|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 4 then > printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel); > else > printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel, Re(value), Im(value), postlabel) else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value), Im(value), postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number -1 > if vallen = 5 then # if number 0 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number -1 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 0 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 1 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 2 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 3 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 3 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 2 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 2 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 3 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 4 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 5 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 6 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 6 > else > printf(" 0.0 Seconds\n"); > fi;# end if 5 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 5 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 6; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 5; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 5 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 6; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 5; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_complex := proc(file,x) > fprintf(file,""); > fprintf(file,"%g + %g I",Re(x),Im(x)); > fprintf(file,""); > end; logitem_complex := proc(file, x) fprintf(file, ""); fprintf(file, "%g + %g I", Re(x), Im(x)); fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 5 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 6 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 7 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 8 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 9 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 10 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 11 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 11 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 21 # Begin Function number 22 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 22 # Begin Function number 23 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 11 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 11; > if (errflag) then # if number 11 > quit; > fi;# end if 11 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 23 # Begin Function number 24 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 11 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 12 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 12 > fi;# end if 11; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 24 # Begin Function number 25 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 11 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 11; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 25 # Begin Function number 26 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalc(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalc(in_val); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 11 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 30 # Begin Function number 31 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 14 > if (rcs > glob__0) then # if number 15 > rad_c := float_abs( sqrt(rcs) * float_abs(glob_h)); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 13 > fi;# end if 12 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 11; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := float_abs(sqrt(rcs)*float_abs(glob_h)) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 31 # Begin Function number 32 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 32 # Begin Function number 33 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 33 # Begin Function number 34 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 11 > if (array_fact_1[nnn] = 0) then # if number 12 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 12; > else > ret := factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11 > if (array_fact_2[mmm,nnn] = 0) then # if number 12 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 12; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 35 # Begin Function number 36 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 36 # Begin Function number 37 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 37 # Begin Function number 38 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 38 # Begin Function number 39 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 39 # Begin Function number 40 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 40 # Begin Function number 41 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 41 # Begin Function number 42 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 42 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0)))); > end; exact_soln_y := proc(x) return sin(sqrt(c(2.0)*c(x) + c(3.0))) - sqrt(c(2.0)*c(x) + c(3.0))*cos(sqrt(c(2.0)*c(x) + c(3.0))) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 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# Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > ind_var := array_x[1]; > omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > abserr := float_abs(numeric_val - closed_form_val_y); > if (float_abs(closed_form_val_y) > 0.0) then # if number 3 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 4 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > fi;# end if 4; > else > ; > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 3; > if (glob_good_digits < glob_min_good_digits) then # if number 3 > glob_min_good_digits := glob_good_digits; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,4," "); > omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > #BOTTOM DISPLAY ALOT > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ind_var := array_x[1]; omniout_complex(ALWAYS, "x[1] ", 33, ind_var, 20, " "); term_no := 1; numeric_val := array_y[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_complex(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); abserr := float_abs(numeric_val - closed_form_val_y); if 0. < float_abs(closed_form_val_y) then relerr := abserr/float_abs(closed_form_val_y); if 0. < float_abs(c(relerr)) then glob_good_digits := round(-log10(relerr)) else relerr := 0.; glob_good_digits := Digits - 2 end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 4, " "); omniout_float(ALWAYS, "relative error ", 4, relerr*glob__100, 4, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " ") end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > ; > if (true) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; display_poles() end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > array_tmp4_g[1] := cos(array_tmp3[1]); > array_tmp4[1] := sin(array_tmp3[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2; > #emit pre sin FULL $eq_no = 1 > array_tmp4_g[2] := (neg(att(1,array_tmp4,array_tmp3,1))); > array_tmp4[2] := (att(1,array_tmp4_g,array_tmp3,1)); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0; > array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre sin FULL $eq_no = 1 > array_tmp4_g[3] := (neg(att(2,array_tmp4,array_tmp3,1))); > array_tmp4[3] := (att(2,array_tmp4_g,array_tmp3,1)); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0; > array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre sin FULL $eq_no = 1 > array_tmp4_g[4] := (neg(att(3,array_tmp4,array_tmp3,1))); > array_tmp4[4] := (att(3,array_tmp4_g,array_tmp3,1)); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0; > array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre sin FULL $eq_no = 1 > array_tmp4_g[5] := (neg(att(4,array_tmp4,array_tmp3,1))); > array_tmp4[5] := (att(4,array_tmp4_g,array_tmp3,1)); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0; > array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2; > #emit sin FULL $eq_no = 1 > array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_tmp3,1); > array_tmp4_g[kkk] := neg(att(kkk-1,array_tmp4,array_tmp3,1)); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4_g[1] := cos(array_tmp3[1]); array_tmp4[1] := sin(array_tmp3[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2); array_tmp4_g[2] := neg(att(1, array_tmp4, array_tmp3, 1)); array_tmp4[2] := att(1, array_tmp4_g, array_tmp3, 1); array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[3] := 0; array_tmp3[3] := neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_g[3] := neg(att(2, array_tmp4, array_tmp3, 1)); array_tmp4[3] := att(2, array_tmp4_g, array_tmp3, 1); array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[4] := 0; array_tmp3[4] := neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_g[4] := neg(att(3, array_tmp4, array_tmp3, 1)); array_tmp4[4] := att(3, array_tmp4_g, array_tmp3, 1); array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[5] := 0; array_tmp3[5] := neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_g[5] := neg(att(4, array_tmp4, array_tmp3, 1)); array_tmp4[5] := att(4, array_tmp4_g, array_tmp3, 1); array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp3[kkk] := 0; array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/( array_tmp3[1]*glob__2); array_tmp4[kkk] := att(kkk - 1, array_tmp4_g, array_tmp3, 1); array_tmp4_g[kkk] := neg(att(kkk - 1, array_tmp4, array_tmp3, 1)); array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=40; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(40),[]); > array_x:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_tmp4_g:= Array(0..(40),[]); > array_tmp4:= Array(0..(40),[]); > array_tmp5:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(40) ,(0..40+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 40) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=40) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4_g); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_2D0); > array_const_2D0[1] := c(2.0); > zero_ats_ar(array_const_3D0); > array_const_3D0[1] := c(3.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > array_y_set_initial[1,31] := false; > array_y_set_initial[1,32] := false; > array_y_set_initial[1,33] := false; > array_y_set_initial[1,34] := false; > array_y_set_initial[1,35] := false; > array_y_set_initial[1,36] := false; > array_y_set_initial[1,37] := false; > array_y_set_initial[1,38] := false; > array_y_set_initial[1,39] := false; > array_y_set_initial[1,40] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 40; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sin_sqrt_linpostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 2.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_h := c(0.0001);"); > omniout_str(ALWAYS,"glob_upper_ratio_limit := c(1.001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit := c(0.999);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-1.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 2.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_h := c(0.0001); > glob_upper_ratio_limit := c(1.001); > glob_lower_ratio_limit := c(0.999); > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(-1.5); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(0.5); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=10000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1 > #left paren 0001C > if (true) then # if number 10 > omniout_str(INFO," "); > fi;# end if 10; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > atomall(); > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10 > display_alot(current_iter); > fi;# end if 10; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (true) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2017-11-26T16:28:43-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sin_sqrt_lin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ") > ; > logitem_complex(html_log_file,x_start) > ; > logitem_complex(html_log_file,x_end) > ; > logitem_complex(html_log_file,array_x[1]) > ; > logitem_complex(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > glob_desired_digits_correct := 0.0; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > glob_least_ratio_sing := 0; > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > glob_least_6_sing := 0.0; > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 309 ") > ; > logitem_str(html_log_file,"sin_sqrt_lin diffeq.mxt") > ; > logitem_str(html_log_file,"sin_sqrt_lin maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 40; Digits := 32; max_terms := 40; glob_html_log := true; array_y_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 40, []); array_x := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_tmp4_g := Array(0 .. 40, []); array_tmp4 := Array(0 .. 40, []); array_tmp5 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y_higher := Array(0 .. 2, 0 .. 41, []); array_y_higher_work := Array(0 .. 2, 0 .. 41, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y_set_initial := Array(0 .. 2, 0 .. 41, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 40 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 40 do term := 1; while term <= 40 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4_g); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_2D0); array_const_2D0[1] := c(2.0); zero_ats_ar(array_const_3D0); array_const_3D0[1] := c(3.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; array_y_set_initial[1, 31] := false; array_y_set_initial[1, 32] := false; array_y_set_initial[1, 33] := false; array_y_set_initial[1, 34] := false; array_y_set_initial[1, 35] := false; array_y_set_initial[1, 36] := false; array_y_set_initial[1, 37] := false; array_y_set_initial[1, 38] := false; array_y_set_initial[1, 39] := false; array_y_set_initial[1, 40] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 40; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sin_sqrt_linpostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( sqrt ( 2.0 \ * x + 3.0 ) ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 2.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_h := c(0.0001);"); omniout_str(ALWAYS, "glob_upper_ratio_limit := c(1.001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit := c(0.999);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-1.