absolute error = 2.281e-05 relative error = 0.002114 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.92 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4529 1.587 h = 0.001 0.001 y[1] (numeric) = 0.688253920478 0.832026696386 y[1] (closed_form) = 0.68825541002 0.832049405026 absolute error = 2.276e-05 relative error = 0.002108 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.922 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = 0.688612332525 0.832739561727 y[1] (closed_form) = 0.688613961628 0.83276218553 absolute error = 2.268e-05 relative error = 0.002099 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.923 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.454 1.592 h = 0.003 0.006 y[1] (numeric) = 0.687957116287 0.834900436884 y[1] (closed_form) = 0.687958087855 0.834923006056 absolute error = 2.259e-05 relative error = 0.002088 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.925 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3671.8MB, alloc=52.3MB, time=45.08 x[1] = 0.457 1.598 h = 0.0001 0.005 y[1] (numeric) = 0.688498042709 0.838648911553 y[1] (closed_form) = 0.688499068703 0.838672722735 absolute error = 2.383e-05 relative error = 0.002196 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.931 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = 0.687659623015 0.841349019276 y[1] (closed_form) = 0.687660751694 0.841372030508 absolute error = 2.304e-05 relative error = 0.00212 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.934 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4572 1.606 h = 0.001 0.001 y[1] (numeric) = 0.687176550897 0.842976111084 y[1] (closed_form) = 0.687177987565 0.842999054052 absolute error = 2.299e-05 relative error = 0.002114 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.935 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4582 1.607 h = 0.001 0.003 y[1] (numeric) = 0.68753389152 0.843691669162 y[1] (closed_form) = 0.68753546733 0.843714527346 absolute error = 2.291e-05 relative error = 0.002105 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.937 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = 0.687533248307 0.845480547205 y[1] (closed_form) = 0.687534533598 0.845503566488 absolute error = 2.306e-05 relative error = 0.002116 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.939 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3717.4MB, alloc=52.3MB, time=45.64 x[1] = 0.4593 1.614 h = 0.003 0.006 y[1] (numeric) = 0.686869028396 0.847645612532 y[1] (closed_form) = 0.686870068835 0.847668490619 absolute error = 2.290e-05 relative error = 0.002099 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.942 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = 0.687399845574 0.851406430652 y[1] (closed_form) = 0.687400941746 0.851430547254 absolute error = 2.414e-05 relative error = 0.002206 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.947 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = 0.686550681287 0.854111609942 y[1] (closed_form) = 0.686551878929 0.854134928683 absolute error = 2.335e-05 relative error = 0.002131 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4625 1.628 h = 0.001 0.001 y[1] (numeric) = 0.686061205209 0.855741833443 y[1] (closed_form) = 0.68606270991 0.855765083751 absolute error = 2.330e-05 relative error = 0.002124 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.952 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4635 1.629 h = 0.001 0.003 y[1] (numeric) = 0.686417351177 0.856460529705 y[1] (closed_form) = 0.686418994537 0.856483695303 absolute error = 2.322e-05 relative error = 0.002116 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.953 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3763.0MB, alloc=52.3MB, time=46.20 x[1] = 0.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = 0.686411180311 0.858254488027 y[1] (closed_form) = 0.686412534142 0.858277814614 absolute error = 2.337e-05 relative error = 0.002126 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.956 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4646 1.636 h = 0.003 0.006 y[1] (numeric) = 0.685738397417 0.860423654952 y[1] (closed_form) = 0.68573950691 0.860446841014 absolute error = 2.321e-05 relative error = 0.00211 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.958 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = 0.686259147616 0.864196794115 y[1] (closed_form) = 0.686260314103 0.864221215204 absolute error = 2.445e-05 relative error = 0.002215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.964 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = 0.685399274241 0.86690704331 y[1] (closed_form) = 0.685400541014 0.866930668626 absolute error = 2.366e-05 relative error = 0.002141 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.967 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4678 1.65 h = 0.001 0.001 y[1] (numeric) = 0.684903415498 0.868540397167 y[1] (closed_form) = 0.684904988403 0.868563953894 absolute error = 2.361e-05 relative error = 0.002134 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.969 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3808.6MB, alloc=52.3MB, time=46.76 x[1] = 0.4688 1.651 h = 0.001 0.003 y[1] (numeric) = 0.685258373698 0.869262224295 y[1] (closed_form) = 0.685260084783 0.86928569639 absolute error = 2.353e-05 relative error = 0.002126 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = 0.685246696257 0.871061255157 y[1] (closed_form) = 0.685248118795 0.871084888122 absolute error = 2.368e-05 relative error = 0.002136 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.972 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4699 1.658 h = 0.003 0.006 y[1] (numeric) = 0.684565378714 0.873234522062 y[1] (closed_form) = 0.684566557432 0.873258015164 absolute error = 2.352e-05 relative error = 0.00212 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.975 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = 0.685076103714 0.877019959551 y[1] (closed_form) = 0.685077340644 0.877044684198 absolute error = 2.476e-05 relative error = 0.002224 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.981 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.473 1.669 h = 0.0001 0.003 y[1] (numeric) = 0.684205556534 0.879735276625 y[1] (closed_form) = 0.684206892595 0.87975920759 absolute error = 2.397e-05 relative error = 0.002151 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.984 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3854.1MB, alloc=52.3MB, time=47.32 x[1] = 0.4731 1.672 h = 0.001 0.001 y[1] (numeric) = 0.683703336281 0.88137175929 y[1] (closed_form) = 0.68370497755 0.881395621518 absolute error = 2.392e-05 relative error = 0.002144 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.985 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4741 1.673 h = 0.001 0.003 y[1] (numeric) = 0.684057113484 0.882096709937 y[1] (closed_form) = 0.684058892458 0.882120487616 absolute error = 2.384e-05 relative error = 0.002136 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.987 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = 0.684039950342 0.883900805426 y[1] (closed_form) = 0.684041441743 0.883924743846 absolute error = 2.398e-05 relative error = 0.002146 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.989 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4752 1.68 h = 0.003 0.006 y[1] (numeric) = 0.6833501263 0.886078170409 y[1] (closed_form) = 0.683351374405 0.886101969619 absolute error = 2.383e-05 relative error = 0.00213 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.991 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = 0.683850867403 0.889875883206 y[1] (closed_form) = 0.683852174895 0.889900910487 absolute error = 2.506e-05 relative error = 0.002233 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.997 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3899.7MB, alloc=52.3MB, time=47.88 x[1] = 0.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = 0.682969681474 0.892596265782 y[1] (closed_form) = 0.682971086967 0.892620501471 absolute error = 2.428e-05 relative error = 0.00216 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4784 1.694 h = 0.001 0.001 y[1] (numeric) = 0.682461120727 0.894235875497 y[1] (closed_form) = 0.682462830511 0.894260042312 absolute error = 2.423e-05 relative error = 0.002154 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.002 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = 0.682813723587 0.89496394229 y[1] (closed_form) = 0.682815570604 0.894988024644 absolute error = 2.415e-05 relative error = 0.002146 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.003 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4795 1.699 h = 0.003 0.006 y[1] (numeric) = 0.682116957247 0.897144643829 y[1] (closed_form) = 0.682118155224 0.897168675855 absolute error = 2.406e-05 relative error = 0.002135 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.006 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = 0.68260899141 0.900952785881 y[1] (closed_form) = 0.682610249793 0.900978043008 absolute error = 2.529e-05 relative error = 0.002237 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.012 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3945.2MB, alloc=52.3MB, time=48.44 x[1] = 0.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = 0.681718615601 0.903677400344 y[1] (closed_form) = 0.681719971013 0.903701867664 absolute error = 2.450e-05 relative error = 0.002165 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.015 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4827 1.713 h = 0.001 0.001 y[1] (numeric) = 0.681204576675 0.905319624965 y[1] (closed_form) = 0.68120623559 0.905344023291 absolute error = 2.445e-05 relative error = 0.002158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.016 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4837 1.714 h = 0.001 0.003 y[1] (numeric) = 0.681556136944 0.906050354226 y[1] (closed_form) = 0.681557932688 0.906074668163 absolute error = 2.438e-05 relative error = 0.00215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.018 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = 0.681528760957 0.907863787403 y[1] (closed_form) = 0.681530270925 0.907888261828 absolute error = 2.452e-05 relative error = 0.00216 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4848 1.721 h = 0.003 0.006 y[1] (numeric) = 0.680823133856 0.910048671398 y[1] (closed_form) = 0.680824401502 0.91007300781 absolute error = 2.437e-05 relative error = 0.002144 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.023 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3990.7MB, alloc=52.3MB, time=48.99 x[1] = 0.