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)\ *c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "next_delta := proc()"); omniout_str(ALWAYS, "global glob_nxt, x_delta;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); 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omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.000 + 0.000 * I ];"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;"); omniout_str(ALWAYS, "it := x_delta[glob_nxt];"); omniout_str(ALWAYS, "return it;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 2.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c(0.0001); glob_upper_ratio_limit := c(1.001); glob_lower_ratio_limit := c(0.999); glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(-1.5); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(0.5); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 10000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius ; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and (glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do omniout_str(INFO, " "); found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); atomall(); if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin ( sqrt ( 2.\ 0 * x + 3.0 ) ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2017-11-26T16:28:43-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sin_sqrt_lin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = si\ n ( sqrt ( 2.0 * x + 3.0 ) ) ; "); logitem_complex(html_log_file, x_start); logitem_complex(html_log_file, x_end); logitem_complex(html_log_file, array_x[1]); logitem_complex(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); glob_desired_digits_correct := 0.; logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then glob_least_ratio_sing := 0; logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then glob_least_6_sing := 0.; logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 309 "); logitem_str(html_log_file, "sin_sqrt_lin diffeq.mxt"); logitem_str(html_log_file, "sin_sqrt_lin maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.8MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostcpx.cpx################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 2.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c(0.0001); glob_upper_ratio_limit := c(1.001); glob_lower_ratio_limit := c(0.999); glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(-1.5); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(0.5); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=10000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0)))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 2.1 0.1 h = 0.0001 0.005 y[1] (numeric) = 2.85047505309 0.0442459135344 y[1] (closed_form) = 2.85047505309 0.0442459135344 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 3.601 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=29.5MB, alloc=40.3MB, time=0.38 x[1] = 2.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = 2.85068645683 0.0464551154617 y[1] (closed_form) = 2.85069063711 0.0464549678486 absolute error = 4.183e-06 relative error = 0.0001467 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.602 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1002 0.108 h = 0.001 0.001 y[1] (numeric) = 2.85083601474 0.047779054587 y[1] (closed_form) = 2.8508416992 0.0477788143246 absolute error = 5.690e-06 relative error = 0.0001995 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.602 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1012 0.109 h = 0.001 0.003 y[1] (numeric) = 2.85131457626 0.0481854022673 y[1] (closed_form) = 2.85132026241 0.048184827533 absolute error = 5.715e-06 relative error = 0.0002004 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.603 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=75.0MB, alloc=52.3MB, time=0.97 x[1] = 2.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = 2.85186602721 0.0494753244495 y[1] (closed_form) = 2.85187305656 0.0494737525679 absolute error = 7.203e-06 relative error = 0.0002525 % Correct digits = 6 Radius of convergence (given) for eq 1 = 3.604 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1023 0.116 h = 0.003 0.006 y[1] (numeric) = 2.8520599999 0.051238747827 y[1] (closed_form) = 2.85206970516 0.0512370557929 absolute error = 9.852e-06 relative error = 0.0003454 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.604 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = 2.85361801751 0.053772978752 y[1] (closed_form) = 2.85363227212 0.0537652875722 absolute error = 1.620e-05 relative error = 0.0005675 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.607 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=120.6MB, alloc=52.3MB, time=1.53 x[1] = 2.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = 2.8538660938 0.0559727578216 y[1] (closed_form) = 2.85388453283 0.0559649229226 absolute error = 2.003e-05 relative error = 0.0007019 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.608 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1055 0.13 h = 0.001 0.001 y[1] (numeric) = 2.85403758994 0.057290752862 y[1] (closed_form) = 2.8540575342 0.0572828265509 absolute error = 2.146e-05 relative error = 0.0007518 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.608 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1065 0.131 h = 0.001 0.003 y[1] (numeric) = 2.8545217879 0.0576879944432 y[1] (closed_form) = 2.85454173414 0.0576797334445 absolute error = 2.159e-05 relative error = 0.0007562 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.609 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=166.0MB, alloc=52.3MB, time=2.09 x[1] = 2.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = 2.85509361943 0.0589653405842 y[1] (closed_form) = 2.85511491058 0.058956082934 absolute error = 2.322e-05 relative error = 0.000813 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1076 0.138 h = 0.003 0.006 y[1] (numeric) = 2.85531690956 0.0607210902356 y[1] (closed_form) = 2.8553408785 0.0607117146188 absolute error = 2.574e-05 relative error = 0.0009012 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = 2.85691396992 0.0632228022924 y[1] (closed_form) = 2.85694249634 0.0632074272758 absolute error = 3.241e-05 relative error = 0.001134 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.613 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=211.4MB, alloc=52.3MB, time=2.65 x[1] = 2.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = 2.85719875214 0.0654131838236 y[1] (closed_form) = 2.85723146599 0.0653976684279 absolute error = 3.621e-05 relative error = 0.001267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.614 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1108 0.152 h = 0.001 0.001 y[1] (numeric) = 2.85739220625 0.066725249269 y[1] (closed_form) = 2.85742642647 0.0667096436281 absolute error = 3.761e-05 relative error = 0.001316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.614 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1118 0.153 h = 0.001 0.003 y[1] (numeric) = 2.85788205213 0.0671133832738 y[1] (closed_form) = 2.85791627461 0.0670974427066 absolute error = 3.775e-05 relative error = 0.001321 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.615 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=256.9MB, alloc=52.3MB, time=3.21 x[1] = 2.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = 2.85847428863 0.0683781617744 y[1] (closed_form) = 2.85850985781 0.0683612249262 absolute error = 3.940e-05 relative error = 0.001378 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.616 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1129 0.16 h = 0.003 0.006 y[1] (numeric) = 2.85872692285 0.0701262566308 y[1] (closed_form) = 2.85876517187 0.0701092038788 absolute error = 4.188e-05 relative error = 0.001464 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.616 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = 2.86036308025 0.0725954589567 y[1] (closed_form) = 2.8604058949 0.0725724059494 absolute error = 4.863e-05 relative error = 0.001699 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=302.5MB, alloc=52.3MB, time=3.77 x[1] = 2.116 0.171 h = 0.0001 0.003 y[1] (numeric) = 2.86068460247 0.0747764656916 y[1] (closed_form) = 2.86073160785 0.0747532754542 absolute error = 5.241e-05 relative error = 0.001832 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1161 0.174 h = 0.001 0.001 y[1] (numeric) = 2.8609000355 0.0760826146845 y[1] (closed_form) = 2.8609485485 0.0760593352968 absolute error = 5.381e-05 relative error = 0.00188 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1171 0.175 h = 0.001 0.003 y[1] (numeric) = 2.86139554076 0.0764616387775 y[1] (closed_form) = 2.86144405627 0.0764380242025 absolute error = 5.396e-05 relative error = 0.001885 % Correct digits = 5 memory used=348.0MB, alloc=52.3MB, time=4.33 Radius of convergence (given) for eq 1 = 3.621 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = 2.86200820749 0.0777138563091 y[1] (closed_form) = 2.86205807152 0.0776892456982 absolute error = 5.561e-05 relative error = 0.001942 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.622 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1182 0.182 h = 0.003 0.006 y[1] (numeric) = 2.86229021408 0.0794543135143 y[1] (closed_form) = 2.86234276018 0.079429588937 absolute error = 5.807e-05 relative error = 0.002028 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.623 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=393.5MB, alloc=52.3MB, time=4.89 x[1] = 2.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = 2.863965524 0.0818910113638 y[1] (closed_form) = 2.86402264393 0.081860285076 absolute error = 6.486e-05 relative error = 0.002264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.626 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = 2.86432382232 0.084062663812 y[1] (closed_form) = 2.86438513655 0.0840318032487 absolute error = 6.864e-05 relative error = 0.002395 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.626 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1214 0.196 h = 0.001 0.001 y[1] (numeric) = 2.86456125643 0.0853629081349 y[1] (closed_form) = 2.86462407962 0.0853319594433 absolute error = 7.003e-05 relative error = 0.002444 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.627 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=439.1MB, alloc=52.3MB, time=5.45 x[1] = 2.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = 2.86506243251 0.0857328191261 y[1] (closed_form) = 2.86512525846 0.085701534964 absolute error = 7.018e-05 relative error = 0.002449 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.628 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1225 0.201 h = 0.003 0.006 y[1] (numeric) = 2.8653698366 0.087467065055 y[1] (closed_form) = 2.8654353465 0.0874356682843 absolute error = 7.265e-05 relative error = 0.002534 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.628 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = 2.86707928018 0.0898762526803 y[1] (closed_form) = 2.86714937103 0.0898388525658 absolute error = 7.944e-05 relative error = 0.00277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.631 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=484.6MB, alloc=52.3MB, time=6.01 x[1] = 2.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = 2.86746937573 0.0920403066726 y[1] (closed_form) = 2.86754366414 0.0920027747145 absolute error = 8.323e-05 relative error = 0.002901 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.632 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1257 0.215 h = 0.001 0.001 y[1] (numeric) = 2.86772583646 0.0933357392974 y[1] (closed_form) = 2.86780163504 0.0932981200491 absolute error = 8.462e-05 relative error = 0.002949 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.632 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1267 0.216 h = 0.001 0.003 y[1] (numeric) = 2.86823201153 0.0936978705653 y[1] (closed_form) = 2.86830781308 0.0936599155877 absolute error = 8.477e-05 relative error = 0.002954 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.633 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=530.1MB, alloc=52.3MB, time=6.57 x[1] = 2.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = 2.86888291359 0.0949269709874 y[1] (closed_form) = 2.86896006716 0.0948880201186 absolute error = 8.643e-05 relative error = 0.003011 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.634 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1278 0.223 h = 0.003 0.006 y[1] (numeric) = 2.86921974663 0.0966536064955 y[1] (closed_form) = 2.86929958684 0.0966145449563 absolute error = 8.888e-05 relative error = 0.003096 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.635 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = 2.87096844902 0.0990302897728 y[1] (closed_form) = 2.87105287843 0.0989852223236 absolute error = 9.570e-05 relative error = 0.003331 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.638 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=575.6MB, alloc=52.3MB, time=7.13 x[1] = 2.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = 2.87139539298 0.101185022116 y[1] (closed_form) = 2.87148402402 0.10113982541 absolute error = 9.949e-05 relative error = 0.003463 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.638 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.131 0.237 h = 0.001 0.001 y[1] (numeric) = 2.87167389905 0.102474568631 y[1] (closed_form) = 2.87176404177 0.10242928552 absolute error = 0.0001009 relative error = 0.003511 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.639 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.132 0.238 h = 0.001 0.003 y[1] (numeric) = 2.87218576616 0.102827578734 y[1] (closed_form) = 2.87227591207 0.10278195957 absolute error = 0.000101 relative error = 0.003515 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.64 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=621.2MB, alloc=52.3MB, time=7.70 x[1] = 2.133 0.241 h = 0.0001 0.004 y[1] (numeric) = 2.87285717499 0.10404412801 y[1] (closed_form) = 2.87294867486 0.10399751284 absolute error = 0.0001027 relative error = 0.003572 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.641 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1331 0.245 h = 0.003 0.006 y[1] (numeric) = 2.87322346994 0.105763165293 y[1] (closed_form) = 2.87331765917 0.105716441023 absolute error = 0.0001051 relative error = 0.003657 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.641 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = 2.87501148977 0.108107338371 y[1] (closed_form) = 2.87511027646 0.108054605031 absolute error = 0.000112 relative error = 0.003892 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.645 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=666.6MB, alloc=52.3MB, time=8.26 x[1] = 2.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = 2.8754753239 0.110252763099 y[1] (closed_form) = 2.87557831656 0.110199902887 absolute error = 0.0001158 relative error = 0.004023 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.645 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1363 0.259 h = 0.001 0.001 y[1] (numeric) = 2.87577590078 0.111536431346 y[1] (closed_form) = 2.87588040672 0.111483485537 absolute error = 0.0001172 relative error = 0.004071 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.646 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1373 0.26 h = 0.001 0.003 y[1] (numeric) = 2.87629347125 0.111880314669 y[1] (closed_form) = 2.87639798057 0.111827032462 absolute error = 0.0001173 relative error = 0.004075 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.647 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=711.8MB, alloc=52.3MB, time=8.81 x[1] = 2.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = 2.87698541505 0.113084312756 y[1] (closed_form) = 2.87709128033 0.113030034304 absolute error = 0.000119 relative error = 0.004132 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.648 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1384 0.267 h = 0.003 0.006 y[1] (numeric) = 2.87738120624 0.114795761924 y[1] (closed_form) = 2.87748976374 0.114741375808 absolute error = 0.0001214 relative error = 0.004216 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.648 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = 2.87920860312 0.117107415066 y[1] (closed_form) = 2.87932176637 0.117047016127 absolute error = 0.0001283 relative error = 0.004451 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.652 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=757.2MB, alloc=52.3MB, time=9.37 x[1] = 2.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = 2.87970937107 0.119243543905 y[1] (closed_form) = 2.87982674487 0.119183020272 absolute error = 0.0001321 relative error = 0.004582 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.652 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1416 0.281 h = 0.001 0.001 y[1] (numeric) = 2.88003204536 0.12052134032 y[1] (closed_form) = 2.88015093413 0.120460731822 absolute error = 0.0001334 relative error = 0.004629 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.652 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1426 0.282 h = 0.001 0.003 y[1] (numeric) = 2.88055533041 0.120856090409 y[1] (closed_form) = 2.88067422274 0.120795145146 absolute error = 0.0001336 relative error = 0.004634 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.653 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=802.4MB, alloc=52.3MB, time=9.92 x[1] = 2.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = 2.88126783808 0.122047535515 y[1] (closed_form) = 2.8813880884 0.121985593642 absolute error = 0.0001353 relative error = 0.00469 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.655 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1437 0.289 h = 0.003 0.006 y[1] (numeric) = 2.88169316133 0.123751404814 y[1] (closed_form) = 2.8818161069 0.12368935658 absolute error = 0.0001377 relative error = 0.004774 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.655 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = 2.88355999579 0.126030524396 y[1] (closed_form) = 2.88368755539 0.125962458995 absolute error = 0.0001446 relative error = 0.005009 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.659 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=847.6MB, alloc=52.3MB, time=10.48 x[1] = 2.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = 2.88409774305 0.128157366746 y[1] (closed_form) = 2.88422951803 0.128089178621 absolute error = 0.0001484 relative error = 0.005139 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.659 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1469 0.303 h = 0.001 0.001 y[1] (numeric) = 2.88444254242 0.129429296352 y[1] (closed_form) = 2.88457583415 0.129361024016 absolute error = 0.0001498 relative error = 0.005187 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.659 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = 2.8849715532 0.129754905916 y[1] (closed_form) = 2.88510484867 0.129686296428 absolute error = 0.0001499 relative error = 0.005191 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.661 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=892.9MB, alloc=52.3MB, time=11.04 x[1] = 2.148 0.308 h = 0.003 0.006 y[1] (numeric) = 2.88542241677 0.131452608512 y[1] (closed_form) = 2.88555841009 0.131383893482 absolute error = 0.0001524 relative error = 0.005275 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.661 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.151 0.314 h = 0.0001 0.005 y[1] (numeric) = 2.88732363476 0.133704181191 y[1] (closed_form) = 2.88746424927 0.133629444884 absolute error = 0.0001592 relative error = 0.005509 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.664 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = 2.88789336089 0.135823477047 y[1] (closed_form) = 2.88803819513 0.135748619603 absolute error = 0.000163 relative error = 0.005639 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.665 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=938.1MB, alloc=52.3MB, time=11.59 x[1] = 2.1512 0.322 h = 0.001 0.001 y[1] (numeric) = 2.88825729759 0.137090623656 y[1] (closed_form) = 2.88840365019 0.137015682524 absolute error = 0.0001644 relative error = 0.005686 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.665 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1522 0.323 h = 0.001 0.003 y[1] (numeric) = 2.88879135476 0.137408427272 y[1] (closed_form) = 2.88893771123 0.13733314864 absolute error = 0.0001646 relative error = 0.005691 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.666 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = 2.88954235585 0.138576749232 y[1] (closed_form) = 2.88969007416 0.138500472996 absolute error = 0.0001662 relative error = 0.005747 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.668 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=983.5MB, alloc=52.3MB, time=12.15 x[1] = 2.1533 0.33 h = 0.003 0.006 y[1] (numeric) = 2.89002282178 0.140266882533 y[1] (closed_form) = 2.8901732414 0.140190502038 absolute error = 0.0001687 relative error = 0.00583 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.668 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = 2.89196359249 0.142485886713 y[1] (closed_form) = 2.89211864156 0.142403479504 absolute error = 0.0001756 relative error = 0.006064 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.672 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = 2.8925703873 0.144595907914 y[1] (closed_form) = 2.8927296614 0.144513381145 absolute error = 0.0001794 relative error = 0.006194 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.672 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1028.7MB, alloc=52.3MB, time=12.70 x[1] = 2.1565 0.344 h = 0.001 0.001 y[1] (numeric) = 2.89295650337 0.145857193622 y[1] (closed_form) = 2.89311729777 0.145774583673 absolute error = 0.0001808 relative error = 0.00624 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.673 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1575 0.345 h = 0.001 0.003 y[1] (numeric) = 2.89349630686 0.146165841069 y[1] (closed_form) = 2.89365710528 0.146082893194 absolute error = 0.0001809 relative error = 0.006245 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.674 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = 2.89426795819 0.147321595598 y[1] (closed_form) = 2.89443012056 0.147237649394 absolute error = 0.0001826 relative error = 0.006301 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.675 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1074.1MB, alloc=52.3MB, time=13.26 x[1] = 2.1586 0.352 h = 0.003 0.006 y[1] (numeric) = 2.89477806651 0.149004162697 y[1] (closed_form) = 2.89494293368 0.148920113144 absolute error = 0.0001851 relative error = 0.006384 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.675 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = 2.89675845282 0.15119057366 y[1] (closed_form) = 2.89692795767 0.151100491375 absolute error = 0.000192 relative error = 0.006617 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.679 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = 2.89740236689 0.153291322881 y[1] (closed_form) = 2.89757610231 0.153201122395 absolute error = 0.0001958 relative error = 0.006746 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1119.4MB, alloc=52.3MB, time=13.82 x[1] = 2.1618 0.366 h = 0.001 0.001 y[1] (numeric) = 2.89781069299 0.154546748625 y[1] (closed_form) = 2.89798595073 0.154456465386 absolute error = 0.0001971 relative error = 0.006793 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1628 0.367 h = 0.001 0.003 y[1] (numeric) = 2.89835625367 0.154846230246 y[1] (closed_form) = 2.89853151555 0.154755608637 absolute error = 0.0001973 relative error = 0.006797 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.681 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = 2.89914858658 0.155989408776 y[1] (closed_form) = 2.89932521456 0.155897787984 absolute error = 0.000199 relative error = 0.006853 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.682 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1164.7MB, alloc=52.3MB, time=14.38 x[1] = 2.1639 0.374 h = 0.003 0.006 y[1] (numeric) = 2.89968837855 0.157664410621 y[1] (closed_form) = 2.89986771497 0.157572687249 absolute error = 0.0002014 relative error = 0.006936 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.683 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = 2.90170844402 0.159818199778 y[1] (closed_form) = 2.90189242631 0.159720437075 absolute error = 0.0002083 relative error = 0.007169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.687 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.167 0.385 h = 0.0001 0.003 y[1] (numeric) = 2.90238952964 0.161909677305 y[1] (closed_form) = 2.90257774827 0.161811797543 absolute error = 0.0002121 relative error = 0.007298 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.687 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1210.1MB, alloc=52.3MB, time=14.93 x[1] = 2.1671 0.388 h = 0.001 0.001 y[1] (numeric) = 2.90282009741 0.163159242573 y[1] (closed_form) = 2.90300984048 0.163061280403 absolute error = 0.0002135 relative error = 0.007344 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.688 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1681 0.389 h = 0.001 0.003 y[1] (numeric) = 2.90337142601 0.163449547893 y[1] (closed_form) = 2.90356117333 0.163351246888 absolute error = 0.0002137 relative error = 0.007348 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.689 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = 2.9041844724 0.164580140093 y[1] (closed_form) = 2.904375588 0.164480838927 absolute error = 0.0002154 relative error = 0.007404 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.69 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1255.3MB, alloc=52.3MB, time=15.49 x[1] = 2.1692 0.396 h = 0.003 0.006 y[1] (numeric) = 2.90475399063 0.166247575706 y[1] (closed_form) = 2.90494781845 0.166148172586 absolute error = 0.0002178 relative error = 0.007486 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.691 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = 2.90681379946 0.168368710601 y[1] (closed_form) = 2.9070122813 0.168263260973 absolute error = 0.0002248 relative error = 0.007719 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.694 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = 2.90753211053 0.17045091432 y[1] (closed_form) = 2.90773483472 0.170345348552 absolute error = 0.0002286 relative error = 0.007847 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.695 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1300.6MB, alloc=52.3MB, time=16.04 x[1] = 2.1724 0.41 h = 0.001 0.001 y[1] (numeric) = 2.90798495261 0.171694617141 y[1] (closed_form) = 2.90818920344 0.171588969228 absolute error = 0.00023 relative error = 0.007893 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.695 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = 2.90854205972 0.171975734873 y[1] (closed_form) = 2.90874631489 0.171869747642 absolute error = 0.0002301 relative error = 0.007897 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.696 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1735 0.415 h = 0.003 0.006 y[1] (numeric) = 2.90913729074 0.173637010505 y[1] (closed_form) = 2.90934426134 0.173530921564 absolute error = 0.0002326 relative error = 0.00798 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.697 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1346.0MB, alloc=52.3MB, time=16.60 x[1] = 2.