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = 0.681305259995 0.913869045645 y[1] (closed_form) = 0.681306589143 0.9138946037 absolute error = 2.559e-05 relative error = 0.002245 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.028 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = 0.680404310099 0.916598720692 y[1] (closed_form) = 0.6804057352 0.916623491028 absolute error = 2.481e-05 relative error = 0.002173 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.031 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.488 1.735 h = 0.001 0.001 y[1] (numeric) = 0.679883969441 0.918244068799 y[1] (closed_form) = 0.679885697133 0.918268770024 absolute error = 2.476e-05 relative error = 0.002167 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.033 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.489 1.736 h = 0.001 0.003 y[1] (numeric) = 0.680234367541 0.918977900497 y[1] (closed_form) = 0.680236231597 0.919002517427 absolute error = 2.469e-05 relative error = 0.002159 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.035 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.49 1.739 h = 0.0001 0.004 y[1] (numeric) = 0.680201564553 0.920796374993 y[1] (closed_form) = 0.680203143789 0.920821152256 absolute error = 2.483e-05 relative error = 0.002169 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.037 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4036.2MB, alloc=52.3MB, time=49.56 x[1] = 0.4901 1.743 h = 0.003 0.006 y[1] (numeric) = 0.67948751051 0.922985350442 y[1] (closed_form) = 0.679488847955 0.923009990319 absolute error = 2.468e-05 relative error = 0.002153 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.04 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = 0.679959768579 0.926817933062 y[1] (closed_form) = 0.679961168584 0.926843791132 absolute error = 2.590e-05 relative error = 0.002253 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.045 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = 0.679048279006 0.929552665353 y[1] (closed_form) = 0.679049773913 0.929577737792 absolute error = 2.512e-05 relative error = 0.002182 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.048 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4933 1.757 h = 0.001 0.001 y[1] (numeric) = 0.678521657234 0.931201134617 y[1] (closed_form) = 0.678523453825 0.931226137837 absolute error = 2.507e-05 relative error = 0.002176 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.05 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4943 1.758 h = 0.001 0.003 y[1] (numeric) = 0.6788708995 0.931938061311 y[1] (closed_form) = 0.678872831993 0.931962980335 absolute error = 2.499e-05 relative error = 0.002168 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.052 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4081.8MB, alloc=52.3MB, time=50.12 x[1] = 0.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = 0.678832689612 0.933761568588 y[1] (closed_form) = 0.678834338233 0.933786647781 absolute error = 2.513e-05 relative error = 0.002177 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.054 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4954 1.765 h = 0.003 0.006 y[1] (numeric) = 0.678110236072 0.935954632551 y[1] (closed_form) = 0.678111643438 0.935979574978 absolute error = 2.498e-05 relative error = 0.002161 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.057 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = 0.678572665565 0.939799399464 y[1] (closed_form) = 0.678574136507 0.939825556642 absolute error = 2.620e-05 relative error = 0.00226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.062 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = 0.677650670494 0.942539185339 y[1] (closed_form) = 0.677652235314 0.942564558972 absolute error = 2.542e-05 relative error = 0.00219 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.065 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4986 1.779 h = 0.001 0.001 y[1] (numeric) = 0.677117788088 0.944190773243 y[1] (closed_form) = 0.67711965369 0.944216077557 absolute error = 2.537e-05 relative error = 0.002184 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.067 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4127.3MB, alloc=52.3MB, time=50.67 x[1] = 0.4996 1.78 h = 0.001 0.003 y[1] (numeric) = 0.677465880746 0.944930787471 y[1] (closed_form) = 0.677467881791 0.944956007692 absolute error = 2.530e-05 relative error = 0.002176 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.069 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = 0.67742228386 0.946759318843 y[1] (closed_form) = 0.677424001974 0.946784699062 absolute error = 2.544e-05 relative error = 0.002185 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.071 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5007 1.787 h = 0.003 0.006 y[1] (numeric) = 0.676691458085 0.948956468129 y[1] (closed_form) = 0.676692935484 0.948981712192 absolute error = 2.529e-05 relative error = 0.00217 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.074 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = 0.677144098035 0.952813395003 y[1] (closed_form) = 0.677145639987 0.952839850386 absolute error = 2.650e-05 relative error = 0.002267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.08 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = 0.676211631418 0.955558230491 y[1] (closed_form) = 0.676213266251 0.955583904413 absolute error = 2.573e-05 relative error = 0.002198 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.083 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4172.9MB, alloc=52.3MB, time=51.23 x[1] = 0.5039 1.801 h = 0.001 0.001 y[1] (numeric) = 0.675672508718 0.957212934331 y[1] (closed_form) = 0.675674443432 0.957238538845 absolute error = 2.568e-05 relative error = 0.002192 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.084 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = 0.676019457887 0.957956028614 y[1] (closed_form) = 0.67602152759 0.957981549141 absolute error = 2.560e-05 relative error = 0.002184 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.086 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.505 1.806 h = 0.003 0.006 y[1] (numeric) = 0.675281798976 0.960156503299 y[1] (closed_form) = 0.675283228099 0.960181977271 absolute error = 2.551e-05 relative error = 0.002174 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.088 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.508 1.812 h = 0.0001 0.005 y[1] (numeric) = 0.675725898874 0.964023761407 y[1] (closed_form) = 0.675727393401 0.964050443765 absolute error = 2.672e-05 relative error = 0.00227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.094 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = 0.674784385632 0.966772815829 y[1] (closed_form) = 0.674785972178 0.966798718507 absolute error = 2.595e-05 relative error = 0.002201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.097 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4218.5MB, alloc=52.3MB, time=51.79 x[1] = 0.5082 1.82 h = 0.001 0.001 y[1] (numeric) = 0.674239870604 0.968430125455 y[1] (closed_form) = 0.674241756262 0.968455958644 absolute error = 2.590e-05 relative error = 0.002195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.099 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5092 1.821 h = 0.001 0.003 y[1] (numeric) = 0.674585803748 0.969175851419 y[1] (closed_form) = 0.674587824004 0.969201600712 absolute error = 2.583e-05 relative error = 0.002187 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = 0.674532175618 0.971013644233 y[1] (closed_form) = 0.674533914679 0.971039553193 absolute error = 2.597e-05 relative error = 0.002196 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5103 1.828 h = 0.003 0.006 y[1] (numeric) = 0.673785794431 0.973218287049 y[1] (closed_form) = 0.673787293779 0.973244060972 absolute error = 2.582e-05 relative error = 0.002181 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.105 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = 0.674220176509 0.977097659666 y[1] (closed_form) = 0.674221742168 0.977124638562 absolute error = 2.702e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.111 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4264.1MB, alloc=52.3MB, time=52.35 x[1] = 0.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = 0.673268254348 0.979851755904 y[1] (closed_form) = 0.673269911074 0.979877957199 absolute error = 2.625e-05 relative error = 0.002208 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.114 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5135 1.842 h = 0.001 0.001 y[1] (numeric) = 0.672717536537 0.981512176201 y[1] (closed_form) = 0.672719491483 0.981538307935 absolute error = 2.620e-05 relative error = 0.002202 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.116 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5145 1.843 h = 0.001 0.003 y[1] (numeric) = 0.673062337386 0.982260968328 y[1] (closed_form) = 0.673064426484 0.982287016279 absolute error = 2.613e-05 relative error = 0.002195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.118 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = 0.673003378224 0.984103759838 y[1] (closed_form) = 0.673005187047 0.984129967262 absolute error = 2.627e-05 relative error = 0.002203 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5156 1.85 h = 0.003 0.006 y[1] (numeric) = 0.672248701822 0.986312477828 y[1] (closed_form) = 0.672250271479 0.9863385508 absolute error = 2.612e-05 relative error = 0.002188 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.123 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = 0.672673403829 0.990203939957 memory used=4309.7MB, alloc=52.3MB, time=52.91 y[1] (closed_form) = 0.672675040666 0.990231214499 absolute error = 2.732e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.129 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = 0.671711106051 0.992963073185 y[1] (closed_form) = 0.67171283303 0.992989572205 absolute error = 2.656e-05 relative error = 0.002215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5188 1.864 h = 0.001 0.001 y[1] (numeric) = 0.671154205398 0.994626600946 y[1] (closed_form) = 0.671156229709 0.99465303034 absolute error = 2.651e-05 relative error = 0.002209 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.134 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5198 1.865 h = 0.001 0.003 y[1] (numeric) = 0.671497879774 0.995378451712 y[1] (closed_form) = 0.671500037792 0.995404797441 absolute error = 2.643e-05 relative error = 0.002201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.135 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = 0.671433608734 0.997226232698 y[1] (closed_form) = 0.671435487392 0.997252737699 absolute error = 2.657e-05 relative error = 0.00221 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.137 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5209 1.872 h = 0.003 0.006 y[1] (numeric) = 0.67067066367 0.999439021754 y[1] (closed_form) = 0.670672303711 0.999465392879 absolute error = 2.642e-05 relative error = 0.002195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4355.2MB, alloc=52.3MB, time=53.47 x[1] = 0.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = 0.671085722914 1.00334254818 y[1] (closed_form) = 0.671087430968 1.00337011749 absolute error = 2.762e-05 relative error = 0.002288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.146 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.524 1.883 h = 0.0001 0.003 y[1] (numeric) = 0.670113082595 1.0061067133 y[1] (closed_form) = 0.67011487989 1.00613350915 absolute error = 2.686e-05 relative error = 0.002222 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.149 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5241 1.886 h = 0.001 0.001 y[1] (numeric) = 0.669550018903 1.00777334515 y[1] (closed_form) = 0.669552112646 1.00780007132 absolute error = 2.681e-05 relative error = 0.002216 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5251 1.887 h = 0.001 0.003 y[1] (numeric) = 0.669892572524 1.00852824701 y[1] (closed_form) = 0.669894799534 1.00855488964 absolute error = 2.674e-05 relative error = 0.002208 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.152 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = 0.66982300857 1.01038100813 y[1] (closed_form) = 0.669824957128 1.01040780982 absolute error = 2.687e-05 relative error = 0.002217 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.155 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4400.8MB, alloc=52.3MB, time=54.03 x[1] = 0.5262 1.894 h = 0.003 0.006 y[1] (numeric) = 0.669051821215 1.01259786392 y[1] (closed_form) = 0.669053531707 1.01262453231 absolute error = 2.672e-05 relative error = 0.002202 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.157 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = 0.669457274567 1.01651342923 y[1] (closed_form) = 0.66945905387 1.01654129242 absolute error = 2.792e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.163 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = 0.668474324557 1.01928262085 y[1] (closed_form) = 0.668476192223 1.01930971265 absolute error = 2.716e-05 relative error = 0.002228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.166 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5294 1.908 h = 0.001 0.001 y[1] (numeric) = 0.667905117488 1.02095235325 y[1] (closed_form) = 0.667907280723 1.02097937533 absolute error = 2.711e-05 relative error = 0.002222 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.168 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = 0.668246555974 1.02171029867 y[1] (closed_form) = 0.668248852037 1.02173723733 absolute error = 2.704e-05 relative error = 0.002215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4446.4MB, alloc=52.3MB, time=54.59 x[1] = 0.5305 1.913 h = 0.003 0.006 y[1] (numeric) = 0.667468641123 1.02393046403 y[1] (closed_form) = 0.667470305006 1.02395735942 absolute error = 2.695e-05 relative error = 0.002205 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.172 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = 0.667865712247 1.02785625768 y[1] (closed_form) = 0.66786744564 1.02788434497 absolute error = 2.814e-05 relative error = 0.002296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = 0.666873854347 1.03062964914 y[1] (closed_form) = 0.666875675341 1.03065696682 absolute error = 2.738e-05 relative error = 0.00223 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.181 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5337 1.927 h = 0.001 0.001 y[1] (numeric) = 0.666299338032 1.03230197458 y[1] (closed_form) = 0.666301453843 1.03232922249 absolute error = 2.733e-05 relative error = 0.002224 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.183 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5347 1.928 h = 0.001 0.003 y[1] (numeric) = 0.666639784937 1.03306252054 y[1] (closed_form) = 0.666642033201 1.03308968514 absolute error = 2.726e-05 relative error = 0.002217 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.185 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4492.0MB, alloc=52.3MB, time=55.15 x[1] = 0.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = 0.666560362879 1.03492446071 y[1] (closed_form) = 0.666562334365 1.03495178397 absolute error = 2.739e-05 relative error = 0.002225 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.187 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5358 1.935 h = 0.003 0.006 y[1] (numeric) = 0.665773859794 1.03714877402 y[1] (closed_form) = 0.665775594239 1.03717596502 absolute error = 2.725e-05 relative error = 0.002211 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = 0.666161392799 1.04108655917 y[1] (closed_form) = 0.666163197487 1.04111493871 absolute error = 2.844e-05 relative error = 0.002301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.196 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = 0.6651592858 1.04386496679 y[1] (closed_form) = 0.665161177255 1.04389257879 absolute error = 2.768e-05 relative error = 0.002236 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.199 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.539 1.949 h = 0.001 0.001 y[1] (numeric) = 0.664578662376 1.04554038602 y[1] (closed_form) = 0.664580847777 1.04556792822 absolute error = 2.763e-05 relative error = 0.00223 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.201 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4537.5MB, alloc=52.3MB, time=55.70 x[1] = 0.54 1.95 h = 0.001 0.003 y[1] (numeric) = 0.664918004429 1.04630396153 y[1] (closed_form) = 0.664920321852 1.04633142054 absolute error = 2.756e-05 relative error = 0.002223 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.202 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.541 1.953 h = 0.0001 0.004 y[1] (numeric) = 0.664833342789 1.04817085464 y[1] (closed_form) = 0.664835384323 1.04819847209 absolute error = 2.769e-05 relative error = 0.002231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.205 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5411 1.957 h = 0.003 0.006 y[1] (numeric) = 0.664038671906 1.05039922143 y[1] (closed_form) = 0.664040476955 1.05042670717 absolute error = 2.754e-05 relative error = 0.002217 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.207 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = 0.664416702443 1.05434897211 y[1] (closed_form) = 0.664418578436 1.05437764304 absolute error = 2.873e-05 relative error = 0.002305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = 0.663404378551 1.05713238976 y[1] (closed_form) = 0.663406340498 1.05716029521 absolute error = 2.797e-05 relative error = 0.002241 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.217 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4583.1MB, alloc=52.3MB, time=56.26 x[1] = 0.5443 1.971 h = 0.001 0.001 y[1] (numeric) = 0.662817667289 1.05881089879 y[1] (closed_form) = 0.662819922315 1.05883873441 absolute error = 2.793e-05 relative error = 0.002236 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.218 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5453 1.972 h = 0.001 0.003 y[1] (numeric) = 0.663155909832 1.05957749628 y[1] (closed_form) = 0.663158296453 1.05960524884 absolute error = 2.785e-05 relative error = 0.002228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = 0.663066026856 1.06144933255 y[1] (closed_form) = 0.663068138469 1.06147724332 absolute error = 2.799e-05 relative error = 0.002236 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.222 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5464 1.979 h = 0.003 0.006 y[1] (numeric) = 0.662263213844 1.06368174767 y[1] (closed_form) = 0.662265089533 1.06370952726 absolute error = 2.784e-05 relative error = 0.002222 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.225 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = 0.662631777148 1.06764343775 y[1] (closed_form) = 0.662633724446 1.06767239919 absolute error = 2.903e-05 relative error = 0.00231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.231 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4628.8MB, alloc=52.3MB, time=56.82 x[1] = 0.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = 0.661609268345 1.07043185904 y[1] (closed_form) = 0.661611300808 1.07046005707 absolute error = 2.827e-05 relative error = 0.002247 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.234 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5496 1.993 h = 0.001 0.001 y[1] (numeric) = 0.661016488378 1.07211345375 y[1] (closed_form) = 0.661018813058 1.07214158193 absolute error = 2.822e-05 relative error = 0.002241 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.236 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5506 1.994 h = 0.001 0.003 y[1] (numeric) = 0.661353636656 1.07288306563 y[1] (closed_form) = 0.661356092507 1.07291111089 absolute error = 2.815e-05 relative error = 0.002234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.238 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = 0.66125855041 1.07475983515 y[1] (closed_form) = 0.661260732127 1.07478803837 absolute error = 2.829e-05 relative error = 0.002242 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5517 2.001 h = 0.003 0.006 y[1] (numeric) = 0.660447620759 1.07699629327 y[1] (closed_form) = 0.660449567113 1.07702436585 absolute error = 2.814e-05 relative error = 0.002227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.243 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4674.4MB, alloc=52.3MB, time=57.38 x[1] = 0.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = 0.660806751651 1.08096989644 y[1] (closed_form) = 0.660808770249 1.08099914755 absolute error = 2.932e-05 relative error = 0.002314 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.249 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = 0.659774089694 1.08376331475 y[1] (closed_form) = 0.659776192689 1.0837918045 absolute error = 2.857e-05 relative error = 0.002251 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.252 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5549 2.015 h = 0.001 0.001 y[1] (numeric) = 0.659175260019 1.08544799087 y[1] (closed_form) = 0.659177654373 1.08547641076 absolute error = 2.852e-05 relative error = 0.002246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.254 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = 0.659511319188 1.08622060955 y[1] (closed_form) = 0.659513844291 1.08624894666 absolute error = 2.845e-05 relative error = 0.002239 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.255 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.556 2.02 h = 0.003 0.006 y[1] (numeric) = 0.658693764188 1.0884603573 y[1] (closed_form) = 0.658695665426 1.08848865398 absolute error = 2.836e-05 relative error = 0.002229 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.258 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4719.9MB, alloc=52.3MB, time=57.94 x[1] = 0.559 2.026 h = 0.0001 0.005 y[1] (numeric) = 0.659044662067 1.09244408188 y[1] (closed_form) = 0.659046636111 1.09247355424 absolute error = 2.954e-05 relative error = 0.002315 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.264 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = 0.658003226461 1.09524167554 y[1] (closed_form) = 0.658005284234 1.09527038829 absolute error = 2.879e-05 relative error = 0.002253 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.267 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5592 2.034 h = 0.001 0.001 y[1] (numeric) = 0.657399167875 1.09692892875 y[1] (closed_form) = 0.657401516271 1.09695757163 absolute error = 2.874e-05 relative error = 0.002247 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.269 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5602 2.035 h = 0.001 0.003 y[1] (numeric) = 0.657734257937 1.09770411662 y[1] (closed_form) = 0.657736736722 1.09773267684 absolute error = 2.867e-05 relative error = 0.00224 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = 0.657629478601 1.09958997758 y[1] (closed_form) = 0.657631684866 1.09961869531 absolute error = 2.880e-05 relative error = 0.002248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.273 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4765.5MB, alloc=52.3MB, time=58.50 x[1] = 0.5613 2.042 h = 0.003 0.006 y[1] (numeric) = 0.656803465005 1.10183384795 y[1] (closed_form) = 0.656805436947 1.10186243601 absolute error = 2.866e-05 relative error = 0.002234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.276 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = 0.657144994503 1.10582943667 y[1] (closed_form) = 0.657147039827 1.1058591971 absolute error = 2.983e-05 relative error = 0.002319 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.282 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = 0.65609346433 1.10863201477 y[1] (closed_form) = 0.656095592655 1.10866101764 absolute error = 2.908e-05 relative error = 0.002257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.285 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5645 2.056 h = 0.001 0.001 y[1] (numeric) = 0.65548339108 1.1103223413 y[1] (closed_form) = 0.655485809178 1.11035127431 absolute error = 2.903e-05 relative error = 0.002252 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.287 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5655 2.057 h = 0.001 0.003 y[1] (numeric) = 0.655817401471 1.11110052191 y[1] (closed_form) = 0.655819949543 1.1111293724 absolute error = 2.896e-05 relative error = 0.002245 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.288 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4811.0MB, alloc=52.3MB, time=59.06 x[1] = 0.