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = 2.91123175075 0.175730483236 y[1] (closed_form) = 2.91144338245 0.175618341244 absolute error = 0.0002395 relative error = 0.008211 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.701 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = 2.91198225922 0.177805145164 y[1] (closed_form) = 2.91219813863 0.177692887719 absolute error = 0.0002433 relative error = 0.00834 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.701 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1767 0.429 h = 0.001 0.001 y[1] (numeric) = 2.91245437102 0.179044064966 y[1] (closed_form) = 2.91267177901 0.178931725564 absolute error = 0.0002447 relative error = 0.008386 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.702 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1391.5MB, alloc=52.3MB, time=17.16 x[1] = 2.1777 0.43 h = 0.001 0.003 y[1] (numeric) = 2.91301657008 0.179317333676 y[1] (closed_form) = 2.91323398248 0.179204654526 absolute error = 0.0002449 relative error = 0.00839 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.703 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = 2.91386839648 0.180424719784 y[1] (closed_form) = 2.91408718128 0.180311038344 absolute error = 0.0002466 relative error = 0.008445 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.704 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1436.9MB, alloc=52.3MB, time=17.72 x[1] = 2.1788 0.437 h = 0.003 0.006 y[1] (numeric) = 2.91449343634 0.182078422521 y[1] (closed_form) = 2.91471494079 0.181964639958 absolute error = 0.000249 relative error = 0.008527 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.705 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = 2.91662776116 0.184139171108 y[1] (closed_form) = 2.91685393476 0.184019327249 absolute error = 0.000256 relative error = 0.008758 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.708 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = 2.91741559978 0.186204549539 y[1] (closed_form) = 2.91764602753 0.18608459073 absolute error = 0.0002598 relative error = 0.008886 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.709 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1482.1MB, alloc=52.3MB, time=18.28 x[1] = 2.182 0.451 h = 0.001 0.001 y[1] (numeric) = 2.91791004914 0.187437599735 y[1] (closed_form) = 2.91814200781 0.187317559079 absolute error = 0.0002612 relative error = 0.008932 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.183 0.452 h = 0.001 0.003 y[1] (numeric) = 2.91847804618 0.187701657832 y[1] (closed_form) = 2.91871000932 0.187581276908 absolute error = 0.0002613 relative error = 0.008936 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.711 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.184 0.455 h = 0.0001 0.004 y[1] (numeric) = 2.91935068041 0.188796418726 y[1] (closed_form) = 2.91958401819 0.188675034176 absolute error = 0.000263 relative error = 0.00899 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.712 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1527.4MB, alloc=52.3MB, time=18.84 x[1] = 2.1841 0.459 h = 0.003 0.006 y[1] (numeric) = 2.92000557549 0.19044254227 y[1] (closed_form) = 2.92024163712 0.190321056808 absolute error = 0.0002655 relative error = 0.009072 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.713 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = 2.92217983086 0.192470523238 y[1] (closed_form) = 2.92242056964 0.192342967666 absolute error = 0.0002724 relative error = 0.009302 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.716 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = 2.92300505811 0.19452660913 y[1] (closed_form) = 2.92325005768 0.194398938884 absolute error = 0.0002763 relative error = 0.00943 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.717 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1572.7MB, alloc=52.3MB, time=19.39 x[1] = 2.1873 0.473 h = 0.001 0.001 y[1] (numeric) = 2.92352188031 0.19575378355 y[1] (closed_form) = 2.92376841323 0.195626031481 absolute error = 0.0002777 relative error = 0.009476 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.718 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1883 0.474 h = 0.001 0.003 y[1] (numeric) = 2.92409568547 0.196008617449 y[1] (closed_form) = 2.92434222289 0.195880524574 absolute error = 0.0002778 relative error = 0.009479 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.719 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = 2.92498916138 0.197090736 y[1] (closed_form) = 2.92523707571 0.196961638036 absolute error = 0.0002795 relative error = 0.009534 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.72 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1618.0MB, alloc=52.3MB, time=19.95 x[1] = 2.1894 0.481 h = 0.003 0.006 y[1] (numeric) = 2.92567395912 0.19872927186 y[1] (closed_form) = 2.92592460164 0.198600073049 absolute error = 0.000282 relative error = 0.009615 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.721 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = 2.92788821121 0.200724437897 y[1] (closed_form) = 2.9281435388 0.200589159595 absolute error = 0.000289 relative error = 0.009845 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.724 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = 2.92875088702 0.202771219758 y[1] (closed_form) = 2.92901048228 0.202635826827 absolute error = 0.0002928 relative error = 0.009972 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.725 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1663.2MB, alloc=52.3MB, time=20.51 x[1] = 2.1926 0.495 h = 0.001 0.001 y[1] (numeric) = 2.92929011821 0.203992510745 y[1] (closed_form) = 2.92955124931 0.20385703593 absolute error = 0.0002942 relative error = 0.01002 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.726 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1936 0.496 h = 0.001 0.003 y[1] (numeric) = 2.92986974146 0.204238106069 y[1] (closed_form) = 2.93013087709 0.204102289893 absolute error = 0.0002943 relative error = 0.01002 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.727 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = 2.93078409333 0.205307563387 y[1] (closed_form) = 2.93104660815 0.205170740533 absolute error = 0.000296 relative error = 0.01008 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.728 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1708.7MB, alloc=52.3MB, time=21.06 x[1] = 2.1947 0.503 h = 0.003 0.006 y[1] (numeric) = 2.93149884234 0.206938501101 y[1] (closed_form) = 2.93176408983 0.206801577314 absolute error = 0.0002985 relative error = 0.01016 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.729 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = 2.93375315768 0.208900801066 y[1] (closed_form) = 2.93402309808 0.208757787846 absolute error = 0.0003055 relative error = 0.01039 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.733 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = 2.93465334347 0.210938264943 y[1] (closed_form) = 2.93492755863 0.210795136906 absolute error = 0.0003093 relative error = 0.01051 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.733 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1754.0MB, alloc=52.3MB, time=21.62 x[1] = 2.1979 0.517 h = 0.001 0.001 y[1] (numeric) = 2.93521502065 0.212153663348 y[1] (closed_form) = 2.93549077422 0.212010453282 absolute error = 0.0003107 relative error = 0.01056 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.734 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = 2.93580047178 0.212390004934 y[1] (closed_form) = 2.93607622988 0.212246452934 absolute error = 0.0003109 relative error = 0.01056 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.735 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.199 0.522 h = 0.003 0.006 y[1] (numeric) = 2.93654113251 0.214014750339 y[1] (closed_form) = 2.93681962708 0.213871097042 absolute error = 0.0003134 relative error = 0.01064 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.736 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1799.4MB, alloc=52.3MB, time=22.18 x[1] = 2.202 0.528 h = 0.0001 0.005 y[1] (numeric) = 2.93883037887 0.215949194735 y[1] (closed_form) = 2.93911357316 0.21579944309 absolute error = 0.0003204 relative error = 0.01087 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.739 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = 2.93976301354 0.21797907278 y[1] (closed_form) = 2.94005048886 0.217829206057 absolute error = 0.0003242 relative error = 0.011 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.74 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2022 0.536 h = 0.001 0.001 y[1] (numeric) = 2.9403441121 0.21918965857 y[1] (closed_form) = 2.94063312811 0.219039709655 absolute error = 0.0003256 relative error = 0.01104 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.741 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1844.6MB, alloc=52.3MB, time=22.74 x[1] = 2.2032 0.537 h = 0.001 0.003 y[1] (numeric) = 2.94093469784 0.219418091685 y[1] (closed_form) = 2.94122371837 0.219267800328 absolute error = 0.0003258 relative error = 0.01105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.742 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = 2.94188813905 0.22046418275 y[1] (closed_form) = 2.94217854309 0.220312881456 absolute error = 0.0003275 relative error = 0.0111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.743 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2043 0.544 h = 0.003 0.006 y[1] (numeric) = 2.94265884453 0.22208130565 y[1] (closed_form) = 2.94295198992 0.221929902918 absolute error = 0.0003299 relative error = 0.01118 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.744 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1889.9MB, alloc=52.3MB, time=23.29 x[1] = 2.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = 2.94498827943 0.223982779464 y[1] (closed_form) = 2.94528613222 0.223825267401 absolute error = 0.0003369 relative error = 0.01141 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.748 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = 2.94595854234 0.226003307744 y[1] (closed_form) = 2.94626068364 0.22584567998 absolute error = 0.0003408 relative error = 0.01153 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.749 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2075 0.558 h = 0.001 0.001 y[1] (numeric) = 2.94656215806 0.227207980406 y[1] (closed_form) = 2.94686584275 0.227050270142 absolute error = 0.0003422 relative error = 0.01158 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.749 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1935.2MB, alloc=52.3MB, time=23.85 x[1] = 2.2085 0.559 h = 0.001 0.003 y[1] (numeric) = 2.94715858954 0.227427129606 y[1] (closed_form) = 2.94746227873 0.227269076295 absolute error = 0.0003424 relative error = 0.01158 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = 2.94813300723 0.228460496101 y[1] (closed_form) = 2.94843808226 0.228301430909 absolute error = 0.0003441 relative error = 0.01163 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.752 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2096 0.566 h = 0.003 0.006 y[1] (numeric) = 2.94893380943 0.230069980585 y[1] (closed_form) = 2.94924163066 0.229910813436 absolute error = 0.0003465 relative error = 0.01171 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.753 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1980.7MB, alloc=52.3MB, time=24.41 x[1] = 2.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = 2.95130350019 0.231938421788 y[1] (closed_form) = 2.9516160364 0.231773133772 absolute error = 0.0003536 relative error = 0.01194 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.756 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = 2.95231145673 0.23394957927 y[1] (closed_form) = 2.95262828913 0.233784174693 absolute error = 0.0003574 relative error = 0.01207 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.757 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2128 0.58 h = 0.001 0.001 y[1] (numeric) = 2.95293762893 0.235148325368 y[1] (closed_form) = 2.9532560075 0.234982837896 absolute error = 0.0003588 relative error = 0.01211 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.758 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2026.0MB, alloc=52.3MB, time=24.96 x[1] = 2.2138 0.581 h = 0.001 0.003 y[1] (numeric) = 2.95353991534 0.23535817327 y[1] (closed_form) = 2.95385829836 0.235192342129 absolute error = 0.000359 relative error = 0.01211 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.759 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = 2.95453534526 0.236378789521 y[1] (closed_form) = 2.95485511645 0.236211944431 absolute error = 0.0003607 relative error = 0.01217 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2149 0.588 h = 0.003 0.006 y[1] (numeric) = 2.95536629702 0.237980617452 y[1] (closed_form) = 2.9556888194 0.237813669731 absolute error = 0.0003632 relative error = 0.01225 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.761 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2071.4MB, alloc=52.3MB, time=25.52 x[1] = 2.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = 2.95777631111 0.239815960232 y[1] (closed_form) = 2.95810355594 0.23964287956 absolute error = 0.0003702 relative error = 0.01247 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.765 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.218 0.599 h = 0.0001 0.003 y[1] (numeric) = 2.95882202798 0.241817723385 y[1] (closed_form) = 2.95915357687 0.241644525051 absolute error = 0.0003741 relative error = 0.0126 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.766 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2181 0.602 h = 0.001 0.001 y[1] (numeric) = 2.95947079673 0.243010527972 y[1] (closed_form) = 2.95980389464 0.24283724626 absolute error = 0.0003755 relative error = 0.01264 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.767 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2116.7MB, alloc=52.3MB, time=26.08 x[1] = 2.2191 0.603 h = 0.001 0.003 y[1] (numeric) = 2.96007894705 0.243211056431 y[1] (closed_form) = 2.96041204934 0.243037430412 absolute error = 0.0003756 relative error = 0.01265 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.768 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = 2.96109542522 0.24421889501 y[1] (closed_form) = 2.96142991804 0.24404425285 absolute error = 0.0003773 relative error = 0.0127 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.769 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2202 0.61 h = 0.003 0.006 y[1] (numeric) = 2.96195658043 0.245813046243 y[1] (closed_form) = 2.96229382953 0.245638300623 absolute error = 0.0003798 relative error = 0.01278 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.77 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2162.0MB, alloc=52.3MB, time=26.64 x[1] = 2.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = 2.96440698542 0.247615221017 y[1] (closed_form) = 2.96474896433 0.247434329816 absolute error = 0.0003869 relative error = 0.013 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.774 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = 2.96549053058 0.249607563805 y[1] (closed_form) = 2.96583682162 0.249426553601 absolute error = 0.0003907 relative error = 0.01313 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.775 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2234 0.624 h = 0.001 0.001 y[1] (numeric) = 2.96616193669 0.25079441042 y[1] (closed_form) = 2.96650977966 0.250613316266 absolute error = 0.0003922 relative error = 0.01317 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.775 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2207.4MB, alloc=52.3MB, time=27.19 x[1] = 2.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = 2.96677595964 0.250985600533 y[1] (closed_form) = 2.96712380691 0.250804161415 absolute error = 0.0003923 relative error = 0.01318 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.776 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2245 0.629 h = 0.003 0.006 y[1] (numeric) = 2.96766324883 0.252573487144 y[1] (closed_form) = 2.96801385672 0.252391943574 absolute error = 0.0003948 relative error = 0.01325 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.777 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = 2.97014887142 0.254347535649 y[1] (closed_form) = 2.97050421552 0.254159835276 absolute error = 0.0004019 relative error = 0.01348 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.781 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2252.7MB, alloc=52.3MB, time=27.75 x[1] = 2.