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = 0.655707469675 1.11299128744 y[1] (closed_form) = 0.655709746084 1.11302029518 absolute error = 2.910e-05 relative error = 0.002252 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.291 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5666 2.064 h = 0.003 0.006 y[1] (numeric) = 0.654873411441 1.11523918481 y[1] (closed_form) = 0.654875454093 1.11526806339 absolute error = 2.895e-05 relative error = 0.002238 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.294 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = 0.655205606228 1.11924661091 y[1] (closed_form) = 0.655207722807 1.11927665858 absolute error = 3.012e-05 relative error = 0.002323 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = 0.654144012615 1.12205416618 y[1] (closed_form) = 0.654146211487 1.12208345832 absolute error = 2.937e-05 relative error = 0.002262 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.303 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5698 2.078 h = 0.001 0.001 y[1] (numeric) = 0.653527943313 1.12374756136 y[1] (closed_form) = 0.653530431113 1.12377678365 absolute error = 2.933e-05 relative error = 0.002256 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.305 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4856.6MB, alloc=52.3MB, time=59.62 x[1] = 0.5708 2.079 h = 0.001 0.003 y[1] (numeric) = 0.65386087893 1.12452872712 y[1] (closed_form) = 0.653863496292 1.12455786704 absolute error = 2.926e-05 relative error = 0.002249 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.306 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = 0.653745812055 1.12642438694 y[1] (closed_form) = 0.653748158604 1.12645368384 absolute error = 2.939e-05 relative error = 0.002257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.309 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5719 2.086 h = 0.003 0.006 y[1] (numeric) = 0.652903733986 1.12867630526 y[1] (closed_form) = 0.652905847344 1.1287054735 absolute error = 2.924e-05 relative error = 0.002243 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.312 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = 0.653226627337 1.13269554187 y[1] (closed_form) = 0.653228815138 1.13272587592 absolute error = 3.041e-05 relative error = 0.002326 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.318 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.575 2.097 h = 0.0001 0.003 y[1] (numeric) = 0.652155001191 1.13550806679 y[1] (closed_form) = 0.652157270598 1.13553764735 absolute error = 2.967e-05 relative error = 0.002266 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.321 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4902.2MB, alloc=52.3MB, time=60.18 x[1] = 0.5751 2.1 h = 0.001 0.001 y[1] (numeric) = 0.651532954315 1.13720452585 y[1] (closed_form) = 0.651535511809 1.13723403658 absolute error = 2.962e-05 relative error = 0.00226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.323 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5761 2.101 h = 0.001 0.003 y[1] (numeric) = 0.651864819968 1.13798866916 y[1] (closed_form) = 0.651867506616 1.13801809767 absolute error = 2.955e-05 relative error = 0.002253 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.324 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = 0.651744635222 1.13988921289 y[1] (closed_form) = 0.6517470519 1.13991879811 absolute error = 2.968e-05 relative error = 0.002261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.327 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5772 2.108 h = 0.003 0.006 y[1] (numeric) = 0.650894561944 1.14214514595 y[1] (closed_form) = 0.650896745998 1.14217460301 absolute error = 2.954e-05 relative error = 0.002247 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = 0.651208186745 1.14617616605 y[1] (closed_form) = 0.651210445731 1.14620678565 absolute error = 3.070e-05 relative error = 0.002329 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.336 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4947.8MB, alloc=52.3MB, time=60.74 x[1] = 0.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = 0.650126558756 1.1489936529 y[1] (closed_form) = 0.650128898679 1.14902352105 absolute error = 2.996e-05 relative error = 0.002269 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.339 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5804 2.122 h = 0.001 0.001 y[1] (numeric) = 0.649498552651 1.15069317093 y[1] (closed_form) = 0.649501179825 1.15072296927 absolute error = 2.991e-05 relative error = 0.002264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.341 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = 0.649829353063 1.15148028419 y[1] (closed_form) = 0.649832108987 1.15151000046 absolute error = 2.984e-05 relative error = 0.002257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.342 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5815 2.127 h = 0.003 0.006 y[1] (numeric) = 0.64897275315 1.15373948332 y[1] (closed_form) = 0.648974893426 1.1537691616 absolute error = 2.976e-05 relative error = 0.002248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.345 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = 0.649278286012 1.15778051464 y[1] (closed_form) = 0.649280501654 1.15781135266 absolute error = 3.092e-05 relative error = 0.002329 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.351 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4993.4MB, alloc=52.3MB, time=61.30 x[1] = 0.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = 0.6481880142 1.16060214758 y[1] (closed_form) = 0.648190310196 1.16063223589 absolute error = 3.018e-05 relative error = 0.00227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.354 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5847 2.141 h = 0.001 0.001 y[1] (numeric) = 0.647554856824 1.16230422395 y[1] (closed_form) = 0.647557439355 1.16233424246 absolute error = 3.013e-05 relative error = 0.002264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.356 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5857 2.142 h = 0.001 0.003 y[1] (numeric) = 0.647884708776 1.16309387495 y[1] (closed_form) = 0.647887419709 1.16312381153 absolute error = 3.006e-05 relative error = 0.002258 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.358 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = 0.647754988196 1.16500341812 y[1] (closed_form) = 0.647757430714 1.16503351089 absolute error = 3.019e-05 relative error = 0.002265 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5868 2.149 h = 0.003 0.006 y[1] (numeric) = 0.646890055004 1.16726671001 y[1] (closed_form) = 0.64689226595 1.16729667553 absolute error = 3.005e-05 relative error = 0.002251 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.363 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5039.0MB, alloc=52.3MB, time=61.86 x[1] = 0.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = 0.647186379819 1.17131947459 y[1] (closed_form) = 0.647188666567 1.17135059662 absolute error = 3.121e-05 relative error = 0.002332 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.369 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = 0.646086162789 1.17414605494 y[1] (closed_form) = 0.646088529259 1.17417642927 absolute error = 3.047e-05 relative error = 0.002273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.372 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.59 2.163 h = 0.001 0.001 y[1] (numeric) = 0.645447080033 1.17585118102 y[1] (closed_form) = 0.645449732209 1.1758814856 absolute error = 3.042e-05 relative error = 0.002268 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.374 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.591 2.164 h = 0.001 0.003 y[1] (numeric) = 0.645775875401 1.1766437879 y[1] (closed_form) = 0.645778655581 1.17667401069 absolute error = 3.035e-05 relative error = 0.002261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.376 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.592 2.167 h = 0.0001 0.004 y[1] (numeric) = 0.645641085363 1.17855818504 y[1] (closed_form) = 0.645643597952 1.17858856375 absolute error = 3.048e-05 relative error = 0.002268 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.379 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5921 2.171 h = 0.003 0.006 y[1] (numeric) = 0.644768226529 1.18082547328 y[1] (closed_form) = 0.644770508118 1.1808557252 absolute error = 3.034e-05 relative error = 0.002255 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.381 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5084.5MB, alloc=52.3MB, time=62.42 x[1] = 0.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = 0.645055375101 1.18488994375 y[1] (closed_form) = 0.645057732898 1.18492134896 absolute error = 3.149e-05 relative error = 0.002334 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.387 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = 0.643945242928 1.18772146321 y[1] (closed_form) = 0.643947679834 1.18775212274 absolute error = 3.076e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.391 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5953 2.185 h = 0.001 0.001 y[1] (numeric) = 0.643300252764 1.18942963376 y[1] (closed_form) = 0.643302974552 1.18946022358 absolute error = 3.071e-05 relative error = 0.002271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.393 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5963 2.186 h = 0.001 0.003 y[1] (numeric) = 0.643627996034 1.19022518892 y[1] (closed_form) = 0.643630845431 1.19025569712 absolute error = 3.064e-05 relative error = 0.002264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.394 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = 0.643488153096 1.19214442935 y[1] (closed_form) = 0.64349073572 1.19217509317 absolute error = 3.077e-05 relative error = 0.002271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.397 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5130.2MB, alloc=52.3MB, time=62.98 x[1] = 0.5974 2.193 h = 0.003 0.006 y[1] (numeric) = 0.642607392577 1.19441570709 y[1] (closed_form) = 0.642609744772 1.1944462446 absolute error = 3.063e-05 relative error = 0.002258 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.399 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = 0.642885396339 1.19849185599 y[1] (closed_form) = 0.642887825124 1.19852354356 absolute error = 3.178e-05 relative error = 0.002337 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.406 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = 0.641765378884 1.20132830607 y[1] (closed_form) = 0.641767886183 1.20135924998 absolute error = 3.105e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.409 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6006 2.207 h = 0.001 0.001 y[1] (numeric) = 0.641114499154 1.20303951573 y[1] (closed_form) = 0.641117290516 1.20307038997 absolute error = 3.100e-05 relative error = 0.002274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.411 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6016 2.208 h = 0.001 0.003 y[1] (numeric) = 0.641441194733 1.20383801159 y[1] (closed_form) = 0.64144411331 1.20386880437 absolute error = 3.093e-05 relative error = 0.002267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.412 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5175.8MB, alloc=52.3MB, time=63.54 x[1] = 0.