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = 2.97126514595 0.256332198668 y[1] (closed_form) = 2.9716248093 0.256144378043 absolute error = 0.0004058 relative error = 0.0136 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.782 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2277 0.643 h = 0.001 0.001 y[1] (numeric) = 2.97195614203 0.257514172847 y[1] (closed_form) = 2.97231735988 0.257326267742 absolute error = 0.0004072 relative error = 0.01365 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.783 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2287 0.644 h = 0.001 0.003 y[1] (numeric) = 2.97257533832 0.257697379203 y[1] (closed_form) = 2.97293656038 0.257509128558 absolute error = 0.0004073 relative error = 0.01365 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.784 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2298.1MB, alloc=52.3MB, time=28.31 x[1] = 2.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = 2.97363123232 0.258681614279 y[1] (closed_form) = 2.97399384932 0.258492343115 absolute error = 0.000409 relative error = 0.0137 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.785 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2298 0.651 h = 0.003 0.006 y[1] (numeric) = 2.97454882792 0.260261781797 y[1] (closed_form) = 2.97491421104 0.260072405279 absolute error = 0.0004115 relative error = 0.01378 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.786 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = 2.97707496819 0.262002523638 y[1] (closed_form) = 2.97744509465 0.261806976682 absolute error = 0.0004186 relative error = 0.01401 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.79 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2343.5MB, alloc=52.3MB, time=28.86 x[1] = 2.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = 2.97822920108 0.263977711999 y[1] (closed_form) = 2.97860365521 0.263782042997 absolute error = 0.0004225 relative error = 0.01413 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.791 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.233 0.665 h = 0.001 0.001 y[1] (numeric) = 2.97894291258 0.265153694033 y[1] (closed_form) = 2.97931892423 0.264957939813 absolute error = 0.0004239 relative error = 0.01417 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.792 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.234 0.666 h = 0.001 0.003 y[1] (numeric) = 2.97956799732 0.265327524973 y[1] (closed_form) = 2.97994401308 0.265131424528 absolute error = 0.0004241 relative error = 0.01418 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.793 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2388.9MB, alloc=52.3MB, time=29.42 x[1] = 2.235 0.669 h = 0.0001 0.004 y[1] (numeric) = 2.98064504455 0.2662988947 y[1] (closed_form) = 2.98102245763 0.266101771193 absolute error = 0.0004258 relative error = 0.01423 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.794 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2351 0.673 h = 0.003 0.006 y[1] (numeric) = 2.98159300336 0.267871317437 y[1] (closed_form) = 2.98197318799 0.2676740873 absolute error = 0.0004283 relative error = 0.01431 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.795 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = 2.98415972895 0.269578672326 y[1] (closed_form) = 2.98454466392 0.269375257578 absolute error = 0.0004354 relative error = 0.01453 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.799 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2434.3MB, alloc=52.3MB, time=29.98 x[1] = 2.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = 2.9853519916 0.271544352804 y[1] (closed_form) = 2.98574126285 0.271340813971 absolute error = 0.0004393 relative error = 0.01465 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2383 0.687 h = 0.001 0.001 y[1] (numeric) = 2.9860884613 0.272714321884 y[1] (closed_form) = 2.98647929316 0.272510697004 absolute error = 0.0004407 relative error = 0.0147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.801 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2393 0.688 h = 0.001 0.003 y[1] (numeric) = 2.98671944252 0.27287875637 y[1] (closed_form) = 2.98711027834 0.272674784565 absolute error = 0.0004409 relative error = 0.0147 % Correct digits = 4 memory used=2479.8MB, alloc=52.3MB, time=30.54 Radius of convergence (given) for eq 1 = 3.802 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = 2.98781767999 0.273837226589 y[1] (closed_form) = 2.98820991551 0.273632229056 absolute error = 0.0004426 relative error = 0.01475 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.804 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2404 0.695 h = 0.003 0.006 y[1] (numeric) = 2.98879605954 0.275401876612 y[1] (closed_form) = 2.98919107217 0.275196771013 absolute error = 0.0004451 relative error = 0.01483 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.804 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2525.1MB, alloc=52.3MB, time=31.10 x[1] = 2.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = 2.99140343799 0.277075760546 y[1] (closed_form) = 2.99180320781 0.276864455634 absolute error = 0.0004522 relative error = 0.01505 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.808 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = 2.9926338029 0.279031897388 y[1] (closed_form) = 2.99303791779 0.278820466105 absolute error = 0.0004561 relative error = 0.01517 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.809 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2436 0.709 h = 0.001 0.001 y[1] (numeric) = 2.99339307424 0.280195831176 y[1] (closed_form) = 2.99379875291 0.279984312927 absolute error = 0.0004575 relative error = 0.01522 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2570.4MB, alloc=52.3MB, time=31.66 x[1] = 2.2446 0.71 h = 0.001 0.003 y[1] (numeric) = 2.99402995968 0.280350847439 y[1] (closed_form) = 2.99443564214 0.28013898155 absolute error = 0.0004577 relative error = 0.01522 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.811 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = 2.9951494246 0.281296382253 y[1] (closed_form) = 2.99555650914 0.281083487849 absolute error = 0.0004594 relative error = 0.01527 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.813 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2457 0.717 h = 0.003 0.006 y[1] (numeric) = 2.99615828327 0.2828532296 y[1] (closed_form) = 2.99656815059 0.282640225533 absolute error = 0.0004619 relative error = 0.01535 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.814 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2615.7MB, alloc=52.3MB, time=32.21 x[1] = 2.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = 2.99880638198 0.284493554879 y[1] (closed_form) = 2.99922101319 0.284274336271 absolute error = 0.000469 relative error = 0.01557 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.818 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = 3.00007492274 0.286440109799 y[1] (closed_form) = 3.00049390797 0.286220762285 absolute error = 0.0004729 relative error = 0.01569 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.819 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2489 0.731 h = 0.001 0.001 y[1] (numeric) = 3.00085703978 0.287597984428 y[1] (closed_form) = 3.00127759201 0.287378548936 absolute error = 0.0004744 relative error = 0.01573 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2661.0MB, alloc=52.3MB, time=32.77 x[1] = 2.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = 3.00149983689 0.287743559972 y[1] (closed_form) = 3.00192039274 0.287523776112 absolute error = 0.0004745 relative error = 0.01574 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.821 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.25 0.736 h = 0.003 0.006 y[1] (numeric) = 3.00253507201 0.28929402973 y[1] (closed_form) = 3.00295841546 0.289074134562 absolute error = 0.000477 relative error = 0.01581 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.822 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.253 0.742 h = 0.0001 0.005 y[1] (numeric) = 3.00521867643 0.290905881949 y[1] (closed_form) = 3.00564678961 0.29067975879 absolute error = 0.0004842 relative error = 0.01603 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.826 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2706.4MB, alloc=52.3MB, time=33.32 x[1] = 2.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = 3.0065202522 0.292844612435 y[1] (closed_form) = 3.00695272729 0.292618358097 absolute error = 0.0004881 relative error = 0.01616 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2532 0.75 h = 0.001 0.001 y[1] (numeric) = 3.0073221424 0.293997524122 y[1] (closed_form) = 3.00775618731 0.293771180901 absolute error = 0.0004895 relative error = 0.0162 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.827 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2542 0.751 h = 0.001 0.003 y[1] (numeric) = 3.00797014667 0.294135025384 y[1] (closed_form) = 3.00840419504 0.293908333153 absolute error = 0.0004897 relative error = 0.0162 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.829 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2751.8MB, alloc=52.3MB, time=33.88 x[1] = 2.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = 3.00912936565 0.295056642877 y[1] (closed_form) = 3.00956482055 0.294828916651 absolute error = 0.0004914 relative error = 0.01625 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = 3.01019519099 0.296599249295 y[1] (closed_form) = 3.01063343952 0.296371410078 absolute error = 0.0004939 relative error = 0.01633 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.831 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2554 0.762 h = 0.003 0.006 y[1] (numeric) = 3.0112666036 0.298141629022 y[1] (closed_form) = 3.01170764677 0.297913676962 absolute error = 0.0004965 relative error = 0.0164 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.832 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2797.2MB, alloc=52.3MB, time=34.44 x[1] = 2.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = 3.01399937646 0.299715426438 y[1] (closed_form) = 3.01444519749 0.29948122757 absolute error = 0.0005036 relative error = 0.01662 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.836 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = 3.01534625949 0.301644247084 y[1] (closed_form) = 3.01579645344 0.301409913841 absolute error = 0.0005075 relative error = 0.01675 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.837 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2586 0.776 h = 0.001 0.001 y[1] (numeric) = 3.01617527521 0.302790844954 y[1] (closed_form) = 3.01662704294 0.302556421558 absolute error = 0.000509 relative error = 0.01679 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.838 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2842.6MB, alloc=52.3MB, time=35.00 x[1] = 2.2596 0.777 h = 0.001 0.003 y[1] (numeric) = 3.01683058206 0.302917439705 y[1] (closed_form) = 3.01728235302 0.302682666404 absolute error = 0.0005091 relative error = 0.01679 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.839 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = 3.01801531359 0.303824542716 y[1] (closed_form) = 3.01846849399 0.303588731821 absolute error = 0.0005109 relative error = 0.01684 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.841 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2607 0.784 h = 0.003 0.006 y[1] (numeric) = 3.01911738916 0.305359019689 y[1] (closed_form) = 3.01957337029 0.305123093599 absolute error = 0.0005134 relative error = 0.01692 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.842 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2887.9MB, alloc=52.3MB, time=35.56 x[1] = 2.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = 3.02189109029 0.306898973231 y[1] (closed_form) = 3.02235185553 0.306656783524 absolute error = 0.0005205 relative error = 0.01713 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.846 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = 3.0232763809 0.308818084051 y[1] (closed_form) = 3.02374152852 0.308575756679 absolute error = 0.0005245 relative error = 0.01726 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.847 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2639 0.798 h = 0.001 0.001 y[1] (numeric) = 3.02412838098 0.309958543231 y[1] (closed_form) = 3.02459510577 0.309716124419 absolute error = 0.0005259 relative error = 0.0173 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.848 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2933.3MB, alloc=52.3MB, time=36.12 x[1] = 2.2649 0.799 h = 0.001 0.003 y[1] (numeric) = 3.02478962155 0.310075624968 y[1] (closed_form) = 3.02525634935 0.309832855478 absolute error = 0.0005261 relative error = 0.0173 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.849 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = 3.02599573415 0.310969632116 y[1] (closed_form) = 3.02646387375 0.310725821758 absolute error = 0.0005278 relative error = 0.01735 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.266 0.806 h = 0.003 0.006 y[1] (numeric) = 3.02712853444 0.312496167917 y[1] (closed_form) = 3.02759948087 0.312252240119 absolute error = 0.0005304 relative error = 0.01743 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.851 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2978.6MB, alloc=52.3MB, time=36.69 x[1] = 2.269 0.812 h = 0.0001 0.005 y[1] (numeric) = 3.02994323036 0.314002175139 y[1] (closed_form) = 3.03041896697 0.313751966406 absolute error = 0.0005375 relative error = 0.01764 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.855 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = 3.0313670062 0.315911527637 y[1] (closed_form) = 3.03184713482 0.315661177697 absolute error = 0.0005415 relative error = 0.01776 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.857 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2692 0.82 h = 0.001 0.001 y[1] (numeric) = 3.03224203704 0.317045818096 y[1] (closed_form) = 3.03272374628 0.316795375333 absolute error = 0.0005429 relative error = 0.01781 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.857 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3024.0MB, alloc=52.3MB, time=37.24 x[1] = 2.2702 0.821 h = 0.001 0.003 y[1] (numeric) = 3.03290921761 0.317153361451 y[1] (closed_form) = 3.0333909296 0.316902567225 absolute error = 0.0005431 relative error = 0.01781 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.859 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = 3.03413674914 0.318034228184 y[1] (closed_form) = 3.0346198753 0.317782389698 absolute error = 0.0005448 relative error = 0.01786 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2713 0.828 h = 0.003 0.006 y[1] (numeric) = 3.03530033653 0.319552782623 y[1] (closed_form) = 3.03578627572 0.319300824289 absolute error = 0.0005474 relative error = 0.01793 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.861 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3069.3MB, alloc=52.3MB, time=37.80 x[1] = 2.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = 3.03815609336 0.321024737472 y[1] (closed_form) = 3.03864682862 0.32076648038 absolute error = 0.0005545 relative error = 0.01815 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.865 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = 3.03961843297 0.322924280606 y[1] (closed_form) = 3.04011357002 0.322665878507 absolute error = 0.0005585 relative error = 0.01827 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.867 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2745 0.842 h = 0.001 0.001 y[1] (numeric) = 3.04051654148 0.324052370771 y[1] (closed_form) = 3.04101326266 0.323793874375 absolute error = 0.00056 relative error = 0.01831 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.867 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3114.6MB, alloc=52.3MB, time=38.36 x[1] = 2.2755 0.843 h = 0.001 0.003 y[1] (numeric) = 3.04118966801 0.324150349686 y[1] (closed_form) = 3.04168639166 0.323891501027 absolute error = 0.0005601 relative error = 0.01831 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.868 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = 3.04243865639 0.325018029747 y[1] (closed_form) = 3.04293679656 0.324758133318 absolute error = 0.0005619 relative error = 0.01836 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2766 0.85 h = 0.003 0.006 y[1] (numeric) = 3.04363309394 0.326528560592 y[1] (closed_form) = 3.04413405343 0.326268541742 absolute error = 0.0005644 relative error = 0.01844 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.871 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3159.9MB, alloc=52.3MB, time=38.92 x[1] = 2.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = 3.04652997737 0.327966353429 y[1] (closed_form) = 3.04703573864 0.327700017497 absolute error = 0.0005716 relative error = 0.01865 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.875 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = 3.04803096013 0.329856033602 y[1] (closed_form) = 3.04854113313 0.32958954861 absolute error = 0.0005756 relative error = 0.01877 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.877 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2798 0.864 h = 0.001 0.001 y[1] (numeric) = 3.0489521937 0.330977890365 y[1] (closed_form) = 3.04946395438 0.330711309507 absolute error = 0.000577 relative error = 0.01881 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.877 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3205.3MB, alloc=52.3MB, time=39.48 x[1] = 2.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = 3.04963127182 0.331066278096 y[1] (closed_form) = 3.05014303467 0.330799344164 absolute error = 0.0005772 relative error = 0.01881 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.878 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2809 0.869 h = 0.003 0.006 y[1] (numeric) = 3.05085241163 0.332570235842 y[1] (closed_form) = 3.05136699913 0.332303177013 absolute error = 0.0005798 relative error = 0.01889 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.879 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = 3.05378515649 0.333979023594 y[1] (closed_form) = 3.05430455077 0.333705631578 absolute error = 0.000587 relative error = 0.0191 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.884 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3250.7MB, alloc=52.3MB, time=40.04 x[1] = 2.284 0.88 h = 0.0001 0.003 y[1] (numeric) = 3.05531958459 0.335860630814 y[1] (closed_form) = 3.05584339931 0.335587086162 absolute error = 0.0005909 relative error = 0.01922 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.885 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2841 0.883 h = 0.001 0.001 y[1] (numeric) = 3.05626083656 0.336977370624 y[1] (closed_form) = 3.05678624208 0.336703728725 absolute error = 0.0005924 relative error = 0.01926 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.886 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2851 0.884 h = 0.001 0.003 y[1] (numeric) = 3.05694515655 0.337057551632 y[1] (closed_form) = 3.05747056397 0.336783555946 absolute error = 0.0005926 relative error = 0.01926 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.887 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3296.2MB, alloc=52.3MB, time=40.59 x[1] = 2.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = 3.05823433053 0.337900822116 y[1] (closed_form) = 3.0587611589 0.337625771841 absolute error = 0.0005943 relative error = 0.01931 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.889 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2862 0.891 h = 0.003 0.006 y[1] (numeric) = 3.05948643993 0.3393966728 y[1] (closed_form) = 3.06001609959 0.339121494954 absolute error = 0.0005969 relative error = 0.01939 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = 3.06246043374 0.340771085821 y[1] (closed_form) = 3.06299490552 0.340489555542 absolute error = 0.0006041 relative error = 0.0196 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.894 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3341.4MB, alloc=52.3MB, time=41.15 x[1] = 2.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = 3.06403365555 0.342642724531 y[1] (closed_form) = 3.06457255798 0.342361037087 absolute error = 0.0006081 relative error = 0.01972 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.895 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2894 0.905 h = 0.001 0.001 y[1] (numeric) = 3.06499812242 0.343753165812 y[1] (closed_form) = 3.0655386193 0.343471379377 absolute error = 0.0006095 relative error = 0.01976 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.896 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2904 0.906 h = 0.001 0.003 y[1] (numeric) = 3.06568840388 0.343823704135 y[1] (closed_form) = 3.06622890233 0.343541563079 absolute error = 0.0006097 relative error = 0.01976 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.897 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3386.8MB, alloc=52.3MB, time=41.72 x[1] = 2.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = 3.06699914384 0.344653646723 y[1] (closed_form) = 3.06754106556 0.344370447231 absolute error = 0.0006115 relative error = 0.01981 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.899 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2915 0.913 h = 0.003 0.006 y[1] (numeric) = 3.06828228787 0.346141342473 y[1] (closed_form) = 3.06882704744 0.345858012364 absolute error = 0.000614 relative error = 0.01988 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = 3.07129759488 0.347481260973 y[1] (closed_form) = 3.07184717172 0.347191558696 absolute error = 0.0006213 relative error = 0.0201 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.904 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3432.2MB, alloc=52.3MB, time=42.27 x[1] = 2.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = 3.07290969205 0.34934287029 y[1] (closed_form) = 3.07346370988 0.349053006059 absolute error = 0.0006253 relative error = 0.02021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.905 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2947 0.927 h = 0.001 0.001 y[1] (numeric) = 3.07389742248 0.350446975535 y[1] (closed_form) = 3.07445303845 0.350157010477 absolute error = 0.0006267 relative error = 0.02025 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.906 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2957 0.928 h = 0.001 0.003 y[1] (numeric) = 3.07459367007 0.350507842508 y[1] (closed_form) = 3.07514928725 0.350217521983 absolute error = 0.0006269 relative error = 0.02025 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.907 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3477.5MB, alloc=52.3MB, time=42.83 x[1] = 2.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = 3.0759260139 0.35132440443 y[1] (closed_form) = 3.07648305667 0.351033021505 absolute error = 0.0006286 relative error = 0.0203 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.909 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2968 0.935 h = 0.003 0.006 y[1] (numeric) = 3.077240258 0.352803895123 y[1] (closed_form) = 3.07780014526 0.35251237837 absolute error = 0.0006312 relative error = 0.02038 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.91 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = 3.08029694186 0.354109195806 y[1] (closed_form) = 3.08086165133 0.353811286668 absolute error = 0.0006385 relative error = 0.02059 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.915 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3523.0MB, alloc=52.3MB, time=43.38 x[1] = 2.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = 3.08194799672 0.355960712296 y[1] (closed_form) = 3.08251715765 0.355662636155 absolute error = 0.0006425 relative error = 0.02071 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.916 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3 0.949 h = 0.001 0.001 y[1] (numeric) = 3.08295903979 0.357058442464 y[1] (closed_form) = 3.0835298026 0.356760263563 absolute error = 0.000644 relative error = 0.02075 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.917 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.301 0.95 h = 0.001 0.003 y[1] (numeric) = 3.08366125778 0.357109608767 y[1] (closed_form) = 3.08423202144 0.356811073542 absolute error = 0.0006441 relative error = 0.02075 % Correct digits = 4 memory used=3568.4MB, alloc=52.3MB, time=43.94 Radius of convergence (given) for eq 1 = 3.918 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.302 0.953 h = 0.0001 0.004 y[1] (numeric) = 3.08501524332 0.35791273558 y[1] (closed_form) = 3.08558743486 0.357613133876 absolute error = 0.0006459 relative error = 0.02079 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.92 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3021 0.957 h = 0.003 0.006 y[1] (numeric) = 3.08636065347 0.359383969051 y[1] (closed_form) = 3.08693569621 0.359084230141 absolute error = 0.0006485 relative error = 0.02087 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.921 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3613.8MB, alloc=52.3MB, time=44.50 x[1] = 2.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = 3.08945877718 0.360654525138 y[1] (closed_form) = 3.09003864687 0.360348373147 absolute error = 0.0006557 relative error = 0.02108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.925 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = 3.09114887274 0.362495882817 y[1] (closed_form) = 3.09173320451 0.362189558516 absolute error = 0.0006598 relative error = 0.02119 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.926 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3053 0.971 h = 0.001 0.001 y[1] (numeric) = 3.09218327789 0.36358719733 y[1] (closed_form) = 3.09276921531 0.363280768242 absolute error = 0.0006612 relative error = 0.02123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.927 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3659.3MB, alloc=52.3MB, time=45.06 x[1] = 2.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = 3.09289147021 0.363628632993 y[1] (closed_form) = 3.09347740809 0.363321846711 absolute error = 0.0006614 relative error = 0.02123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.928 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3064 0.976 h = 0.003 0.006 y[1] (numeric) = 3.09426385969 0.365093088119 y[1] (closed_form) = 3.09485265448 0.364786161469 absolute error = 0.000664 relative error = 0.02131 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = 3.09739811937 0.366334127691 y[1] (closed_form) = 3.09799174526 0.36602076982 absolute error = 0.0006713 relative error = 0.02152 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.934 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3704.6MB, alloc=52.3MB, time=45.62 x[1] = 2.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = 3.09912200896 0.368167152632 y[1] (closed_form) = 3.09972010621 0.3678536178 absolute error = 0.0006753 relative error = 0.02163 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.935 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3096 0.99 h = 0.001 0.001 y[1] (numeric) = 3.10017664038 0.369253190193 y[1] (closed_form) = 3.1007763466 0.368939548799 absolute error = 0.0006768 relative error = 0.02167 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.936 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3106 0.991 h = 0.001 0.003 y[1] (numeric) = 3.10089009447 0.369286296779 y[1] (closed_form) = 3.10148980081 0.368972297431 absolute error = 0.0006769 relative error = 0.02167 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.937 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3750.0MB, alloc=52.3MB, time=46.18 x[1] = 2.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = 3.10228461223 0.370064532258 y[1] (closed_form) = 3.10288575073 0.369749458565 absolute error = 0.0006787 relative error = 0.02172 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.939 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3117 0.998 h = 0.003 0.006 y[1] (numeric) = 3.10368829234 0.37152062826 y[1] (closed_form) = 3.10429229481 0.371205410708 absolute error = 0.0006813 relative error = 0.02179 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.94 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = 3.10686410885 0.372726678869 y[1] (closed_form) = 3.10747294675 0.372405008521 absolute error = 0.0006886 relative error = 0.022 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.945 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3795.5MB, alloc=52.3MB, time=46.74 x[1] = 2.