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = 0.641296315287 1.20576208454 y[1] (closed_form) = 0.641298967905 1.20579303265 absolute error = 3.106e-05 relative error = 0.002274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.415 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6027 2.215 h = 0.003 0.006 y[1] (numeric) = 0.640407676871 1.20803734481 y[1] (closed_form) = 0.640410099632 1.20806816706 absolute error = 3.092e-05 relative error = 0.002261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.418 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = 0.640676566893 1.21212514455 y[1] (closed_form) = 0.640679066597 1.21215711366 absolute error = 3.207e-05 relative error = 0.002339 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.424 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = 0.639546693805 1.21496651659 y[1] (closed_form) = 0.639549271447 1.21499774405 absolute error = 3.133e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.427 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6059 2.229 h = 0.001 0.001 y[1] (numeric) = 0.638889942223 1.21668075988 y[1] (closed_form) = 0.638892803112 1.21671191773 absolute error = 3.129e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.429 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5221.3MB, alloc=52.3MB, time=64.10 x[1] = 0.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = 0.639215594437 1.21748218886 y[1] (closed_form) = 0.639218582153 1.21751326541 absolute error = 3.122e-05 relative error = 0.00227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.431 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.607 2.234 h = 0.003 0.006 y[1] (numeric) = 0.638320524757 1.21976068847 y[1] (closed_form) = 0.638322904931 1.21979172908 absolute error = 3.113e-05 relative error = 0.002261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.433 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.61 2.24 h = 0.0001 0.005 y[1] (numeric) = 0.638581456242 1.22385838665 y[1] (closed_form) = 0.638583913682 1.22389057137 absolute error = 3.228e-05 relative error = 0.002338 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.439 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = 0.63744306485 1.22670387135 y[1] (closed_form) = 0.637445599722 1.22673531614 absolute error = 3.155e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.443 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6102 2.248 h = 0.001 0.001 y[1] (numeric) = 0.636781237015 1.22842065177 y[1] (closed_form) = 0.636784054434 1.22845202699 absolute error = 3.150e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.445 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5267.0MB, alloc=52.3MB, time=64.66 x[1] = 0.6112 2.249 h = 0.001 0.003 y[1] (numeric) = 0.637105959724 1.22922458704 y[1] (closed_form) = 0.637108903636 1.2292558811 absolute error = 3.143e-05 relative error = 0.00227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.446 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = 0.636951694333 1.23115756376 y[1] (closed_form) = 0.636954373784 1.23118901259 absolute error = 3.156e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.449 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6123 2.256 h = 0.003 0.006 y[1] (numeric) = 0.636048412482 1.23344012231 y[1] (closed_form) = 0.636050863136 1.23347144614 absolute error = 3.142e-05 relative error = 0.002264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.452 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = 0.636300287414 1.23754942012 y[1] (closed_form) = 0.636302815641 1.23758188488 absolute error = 3.256e-05 relative error = 0.00234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.458 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = 0.635152095111 1.24039981052 y[1] (closed_form) = 0.635154700228 1.24043153735 absolute error = 3.183e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.461 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5312.6MB, alloc=52.3MB, time=65.22 x[1] = 0.6155 2.27 h = 0.001 0.001 y[1] (numeric) = 0.634484428113 1.24211961433 y[1] (closed_form) = 0.63448731497 1.24215127166 absolute error = 3.179e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.463 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6165 2.271 h = 0.001 0.003 y[1] (numeric) = 0.634808115393 1.24292646866 y[1] (closed_form) = 0.634811128359 1.24295804499 absolute error = 3.172e-05 relative error = 0.002273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.465 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = 0.634648859635 1.24486424692 y[1] (closed_form) = 0.634651608935 1.24489597772 absolute error = 3.185e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.467 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6176 2.278 h = 0.003 0.006 y[1] (numeric) = 0.633737767092 1.24715076751 y[1] (closed_form) = 0.633740288169 1.24718237375 absolute error = 3.171e-05 relative error = 0.002266 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = 0.633980615523 1.2512716371 y[1] (closed_form) = 0.633983214456 1.2513043811 absolute error = 3.285e-05 relative error = 0.002342 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.476 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5358.2MB, alloc=52.3MB, time=65.78 x[1] = 0.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = 0.632822651365 1.25412692404 y[1] (closed_form) = 0.63282532666 1.2541589321 absolute error = 3.212e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6208 2.292 h = 0.001 0.001 y[1] (numeric) = 0.632149162556 1.25584974547 y[1] (closed_form) = 0.63215211879 1.2558816841 absolute error = 3.208e-05 relative error = 0.002281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.482 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6218 2.293 h = 0.001 0.003 y[1] (numeric) = 0.632471818515 1.25665951129 y[1] (closed_form) = 0.632474900477 1.25669136909 absolute error = 3.201e-05 relative error = 0.002275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.483 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = 0.63230758817 1.25860208007 y[1] (closed_form) = 0.632310407254 1.25863409203 absolute error = 3.214e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.486 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6229 2.3 h = 0.003 0.006 y[1] (numeric) = 0.631388708075 1.26089255517 y[1] (closed_form) = 0.631391299511 1.26092444301 absolute error = 3.199e-05 relative error = 0.002269 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.488 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5403.8MB, alloc=52.3MB, time=66.34 x[1] = 0.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = 0.631622559712 1.26502496861 y[1] (closed_form) = 0.631625229261 1.26505799105 absolute error = 3.313e-05 relative error = 0.002343 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.495 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.626 2.311 h = 0.0001 0.003 y[1] (numeric) = 0.630454852548 1.26788514276 y[1] (closed_form) = 0.63045759795 1.26791743125 absolute error = 3.240e-05 relative error = 0.002288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.498 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6261 2.314 h = 0.001 0.001 y[1] (numeric) = 0.629775559157 1.26961097594 y[1] (closed_form) = 0.629778584698 1.26964319508 absolute error = 3.236e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6271 2.315 h = 0.001 0.003 y[1] (numeric) = 0.630097187828 1.2704236457 y[1] (closed_form) = 0.630100338721 1.27045578417 absolute error = 3.229e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.502 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = 0.629927998519 1.27237099391 y[1] (closed_form) = 0.629930887317 1.27240328623 absolute error = 3.242e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.504 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5449.4MB, alloc=52.3MB, time=66.90 x[1] = 0.6282 2.322 h = 0.003 0.006 y[1] (numeric) = 0.629001353849 1.27466541588 y[1] (closed_form) = 0.629004015573 1.2746975845 absolute error = 3.228e-05 relative error = 0.002271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.507 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = 0.629226238056 1.27880934515 y[1] (closed_form) = 0.629228978129 1.27884264524 absolute error = 3.341e-05 relative error = 0.002344 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.513 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = 0.628048816532 1.28167439702 y[1] (closed_form) = 0.628051631964 1.28170696513 absolute error = 3.269e-05 relative error = 0.00229 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.517 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6314 2.336 h = 0.001 0.001 y[1] (numeric) = 0.627363735661 1.283403236 y[1] (closed_form) = 0.627366830439 1.28343573484 absolute error = 3.265e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.519 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = 0.627684341007 1.28421880213 y[1] (closed_form) = 0.62768756076 1.28425122049 absolute error = 3.258e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.52 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5495.0MB, alloc=52.3MB, time=67.46 x[1] = 0.6325 2.341 h = 0.003 0.006 y[1] (numeric) = 0.626751357208 1.28651643397 y[1] (closed_form) = 0.626753977404 1.28654881812 absolute error = 3.249e-05 relative error = 0.00227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.523 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = 0.626968409087 1.29067014686 y[1] (closed_form) = 0.626971107852 1.29070365979 absolute error = 3.362e-05 relative error = 0.002343 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.529 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = 0.625782590603 1.29353927432 y[1] (closed_form) = 0.625785364292 1.29357205696 absolute error = 3.290e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.532 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6357 2.355 h = 0.001 0.001 y[1] (numeric) = 0.625092505959 1.29527062709 y[1] (closed_form) = 0.625095558312 1.29530334053 absolute error = 3.286e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.535 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6367 2.356 h = 0.001 0.003 y[1] (numeric) = 0.625412199197 1.29608866815 y[1] (closed_form) = 0.625415376205 1.29612130125 absolute error = 3.279e-05 relative error = 0.002278 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.536 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5540.5MB, alloc=52.3MB, time=68.02 x[1] = 0.