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = 3.10862719612 0.374549416447 y[1] (closed_form) = 3.10924051623 0.374227563348 absolute error = 0.0006926 relative error = 0.02212 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.946 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3149 1.012 h = 0.001 0.001 y[1] (numeric) = 3.10970528308 0.375628959362 y[1] (closed_form) = 3.11032021602 0.375306997496 absolute error = 0.0006941 relative error = 0.02216 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.947 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3159 1.013 h = 0.001 0.003 y[1] (numeric) = 3.11042471818 0.375652277877 y[1] (closed_form) = 3.11103965079 0.375329957167 absolute error = 0.0006943 relative error = 0.02216 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.948 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3840.9MB, alloc=52.3MB, time=47.30 x[1] = 2.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = 3.11184098606 0.376416913796 y[1] (closed_form) = 3.1124573531 0.376093514335 absolute error = 0.0006961 relative error = 0.0222 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.317 1.02 h = 0.003 0.006 y[1] (numeric) = 3.11327602436 0.377864592876 y[1] (closed_form) = 3.11389526232 0.377541045699 absolute error = 0.0006987 relative error = 0.02227 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.951 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.32 1.026 h = 0.0001 0.005 y[1] (numeric) = 3.11649345867 0.379035517897 y[1] (closed_form) = 3.11711753614 0.378705495883 absolute error = 0.000706 relative error = 0.02248 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.955 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3886.2MB, alloc=52.3MB, time=47.85 x[1] = 2.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = 3.11829582838 0.380847894855 y[1] (closed_form) = 3.11892439903 0.380517684038 absolute error = 0.00071 relative error = 0.0226 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.957 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3202 1.034 h = 0.001 0.001 y[1] (numeric) = 3.1193974213 0.381920898164 y[1] (closed_form) = 3.12002760868 0.381590576281 absolute error = 0.0007115 relative error = 0.02264 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.958 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3212 1.035 h = 0.001 0.003 y[1] (numeric) = 3.12012284024 0.381934396817 y[1] (closed_form) = 3.12075302685 0.381603715192 absolute error = 0.0007117 relative error = 0.02264 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.959 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3931.6MB, alloc=52.3MB, time=48.42 x[1] = 2.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = 3.12156089566 0.382685372359 y[1] (closed_form) = 3.12219251892 0.382353607464 absolute error = 0.0007135 relative error = 0.02268 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.961 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3223 1.042 h = 0.003 0.006 y[1] (numeric) = 3.12302735998 0.384124574483 y[1] (closed_form) = 3.12366186117 0.383792657846 absolute error = 0.0007161 relative error = 0.02275 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.962 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = 3.12628647223 0.385260233899 y[1] (closed_form) = 3.12692581681 0.384921819923 absolute error = 0.0007234 relative error = 0.02296 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.966 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3977.0MB, alloc=52.3MB, time=48.97 x[1] = 2.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = 3.12812820968 0.38706217444 y[1] (closed_form) = 3.1287720585 0.386723565345 absolute error = 0.0007275 relative error = 0.02308 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.968 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3255 1.056 h = 0.001 0.001 y[1] (numeric) = 3.12925335927 0.388128591653 y[1] (closed_form) = 3.12989882877 0.3877898691 absolute error = 0.0007289 relative error = 0.02311 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.969 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3265 1.057 h = 0.001 0.003 y[1] (numeric) = 3.12998476451 0.388132238036 y[1] (closed_form) = 3.13063023277 0.38779315483 absolute error = 0.0007291 relative error = 0.02311 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4022.2MB, alloc=52.3MB, time=49.53 x[1] = 2.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = 3.13144464473 0.388869490751 y[1] (closed_form) = 3.13209155184 0.388529319645 absolute error = 0.0007309 relative error = 0.02316 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.972 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3276 1.064 h = 0.003 0.006 y[1] (numeric) = 3.13294260326 0.390300153852 y[1] (closed_form) = 3.13359239539 0.389959826809 absolute error = 0.0007335 relative error = 0.02323 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.973 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = 3.13624345276 0.391400404274 y[1] (closed_form) = 3.13689809191 0.391053556936 absolute error = 0.0007408 relative error = 0.02344 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.977 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4067.7MB, alloc=52.3MB, time=50.09 x[1] = 2.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = 3.13812464374 0.393191830063 y[1] (closed_form) = 3.13878379832 0.392844781031 absolute error = 0.0007449 relative error = 0.02355 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.979 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3308 1.078 h = 0.001 0.001 y[1] (numeric) = 3.13927340099 0.394251613166 y[1] (closed_form) = 3.13993418024 0.393904448185 absolute error = 0.0007464 relative error = 0.02359 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.98 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = 3.14001079459 0.394245374256 y[1] (closed_form) = 3.14067157209 0.393897847702 absolute error = 0.0007466 relative error = 0.02359 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.981 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4113.1MB, alloc=52.3MB, time=50.64 x[1] = 2.3319 1.083 h = 0.003 0.006 y[1] (numeric) = 3.14153602015 0.395669012463 y[1] (closed_form) = 3.14219968869 0.395321326119 absolute error = 0.0007492 relative error = 0.02366 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.982 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = 3.14487326669 0.396739164746 y[1] (closed_form) = 3.14554178545 0.396384938025 absolute error = 0.0007566 relative error = 0.02386 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.987 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.335 1.094 h = 0.0001 0.003 y[1] (numeric) = 3.14678861356 0.398521946495 y[1] (closed_form) = 3.14746165756 0.398167512342 absolute error = 0.0007607 relative error = 0.02398 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.988 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4158.5MB, alloc=52.3MB, time=51.20 x[1] = 2.3351 1.097 h = 0.001 0.001 y[1] (numeric) = 3.14795781237 0.399576261608 y[1] (closed_form) = 3.14863248451 0.399221709335 absolute error = 0.0007622 relative error = 0.02401 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.989 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3361 1.098 h = 0.001 0.003 y[1] (numeric) = 3.14870048018 0.39956155822 y[1] (closed_form) = 3.14937515015 0.399206643571 absolute error = 0.0007623 relative error = 0.02401 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.99 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = 3.15020123503 0.400273365214 y[1] (closed_form) = 3.15087734797 0.399917353777 absolute error = 0.0007641 relative error = 0.02406 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.992 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4203.9MB, alloc=52.3MB, time=51.76 x[1] = 2.3372 1.105 h = 0.003 0.006 y[1] (numeric) = 3.1517580833 0.401688344131 y[1] (closed_form) = 3.15243709469 0.40133216859 absolute error = 0.0007668 relative error = 0.02413 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.993 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = 3.15513717687 0.402722812406 y[1] (closed_form) = 3.15582104166 0.402360072695 absolute error = 0.0007741 relative error = 0.02433 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.998 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = 3.15709213912 0.404494927941 y[1] (closed_form) = 3.15778054053 0.404131973733 absolute error = 0.0007782 relative error = 0.02445 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.999 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4249.2MB, alloc=52.3MB, time=52.32 x[1] = 2.3404 1.119 h = 0.001 0.001 y[1] (numeric) = 3.15828504174 0.405542516158 y[1] (closed_form) = 3.15897507535 0.405179441162 absolute error = 0.0007797 relative error = 0.02448 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3414 1.12 h = 0.001 0.003 y[1] (numeric) = 3.15903370106 0.405517864439 y[1] (closed_form) = 3.15972373195 0.40515442613 absolute error = 0.0007799 relative error = 0.02448 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.001 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = 3.16055638699 0.406215761463 y[1] (closed_form) = 3.16124786299 0.405851221418 absolute error = 0.0007817 relative error = 0.02453 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.003 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4294.8MB, alloc=52.3MB, time=52.88 x[1] = 2.3425 1.127 h = 0.003 0.006 y[1] (numeric) = 3.1621449274 0.407622013422 y[1] (closed_form) = 3.16283930913 0.407257304596 absolute error = 0.0007843 relative error = 0.0246 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.004 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = 3.1655659247 0.408620644788 y[1] (closed_form) = 3.16626516276 0.408249347557 absolute error = 0.0007917 relative error = 0.0248 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.009 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = 3.16756058938 0.410382008545 y[1] (closed_form) = 3.16826437555 0.41001048949 absolute error = 0.0007958 relative error = 0.02491 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4340.1MB, alloc=52.3MB, time=53.44 x[1] = 2.3457 1.141 h = 0.001 0.001 y[1] (numeric) = 3.1687772475 0.411422817502 y[1] (closed_form) = 3.16948266995 0.411051174896 absolute error = 0.0007973 relative error = 0.02495 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.011 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3467 1.142 h = 0.001 0.003 y[1] (numeric) = 3.16953189921 0.411388182713 y[1] (closed_form) = 3.17023731839 0.411016175848 absolute error = 0.0007975 relative error = 0.02495 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.013 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = 3.17107655267 0.412072101102 y[1] (closed_form) = 3.17178341908 0.411698987445 absolute error = 0.0007993 relative error = 0.02499 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.014 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4385.5MB, alloc=52.3MB, time=54.00 x[1] = 2.3478 1.149 h = 0.003 0.006 y[1] (numeric) = 3.17269685474 0.41346955622 y[1] (closed_form) = 3.17340663422 0.413096268936 absolute error = 0.000802 relative error = 0.02506 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.016 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = 3.17615981149 0.414432194502 y[1] (closed_form) = 3.17687444997 0.414052294141 absolute error = 0.0008093 relative error = 0.02526 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = 3.17819426602 0.4161827184 y[1] (closed_form) = 3.17891346419 0.415802588625 absolute error = 0.0008135 relative error = 0.02537 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.022 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4430.8MB, alloc=52.3MB, time=54.55 x[1] = 2.351 1.163 h = 0.001 0.001 y[1] (numeric) = 3.17943473152 0.417216694217 y[1] (closed_form) = 3.18015557008 0.416836438031 absolute error = 0.000815 relative error = 0.02541 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.023 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.352 1.164 h = 0.001 0.003 y[1] (numeric) = 3.18019537609 0.417172041037 y[1] (closed_form) = 3.18091621081 0.416791419638 absolute error = 0.0008152 relative error = 0.02541 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.024 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.353 1.167 h = 0.0001 0.004 y[1] (numeric) = 3.18176203327 0.41784191054 y[1] (closed_form) = 3.1824843173 0.417460177183 absolute error = 0.000817 relative error = 0.02545 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.026 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4476.1MB, alloc=52.3MB, time=55.11 x[1] = 2.3531 1.171 h = 0.003 0.006 y[1] (numeric) = 3.1834141668 0.419230496919 y[1] (closed_form) = 3.18413937131 0.41884858492 absolute error = 0.0008196 relative error = 0.02552 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.027 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = 3.18691913767 0.420156982693 y[1] (closed_form) = 3.18764920359 0.419768432515 absolute error = 0.000827 relative error = 0.02572 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.032 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = 3.1889934698 0.421896576138 y[1] (closed_form) = 3.1897281071 0.42150778869 absolute error = 0.0008312 relative error = 0.02583 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.033 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4521.5MB, alloc=52.3MB, time=55.66 x[1] = 2.3563 1.185 h = 0.001 0.001 y[1] (numeric) = 3.19025779474 0.422923663424 y[1] (closed_form) = 3.19099407657 0.42253474661 absolute error = 0.0008327 relative error = 0.02587 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.034 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = 3.1910244322 0.422868955954 y[1] (closed_form) = 3.1917607096 0.422479672965 absolute error = 0.0008329 relative error = 0.02587 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.036 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3574 1.19 h = 0.003 0.006 y[1] (numeric) = 3.1927041283 0.424250229809 y[1] (closed_form) = 3.19344333246 0.423860763626 absolute error = 0.0008355 relative error = 0.02594 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.037 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4566.9MB, alloc=52.3MB, time=56.22 x[1] = 2.