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = 0.625233766859 1.29804482145 y[1] (closed_form) = 0.625236683217 1.29807760779 absolute error = 3.292e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.539 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6378 2.363 h = 0.003 0.006 y[1] (numeric) = 0.624292687925 1.30034647496 y[1] (closed_form) = 0.624295378274 1.30037913841 absolute error = 3.277e-05 relative error = 0.002272 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.541 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = 0.624500826458 1.30451165172 y[1] (closed_form) = 0.624503595567 1.30454544083 absolute error = 3.390e-05 relative error = 0.002344 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.548 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = 0.623305346497 1.30738563916 y[1] (closed_form) = 0.623308190067 1.30741869995 absolute error = 3.318e-05 relative error = 0.002291 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.551 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.641 2.377 h = 0.001 0.001 y[1] (numeric) = 0.622609505947 1.3091199866 y[1] (closed_form) = 0.622612627396 1.30915297828 absolute error = 3.314e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.553 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5586.1MB, alloc=52.3MB, time=68.58 x[1] = 0.642 2.378 h = 0.001 0.003 y[1] (numeric) = 0.622928183131 1.30994091005 y[1] (closed_form) = 0.622931428865 1.30997382156 absolute error = 3.307e-05 relative error = 0.00228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.555 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.643 2.381 h = 0.0001 0.004 y[1] (numeric) = 0.622744835824 1.31190181095 y[1] (closed_form) = 0.622747821674 1.31193487538 absolute error = 3.320e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.557 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6431 2.385 h = 0.003 0.006 y[1] (numeric) = 0.621796057241 1.31420738902 y[1] (closed_form) = 0.621798817658 1.31424033097 absolute error = 3.306e-05 relative error = 0.002274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = 0.621995310842 1.31838400144 y[1] (closed_form) = 0.62199815019 1.31841806595 absolute error = 3.418e-05 relative error = 0.002345 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.566 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = 0.620790197478 1.32126283892 y[1] (closed_form) = 0.620793110838 1.32129617708 absolute error = 3.347e-05 relative error = 0.002292 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.57 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5631.6MB, alloc=52.3MB, time=69.13 x[1] = 0.6463 2.399 h = 0.001 0.001 y[1] (numeric) = 0.620088617779 1.32300017483 y[1] (closed_form) = 0.620091808236 1.32303344397 absolute error = 3.342e-05 relative error = 0.002287 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.572 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6473 2.4 h = 0.001 0.003 y[1] (numeric) = 0.620406282668 1.32382397313 y[1] (closed_form) = 0.620409597045 1.32385716228 absolute error = 3.335e-05 relative error = 0.002281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.573 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = 0.620218035437 1.32578961034 y[1] (closed_form) = 0.62022109069 1.32582295208 absolute error = 3.348e-05 relative error = 0.002287 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.576 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6484 2.407 h = 0.003 0.006 y[1] (numeric) = 0.619261579561 1.32809910485 y[1] (closed_form) = 0.619264409954 1.32813232452 absolute error = 3.334e-05 relative error = 0.002275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.579 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = 0.619451976321 1.33228712466 y[1] (closed_form) = 0.619454885795 1.3323214638 absolute error = 3.446e-05 relative error = 0.002346 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.585 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5677.2MB, alloc=52.3MB, time=69.69 x[1] = 0.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = 0.618237257429 1.33517080211 y[1] (closed_form) = 0.618240240483 1.33520441686 absolute error = 3.375e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.588 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6516 2.421 h = 0.001 0.001 y[1] (numeric) = 0.617529955218 1.3369111202 y[1] (closed_form) = 0.617533214591 1.33694466602 absolute error = 3.370e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.591 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6526 2.422 h = 0.001 0.003 y[1] (numeric) = 0.617846611504 1.33773778583 y[1] (closed_form) = 0.617849994433 1.33777125185 absolute error = 3.364e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.592 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = 0.61765347925 1.33970814801 y[1] (closed_form) = 0.617656603809 1.33974176628 absolute error = 3.376e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.595 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6537 2.429 h = 0.003 0.006 y[1] (numeric) = 0.616689368275 1.34202155073 y[1] (closed_form) = 0.61669226855 1.34205504733 absolute error = 3.362e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.598 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5722.8MB, alloc=52.3MB, time=70.25 x[1] = 0.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = 0.616870935967 1.34622094961 y[1] (closed_form) = 0.61687391545 1.3462555626 absolute error = 3.474e-05 relative error = 0.002346 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.604 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = 0.615646639228 1.34910945682 y[1] (closed_form) = 0.615649691873 1.34914334737 absolute error = 3.403e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.607 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6569 2.443 h = 0.001 0.001 y[1] (numeric) = 0.614933631023 1.3508527507 y[1] (closed_form) = 0.614936959214 1.35088657244 absolute error = 3.399e-05 relative error = 0.00229 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.609 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = 0.615249282331 1.35168227615 y[1] (closed_form) = 0.615252733718 1.35171601827 absolute error = 3.392e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.611 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.658 2.448 h = 0.003 0.006 y[1] (numeric) = 0.614278921246 1.3539988569 y[1] (closed_form) = 0.614281780932 1.35403256622 absolute error = 3.383e-05 relative error = 0.002275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.614 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.661 2.454 h = 0.0001 0.005 y[1] (numeric) = 0.614452776084 1.35820792305 y[1] (closed_form) = 0.614455715107 1.35824274613 absolute error = 3.495e-05 relative error = 0.002344 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5768.4MB, alloc=52.3MB, time=70.81 x[1] = 0.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = 0.613220199706 1.36110046564 y[1] (closed_form) = 0.61322321152 1.36113456794 absolute error = 3.424e-05 relative error = 0.002293 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.623 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6612 2.462 h = 0.001 0.001 y[1] (numeric) = 0.612502257766 1.36284624811 y[1] (closed_form) = 0.612505544462 1.36288028169 absolute error = 3.419e-05 relative error = 0.002288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.625 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6622 2.463 h = 0.001 0.003 y[1] (numeric) = 0.612817012932 1.36367821729 y[1] (closed_form) = 0.612820422514 1.36371217139 absolute error = 3.412e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.627 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = 0.61261477399 1.36565728342 y[1] (closed_form) = 0.612617926596 1.36569138915 absolute error = 3.425e-05 relative error = 0.002288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6633 2.47 h = 0.003 0.006 y[1] (numeric) = 0.611636430886 1.36797784556 y[1] (closed_form) = 0.611639360273 1.36801183037 absolute error = 3.411e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.632 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5813.9MB, alloc=52.3MB, time=71.37 x[1] = 0.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = 0.611801507839 1.37219823826 y[1] (closed_form) = 0.611804516653 1.37223333377 absolute error = 3.522e-05 relative error = 0.002344 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.639 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = 0.610559404732 1.37509559159 y[1] (closed_form) = 0.610562485945 1.37512996826 absolute error = 3.451e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.642 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6665 2.484 h = 0.001 0.001 y[1] (numeric) = 0.6098357873 1.37684433798 y[1] (closed_form) = 0.60983914263 1.37687864605 absolute error = 3.447e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.644 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6675 2.485 h = 0.001 0.003 y[1] (numeric) = 0.61014954415 1.37767915308 y[1] (closed_form) = 0.610153022011 1.37771338185 absolute error = 3.441e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.646 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = 0.609942462158 1.37966291165 y[1] (closed_form) = 0.609945683781 1.37969729171 absolute error = 3.453e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.648 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5859.5MB, alloc=52.3MB, time=71.93 x[1] = 0.6686 2.492 h = 0.003 0.006 y[1] (numeric) = 0.608956526694 1.38198735814 y[1] (closed_form) = 0.608959525675 1.38202161766 absolute error = 3.439e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.651 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = 0.60911285265 1.38621904892 y[1] (closed_form) = 0.609115931126 1.3862544161 absolute error = 3.550e-05 relative error = 0.002345 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.658 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = 0.607861249944 1.3891212024 y[1] (closed_form) = 0.607864400443 1.38915585268 absolute error = 3.479e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.661 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6718 2.506 h = 0.001 0.001 y[1] (numeric) = 0.607131973206 1.39087290612 y[1] (closed_form) = 0.60713539706 1.39090748791 absolute error = 3.475e-05 relative error = 0.00229 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.663 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6728 2.507 h = 0.001 0.003 y[1] (numeric) = 0.607444735181 1.39171055966 y[1] (closed_form) = 0.607448281213 1.39174506233 absolute error = 3.468e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.665 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5905.0MB, alloc=52.3MB, time=72.49 x[1] = 0.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = 0.607232824495 1.39369899918 y[1] (closed_form) = 0.607236115022 1.39373365279 absolute error = 3.481e-05 relative error = 0.00229 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.667 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6739 2.514 h = 0.003 0.006 y[1] (numeric) = 0.606239318273 1.39602732137 y[1] (closed_form) = 0.606242386732 1.39606185483 absolute error = 3.467e-05 relative error = 0.002278 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = 0.606386919816 1.40027028173 y[1] (closed_form) = 0.606390067822 1.40030591983 absolute error = 3.578e-05 relative error = 0.002345 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.676 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.677 2.525 h = 0.0001 0.003 y[1] (numeric) = 0.605125844454 1.40317722465 y[1] (closed_form) = 0.605129064119 1.40321214778 absolute error = 3.507e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6771 2.528 h = 0.001 0.001 y[1] (numeric) = 0.604390924481 1.40493187903 y[1] (closed_form) = 0.604394416744 1.40496673378 absolute error = 3.503e-05 relative error = 0.00229 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.682 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5950.5MB, alloc=52.3MB, time=73.05 x[1] = 0.6781 2.529 h = 0.001 0.003 y[1] (numeric) = 0.604702694959 1.40577236354 y[1] (closed_form) = 0.604706309051 1.40580713937 absolute error = 3.496e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.683 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = 0.604485969797 1.40776547246 y[1] (closed_form) = 0.604489329112 1.40780039888 absolute error = 3.509e-05 relative error = 0.00229 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.686 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6792 2.536 h = 0.003 0.006 y[1] (numeric) = 0.603484914266 1.41009766164 y[1] (closed_form) = 0.603488052088 1.41013246827 absolute error = 3.495e-05 relative error = 0.002278 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.689 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = 0.603623817684 1.41435186302 y[1] (closed_form) = 0.603627035083 1.41438777129 absolute error = 3.605e-05 relative error = 0.002344 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.695 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = 0.602353296422 1.41726358457 y[1] (closed_form) = 0.60235658513 1.41729877978 absolute error = 3.535e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.699 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5996.1MB, alloc=52.3MB, time=73.61 x[1] = 0.6824 2.55 h = 0.001 0.001 y[1] (numeric) = 0.601612749172 1.41902118288 y[1] (closed_form) = 0.601616309726 1.41905630984 absolute error = 3.531e-05 relative error = 0.002291 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.701 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = 0.601923531471 1.41986449091 y[1] (closed_form) = 0.601927213507 1.41989953914 absolute error = 3.524e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.702 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6835 2.555 h = 0.003 0.006 y[1] (numeric) = 0.60091631186 1.4221998242 y[1] (closed_form) = 0.60091940992 1.42223484079 absolute error = 3.515e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.705 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = 0.601047615611 1.42646357542 y[1] (closed_form) = 0.601050793296 1.42649969106 absolute error = 3.626e-05 relative error = 0.002342 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.712 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = 0.599768928171 1.4293792894 y[1] (closed_form) = 0.599772176852 1.42941469362 absolute error = 3.555e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.715 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6041.7MB, alloc=52.3MB, time=74.16 x[1] = 0.6867 2.569 h = 0.001 0.001 y[1] (numeric) = 0.599023514884 1.43113934951 y[1] (closed_form) = 0.599027034765 1.4311746856 absolute error = 3.551e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.717 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6877 2.57 h = 0.001 0.003 y[1] (numeric) = 0.599333415689 1.43198507026 y[1] (closed_form) = 0.599337056753 1.43202032777 absolute error = 3.545e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.719 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = 0.599107713999 1.43398678003 y[1] (closed_form) = 0.599111101629 1.43402218747 absolute error = 3.557e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.721 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6888 2.577 h = 0.003 0.006 y[1] (numeric) = 0.598092621727 1.43632605189 y[1] (closed_form) = 0.598095788928 1.43636134024 absolute error = 3.543e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.724 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = 0.598215275834 1.44060099125 y[1] (closed_form) = 0.598218522658 1.44063737566 absolute error = 3.653e-05 relative error = 0.002342 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.731 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6087.3MB, alloc=52.3MB, time=74.72 x[1] = 0.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = 0.59692719192 1.44352146372 y[1] (closed_form) = 0.596930509415 1.44355713863 absolute error = 3.583e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.734 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.692 2.591 h = 0.001 0.001 y[1] (numeric) = 0.596176180836 1.44528445524 y[1] (closed_form) = 0.596179768783 1.44532006214 absolute error = 3.579e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.736 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.693 2.592 h = 0.001 0.003 y[1] (numeric) = 0.596485099563 1.44613298571 y[1] (closed_form) = 0.596488808352 1.44616851423 absolute error = 3.572e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.738 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.694 2.595 h = 0.0001 0.004 y[1] (numeric) = 0.596254623475 1.44813933182 y[1] (closed_form) = 0.596258079542 1.44817500991 absolute error = 3.585e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.741 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6941 2.599 h = 0.003 0.006 y[1] (numeric) = 0.59523204254 1.45048244544 y[1] (closed_form) = 0.595235278753 1.45051800481 absolute error = 3.571e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.743 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6133.0MB, alloc=52.3MB, time=75.28 x[1] = 0.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = 0.595346072467 1.45476854431 y[1] (closed_form) = 0.595349388282 1.45480519677 absolute error = 3.680e-05 relative error = 0.002341 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = 0.594048618311 1.45769376412 y[1] (closed_form) = 0.594052004484 1.45772970898 absolute error = 3.610e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.753 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6973 2.613 h = 0.001 0.001 y[1] (numeric) = 0.593292025069 1.45945968013 y[1] (closed_form) = 0.593295680954 1.45949555711 absolute error = 3.606e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.755 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6983 2.614 h = 0.001 0.003 y[1] (numeric) = 0.593599964868 1.46031101291 y[1] (closed_form) = 0.593603741255 1.4603468117 absolute error = 3.600e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.757 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = 0.59336472809 1.46232198368 y[1] (closed_form) = 0.593368252462 1.46235793169 absolute error = 3.612e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6178.5MB, alloc=52.3MB, time=75.84 x[1] = 0.6994 2.621 h = 0.003 0.006 y[1] (numeric) = 0.592334679373 1.46466893001 y[1] (closed_form) = 0.592337984464 1.46470475964 absolute error = 3.598e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.762 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = 0.592440110302 1.46896615973 y[1] (closed_form) = 0.592443494958 1.46900307949 absolute error = 3.707e-05 relative error = 0.002341 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.769 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = 0.591133311955 1.47189611563 y[1] (closed_form) = 0.591136766668 1.47193232968 absolute error = 3.638e-05 relative error = 0.002293 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.772 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7026 2.635 h = 0.001 0.001 y[1] (numeric) = 0.590371152088 1.47366494914 y[1] (closed_form) = 0.590374875776 1.47370109546 absolute error = 3.634e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.775 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7036 2.636 h = 0.001 0.003 y[1] (numeric) = 0.590678116049 1.47451907682 y[1] (closed_form) = 0.590681959903 1.47455514514 absolute error = 3.627e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.776 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6224.1MB, alloc=52.3MB, time=76.41 x[1] = 0.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = 0.590438132161 1.47653466056 y[1] (closed_form) = 0.590441724701 1.47657087773 absolute error = 3.639e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.779 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7047 2.643 h = 0.003 0.006 y[1] (numeric) = 0.589400636399 1.47888543043 y[1] (closed_form) = 0.589404010231 1.47892152958 absolute error = 3.626e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.782 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = 0.589497493238 1.48319376233 y[1] (closed_form) = 0.58950094658 1.48323094866 absolute error = 3.735e-05 relative error = 0.00234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.788 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = 0.588181376572 1.48612844298 y[1] (closed_form) = 0.588184899684 1.48616492549 absolute error = 3.665e-05 relative error = 0.002293 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.792 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7079 2.657 h = 0.001 0.001 y[1] (numeric) = 0.587413665504 1.48790018694 y[1] (closed_form) = 0.587417456857 1.48793660187 absolute error = 3.661e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.794 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6269.7MB, alloc=52.3MB, time=76.97 x[1] = 0.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = 0.587719656664 1.48875710215 y[1] (closed_form) = 0.587723567848 1.48879343927 absolute error = 3.655e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.795 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.709 2.662 h = 0.003 0.006 y[1] (numeric) = 0.586676079998 1.49111098047 y[1] (closed_form) = 0.586679414798 1.49114728685 absolute error = 3.646e-05 relative error = 0.002275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.798 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.712 2.668 h = 0.0001 0.005 y[1] (numeric) = 0.5867654445 1.49542874404 y[1] (closed_form) = 0.586768858784 1.49546613507 absolute error = 3.755e-05 relative error = 0.002337 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.804 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = 0.585441271425 1.49836737184 y[1] (closed_form) = 0.585444755218 1.49840406067 absolute error = 3.685e-05 relative error = 0.002291 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.808 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7122 2.676 h = 0.001 0.001 y[1] (numeric) = 0.584668759783 1.50014154947 y[1] (closed_form) = 0.584672511187 1.50017817083 absolute error = 3.681e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6315.3MB, alloc=52.3MB, time=77.52 x[1] = 0.7132 2.677 h = 0.001 0.003 y[1] (numeric) = 0.584973882891 1.50100084664 y[1] (closed_form) = 0.584977753838 1.50103739036 absolute error = 3.675e-05 relative error = 0.002281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.812 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = 0.584725046833 1.50302492661 y[1] (closed_form) = 0.584728667764 1.50306161851 absolute error = 3.687e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.814 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7143 2.684 h = 0.003 0.006 y[1] (numeric) = 0.583673703274 1.50538269845 y[1] (closed_form) = 0.583677106558 1.50541927298 absolute error = 3.673e-05 relative error = 0.002275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.817 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = 0.583754539652 1.5097115111 y[1] (closed_form) = 0.583758022337 1.50974916735 absolute error = 3.782e-05 relative error = 0.002336 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.824 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = 0.582421096073 1.51265484256 y[1] (closed_form) = 0.582424648 1.51269179849 absolute error = 3.713e-05 relative error = 0.00229 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6360.7MB, alloc=52.3MB, time=78.08 x[1] = 0.7175 2.698 h = 0.001 0.001 y[1] (numeric) = 0.581643061732 1.51443191758 y[1] (closed_form) = 0.581646880544 1.51446880619 absolute error = 3.709e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7185 2.699 h = 0.001 0.003 y[1] (numeric) = 0.581947217629 1.5152939886 y[1] (closed_form) = 0.581951155655 1.51533079977 absolute error = 3.702e-05 relative error = 0.002281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.831 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = 0.581693672761 1.51732264806 y[1] (closed_form) = 0.581697361457 1.51735960704 absolute error = 3.714e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.834 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7196 2.706 h = 0.003 0.006 y[1] (numeric) = 0.580634940807 1.51968421709 y[1] (closed_form) = 0.580638412429 1.51972105903 absolute error = 3.701e-05 relative error = 0.002275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.836 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = 0.580707273202 1.52402405008 y[1] (closed_form) = 0.580710824124 1.52406197084 absolute error = 3.809e-05 relative error = 0.002335 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.843 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = 0.579364584493 1.52697207359 y[1] (closed_form) = 0.579368204401 1.52700929589 absolute error = 3.740e-05 relative error = 0.00229 % Correct digits = 5 memory used=6406.4MB, alloc=52.3MB, time=78.64 Radius of convergence (given) for eq 1 = 3.846 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7228 2.72 h = 0.001 0.001 y[1] (numeric) = 0.578581042574 1.52875203879 y[1] (closed_form) = 0.578584928646 1.52878919394 absolute error = 3.736e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7238 2.721 h = 0.001 0.003 y[1] (numeric) = 0.578884234141 1.52961687633 y[1] (closed_form) = 0.5788882391 1.52965395422 absolute error = 3.729e-05 relative error = 0.00228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = 0.578625993566 1.53165010348 y[1] (closed_form) = 0.578629749877 1.53168732881 absolute error = 3.741e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.853 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7249 2.728 h = 0.003 0.006 y[1] (numeric) = 0.577559893412 1.53401546026 y[1] (closed_form) = 0.57756343322 1.53405256888 absolute error = 3.728e-05 relative error = 0.002274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.856 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = 0.577623745704 1.53836628487 y[1] (closed_form) = 0.577627364696 1.53840446941 absolute error = 3.836e-05 relative error = 0.002334 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.862 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6452.0MB, alloc=52.3MB, time=79.20 x[1] = 0.728 2.739 h = 0.0001 0.003 y[1] (numeric) = 0.576271837066 1.5413189887 y[1] (closed_form) = 0.576275524801 1.54135647666 absolute error = 3.767e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.866 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7281 2.742 h = 0.001 0.001 y[1] (numeric) = 0.57548280259 1.54310183685 y[1] (closed_form) = 0.57548675577 1.5431392578 absolute error = 3.763e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.868 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7291 2.743 h = 0.001 0.003 y[1] (numeric) = 0.575785032656 1.54396943356 y[1] (closed_form) = 0.575789104398 1.54400677746 absolute error = 3.757e-05 relative error = 0.00228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.869 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = 0.575522109355 1.54600721659 y[1] (closed_form) = 0.575525933128 1.54604470755 absolute error = 3.769e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.872 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7302 2.75 h = 0.003 0.006 y[1] (numeric) = 0.57444866106 1.5483763516 y[1] (closed_form) = 0.574452268899 1.54841372619 absolute error = 3.755e-05 relative error = 0.002274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.875 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6497.7MB, alloc=52.3MB, time=79.76 x[1] = 0.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = 0.574504056873 1.5527381391 y[1] (closed_form) = 0.574507743765 1.55277658672 absolute error = 3.862e-05 relative error = 0.002333 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.881 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = 0.573142953339 1.55569551147 y[1] (closed_form) = 0.573146708742 1.55573326435 absolute error = 3.794e-05 relative error = 0.002288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.885 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7334 2.764 h = 0.001 0.001 y[1] (numeric) = 0.572348441221 1.55748123525 y[1] (closed_form) = 0.572352461355 1.5575189213 absolute error = 3.790e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.887 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = 0.572649712563 1.55835158383 y[1] (closed_form) = 0.572653850938 1.55838919302 absolute error = 3.784e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.889 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7345 2.769 h = 0.003 0.006 y[1] (numeric) = 0.571570263823 1.56072379011 y[1] (closed_form) = 0.571573833267 1.56076136924 absolute error = 3.775e-05 relative error = 0.002271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.892 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6543.3MB, alloc=52.3MB, time=80.32 x[1] = 0.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = 0.571618269181 1.56509489073 y[1] (closed_form) = 0.571621917588 1.56513354042 absolute error = 3.882e-05 relative error = 0.00233 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.898 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = 0.570249215486 1.56805616298 y[1] (closed_form) = 0.57025293219 1.56809411952 absolute error = 3.814e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.902 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7377 2.783 h = 0.001 0.001 y[1] (numeric) = 0.569449966128 1.56984429113 y[1] (closed_form) = 0.56945394695 1.56988218096 absolute error = 3.810e-05 relative error = 0.002281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.904 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7387 2.784 h = 0.001 0.003 y[1] (numeric) = 0.569750381758 1.5707169912 y[1] (closed_form) = 0.569754480542 1.57075480435 absolute error = 3.803e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.905 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = 0.569478725214 1.57276316472 y[1] (closed_form) = 0.569482577281 1.57280112423 absolute error = 3.815e-05 relative error = 0.002281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.908 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6588.8MB, alloc=52.3MB, time=80.88 x[1] = 0.7398 2.791 h = 0.003 0.006 y[1] (numeric) = 0.568391611927 1.57513921762 y[1] (closed_form) = 0.568395249116 1.57517706137 absolute error = 3.802e-05 relative error = 0.00227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.911 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = 0.568431204438 1.57952122792 y[1] (closed_form) = 0.568434920432 1.57956013937 absolute error = 3.909e-05 relative error = 0.002328 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.917 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = 0.567053002125 1.58248714683 y[1] (closed_form) = 0.567056786203 1.58252536698 absolute error = 3.841e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.921 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.743 2.805 h = 0.001 0.001 y[1] (numeric) = 0.5662483027 1.58427813709 y[1] (closed_form) = 0.566252350189 1.5843162907 absolute error = 3.837e-05 relative error = 0.00228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.923 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.744 2.806 h = 0.001 0.003 y[1] (numeric) = 0.56654776473 1.5851535755 y[1] (closed_form) = 0.566551929863 1.58519165262 absolute error = 3.830e-05 relative error = 0.002275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.925 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6634.3MB, alloc=52.3MB, time=81.44 x[1] = 0.745 2.809 h = 0.0001 0.004 y[1] (numeric) = 0.566271462098 1.58720427112 y[1] (closed_form) = 0.566275381178 1.58724249423 absolute error = 3.842e-05 relative error = 0.00228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.928 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7451 2.813 h = 0.003 0.006 y[1] (numeric) = 0.565177057422 1.58958407493 y[1] (closed_form) = 0.565180762192 1.58962218259 absolute error = 3.829e-05 relative error = 0.002269 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = 0.565208259998 1.59397696618 y[1] (closed_form) = 0.565212043401 1.59401613868 absolute error = 3.935e-05 relative error = 0.002327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.937 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = 0.563820933626 1.59694751972 y[1] (closed_form) = 0.56382478491 1.59698600277 absolute error = 3.868e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.941 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7483 2.827 h = 0.001 0.001 y[1] (numeric) = 0.563010798763 1.59874136465 y[1] (closed_form) = 0.563014912755 1.59877978133 absolute error = 3.864e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.943 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6679.9MB, alloc=52.3MB, time=82.00 x[1] = 0.7493 2.828 h = 0.001 0.003 y[1] (numeric) = 0.56330930983 1.59961953414 y[1] (closed_form) = 0.563313541151 1.59965787452 absolute error = 3.857e-05 relative error = 0.002274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.944 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = 0.563028373646 1.60167473998 y[1] (closed_form) = 0.563032359572 1.60171322598 absolute error = 3.869e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.947 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7504 2.835 h = 0.003 0.006 y[1] (numeric) = 0.561926697124 1.60405828494 y[1] (closed_form) = 0.561930469309 1.60409665579 absolute error = 3.856e-05 relative error = 0.002268 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = 0.561949532436 1.6084620284 y[1] (closed_form) = 0.561953383068 1.60850146127 absolute error = 3.962e-05 relative error = 0.002325 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.956 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = 0.5605531064 1.61143720447 y[1] (closed_form) = 0.56055702472 1.61147594972 absolute error = 3.894e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6725.4MB, alloc=52.3MB, time=82.56 x[1] = 0.7536 2.849 h = 0.001 0.001 y[1] (numeric) = 0.559737550631 1.6132338966 y[1] (closed_form) = 0.55974173096 1.61327257564 absolute error = 3.890e-05 relative error = 0.002278 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.962 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7546 2.85 h = 0.001 0.003 y[1] (numeric) = 0.560035113325 1.61411478991 y[1] (closed_form) = 0.560039410669 1.61415339287 absolute error = 3.884e-05 relative error = 0.002273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.964 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = 0.559749556013 1.61617449408 y[1] (closed_form) = 0.559753608618 1.61621324226 absolute error = 3.896e-05 relative error = 0.002278 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.966 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7557 2.857 h = 0.003 0.006 y[1] (numeric) = 0.558640627059 1.61856177037 y[1] (closed_form) = 0.558644466488 1.61860040372 absolute error = 3.882e-05 relative error = 0.002267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.969 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = 0.55865511754 1.62297633731 y[1] (closed_form) = 0.558659035219 1.62301602985 absolute error = 3.989e-05 relative error = 0.002324 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.976 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6771.0MB, alloc=52.3MB, time=83.12 x[1] = 0.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = 0.557249616075 1.62595612375 y[1] (closed_form) = 0.557253601259 1.62599513049 absolute error = 3.921e-05 relative error = 0.002281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.979 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7589 2.871 h = 0.001 0.001 y[1] (numeric) = 0.556428653834 1.62775565556 y[1] (closed_form) = 0.556432900331 1.62779459628 absolute error = 3.917e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.982 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7599 2.872 h = 0.001 0.003 y[1] (numeric) = 0.556725270697 1.62863926546 y[1] (closed_form) = 0.556729633898 1.62867813029 absolute error = 3.911e-05 relative error = 0.002272 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.983 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 754 Total Elapsed Time = 1 Minutes 23 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 1 Minutes 23 Seconds > quit memory used=6802.4MB, alloc=52.3MB, time=83.49