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = 3.1962457398 0.425145967925 y[1] (closed_form) = 3.19698980754 0.424749841637 absolute error = 0.0008429 relative error = 0.02614 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.041 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = 3.19835459946 0.426876554788 y[1] (closed_form) = 3.19910324881 0.426480184399 absolute error = 0.0008471 relative error = 0.02625 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.043 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3606 1.204 h = 0.001 0.001 y[1] (numeric) = 3.19963958659 0.427897952208 y[1] (closed_form) = 3.20038988408 0.427501449883 absolute error = 0.0008486 relative error = 0.02628 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.044 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4612.3MB, alloc=52.3MB, time=56.78 x[1] = 2.3616 1.205 h = 0.001 0.003 y[1] (numeric) = 3.2004115026 0.427834632541 y[1] (closed_form) = 3.20116179515 0.4274377632 absolute error = 0.0008488 relative error = 0.02628 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.045 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = 3.20201936833 0.428478431083 y[1] (closed_form) = 3.20277111405 0.42808043991 absolute error = 0.0008506 relative error = 0.02632 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.047 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3627 1.212 h = 0.003 0.006 y[1] (numeric) = 3.2037310271 0.429850697716 y[1] (closed_form) = 3.20448570728 0.429452518206 absolute error = 0.0008533 relative error = 0.02639 % Correct digits = 4 memory used=4657.8MB, alloc=52.3MB, time=57.34 Radius of convergence (given) for eq 1 = 4.048 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = 3.20731475357 0.430709978741 y[1] (closed_form) = 3.20807429926 0.430305113231 absolute error = 0.0008607 relative error = 0.02659 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.053 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = 3.20946365607 0.432429460957 y[1] (closed_form) = 3.21022779521 0.432024343002 absolute error = 0.0008649 relative error = 0.0267 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.055 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4703.1MB, alloc=52.3MB, time=57.90 x[1] = 2.3659 1.226 h = 0.001 0.001 y[1] (numeric) = 3.21077260058 0.433443863391 y[1] (closed_form) = 3.21153839207 0.433038610366 absolute error = 0.0008664 relative error = 0.02674 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.056 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3669 1.227 h = 0.001 0.003 y[1] (numeric) = 3.21155050886 0.43337042112 y[1] (closed_form) = 3.21231629477 0.432964800102 absolute error = 0.0008666 relative error = 0.02673 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.057 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = 3.21318048114 0.433999961543 y[1] (closed_form) = 3.21394772221 0.433593213221 absolute error = 0.0008684 relative error = 0.02678 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.059 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4748.7MB, alloc=52.3MB, time=58.45 x[1] = 2.368 1.234 h = 0.003 0.006 y[1] (numeric) = 3.21492417322 0.435363143507 y[1] (closed_form) = 3.21569435633 0.43495620135 absolute error = 0.0008711 relative error = 0.02684 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.371 1.24 h = 0.0001 0.005 y[1] (numeric) = 3.21855006624 0.436185798857 y[1] (closed_form) = 3.21932511649 0.435772144387 absolute error = 0.0008785 relative error = 0.02704 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.065 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = 3.22073910013 0.437894078678 y[1] (closed_form) = 3.22151875577 0.437480163154 absolute error = 0.0008827 relative error = 0.02715 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.066 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4794.1MB, alloc=52.3MB, time=59.01 x[1] = 2.3712 1.248 h = 0.001 0.001 y[1] (numeric) = 3.2220720545 0.438901426434 y[1] (closed_form) = 3.22285336672 0.438487372611 absolute error = 0.0008842 relative error = 0.02719 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.067 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3722 1.249 h = 0.001 0.003 y[1] (numeric) = 3.22285595384 0.438817824051 y[1] (closed_form) = 3.22363725982 0.43840340125 absolute error = 0.0008844 relative error = 0.02718 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.069 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = 3.22450806769 0.439433030064 y[1] (closed_form) = 3.22529083081 0.439017474382 absolute error = 0.0008862 relative error = 0.02723 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.071 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4839.5MB, alloc=52.3MB, time=59.57 x[1] = 2.3733 1.256 h = 0.003 0.006 y[1] (numeric) = 3.2262838637 0.440787047729 y[1] (closed_form) = 3.22706957646 0.440371292543 absolute error = 0.0008889 relative error = 0.02729 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.072 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = 3.22995197365 0.441572905674 y[1] (closed_form) = 3.23074255493 0.44115041145 absolute error = 0.0008964 relative error = 0.02749 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.077 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = 3.23218122771 0.44326988286 y[1] (closed_form) = 3.23297642638 0.442847118711 absolute error = 0.0009006 relative error = 0.0276 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.078 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4885.0MB, alloc=52.3MB, time=60.13 x[1] = 2.3765 1.27 h = 0.001 0.001 y[1] (numeric) = 3.2335382445 0.444270114751 y[1] (closed_form) = 3.234335104 0.443847208977 absolute error = 0.0009021 relative error = 0.02763 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.079 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3775 1.271 h = 0.001 0.003 y[1] (numeric) = 3.23432813325 0.444176314201 y[1] (closed_form) = 3.23512498584 0.443753038458 absolute error = 0.0009023 relative error = 0.02763 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = 3.23600242337 0.444777107973 y[1] (closed_form) = 3.23680073502 0.444352693667 absolute error = 0.0009041 relative error = 0.02767 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.082 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4930.4MB, alloc=52.3MB, time=60.68 x[1] = 2.3786 1.278 h = 0.003 0.006 y[1] (numeric) = 3.23781039406 0.446121879719 y[1] (closed_form) = 3.23861166302 0.445697260071 absolute error = 0.0009068 relative error = 0.02774 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.084 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = 3.24152077013 0.44687076541 y[1] (closed_form) = 3.24232690869 0.446439379592 absolute error = 0.0009143 relative error = 0.02794 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.088 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = 3.24379033331 0.44855633724 y[1] (closed_form) = 3.24460110135 0.448124672361 absolute error = 0.0009185 relative error = 0.02804 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4975.9MB, alloc=52.3MB, time=61.24 x[1] = 2.3818 1.292 h = 0.001 0.001 y[1] (numeric) = 3.24517146517 0.449549390587 y[1] (closed_form) = 3.24598389832 0.449117580663 absolute error = 0.0009201 relative error = 0.02808 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.091 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = 3.24596734122 0.449445353277 y[1] (closed_form) = 3.24677976677 0.449013172386 absolute error = 0.0009202 relative error = 0.02808 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.092 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3829 1.297 h = 0.003 0.006 y[1] (numeric) = 3.24780317526 0.450782484165 y[1] (closed_form) = 3.24861856461 0.450350092681 absolute error = 0.0009229 relative error = 0.02814 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.094 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5021.2MB, alloc=52.3MB, time=61.80 x[1] = 2.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = 3.25155041433 0.451499907241 y[1] (closed_form) = 3.25237067434 0.451060725918 absolute error = 0.0009304 relative error = 0.02834 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.099 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.386 1.308 h = 0.0001 0.003 y[1] (numeric) = 3.25385488317 0.453176059181 y[1] (closed_form) = 3.25467978323 0.452736590867 absolute error = 0.0009347 relative error = 0.02844 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3861 1.311 h = 0.001 0.001 y[1] (numeric) = 3.25525690126 0.454163170264 y[1] (closed_form) = 3.25608347016 0.453723553936 absolute error = 0.0009362 relative error = 0.02848 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.101 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5066.6MB, alloc=52.3MB, time=62.36 x[1] = 2.3871 1.312 h = 0.001 0.003 y[1] (numeric) = 3.25605805152 0.45405036146 y[1] (closed_form) = 3.25688461221 0.453610373292 absolute error = 0.0009364 relative error = 0.02848 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = 3.25777387147 0.45462439016 y[1] (closed_form) = 3.2586018948 0.454183252602 absolute error = 0.0009382 relative error = 0.02852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.104 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3882 1.319 h = 0.003 0.006 y[1] (numeric) = 3.25964201299 0.45595211864 y[1] (closed_form) = 3.26047300807 0.455510764518 absolute error = 0.0009409 relative error = 0.02858 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.106 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5112.1MB, alloc=52.3MB, time=62.92 x[1] = 2.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = 3.26343160854 0.456632236447 y[1] (closed_form) = 3.26426747483 0.456184064607 absolute error = 0.0009484 relative error = 0.02878 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.111 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = 3.26577655368 0.458296786374 y[1] (closed_form) = 3.26661707225 0.457848317918 absolute error = 0.0009527 relative error = 0.02888 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.112 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3914 1.333 h = 0.001 0.001 y[1] (numeric) = 3.26720278575 0.459276598962 y[1] (closed_form) = 3.26804497749 0.458827978893 absolute error = 0.0009542 relative error = 0.02892 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.113 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5157.5MB, alloc=52.3MB, time=63.47 x[1] = 2.3924 1.334 h = 0.001 0.003 y[1] (numeric) = 3.26800991866 0.45915348014 y[1] (closed_form) = 3.26885210145 0.45870448722 absolute error = 0.0009544 relative error = 0.02891 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.115 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = 3.269748013 0.459712865937 y[1] (closed_form) = 3.27059166025 0.45926271765 absolute error = 0.0009562 relative error = 0.02895 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.117 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3935 1.341 h = 0.003 0.006 y[1] (numeric) = 3.27164853324 0.461031104912 y[1] (closed_form) = 3.27249516004 0.46058073374 absolute error = 0.000959 relative error = 0.02902 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.118 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5203.0MB, alloc=52.3MB, time=64.03 x[1] = 2.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = 3.27548053087 0.46167373381 y[1] (closed_form) = 3.27633202915 0.461216516646 absolute error = 0.0009665 relative error = 0.02921 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.123 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = 3.27786604162 0.463326571946 y[1] (closed_form) = 3.27872220447 0.462869048279 absolute error = 0.0009707 relative error = 0.02932 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.124 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3967 1.355 h = 0.001 0.001 y[1] (numeric) = 3.27931654048 0.464299019123 y[1] (closed_form) = 3.28017438084 0.463841340149 absolute error = 0.0009723 relative error = 0.02935 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.126 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5248.4MB, alloc=52.3MB, time=64.59 x[1] = 2.3977 1.356 h = 0.001 0.003 y[1] (numeric) = 3.28012965262 0.464165550184 y[1] (closed_form) = 3.28098748328 0.463707497342 absolute error = 0.0009725 relative error = 0.02935 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.127 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = 3.28189005454 0.4647102094 y[1] (closed_form) = 3.28274935145 0.464250995112 absolute error = 0.0009743 relative error = 0.02939 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.129 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3988 1.363 h = 0.003 0.006 y[1] (numeric) = 3.28382302463 0.466018869627 y[1] (closed_form) = 3.2846853089 0.465559425963 absolute error = 0.000977 relative error = 0.02945 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5293.9MB, alloc=52.3MB, time=65.14 x[1] = 2.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = 3.28769746857 0.466623822961 y[1] (closed_form) = 3.28856462431 0.466157504645 absolute error = 0.0009846 relative error = 0.02964 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.135 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = 3.29012363432 0.468264837077 y[1] (closed_form) = 3.29099546698 0.467798202106 absolute error = 0.0009889 relative error = 0.02975 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.137 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.402 1.377 h = 0.001 0.001 y[1] (numeric) = 3.2915984528 0.469229850455 y[1] (closed_form) = 3.29247196732 0.468763056388 absolute error = 0.0009904 relative error = 0.02978 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.138 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5339.2MB, alloc=52.3MB, time=65.70 x[1] = 2.403 1.378 h = 0.001 0.003 y[1] (numeric) = 3.29241754027 0.469085990793 y[1] (closed_form) = 3.29329104432 0.468618821836 absolute error = 0.0009906 relative error = 0.02978 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.139 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.404 1.381 h = 0.0001 0.004 y[1] (numeric) = 3.29420028254 0.46961583826 y[1] (closed_form) = 3.29507525459 0.469147501678 absolute error = 0.0009924 relative error = 0.02982 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.141 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4041 1.385 h = 0.003 0.006 y[1] (numeric) = 3.29616577359 0.470914828536 y[1] (closed_form) = 3.29704374087 0.47044625592 absolute error = 0.0009952 relative error = 0.02988 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.142 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5384.7MB, alloc=52.3MB, time=66.26 x[1] = 2.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = 3.30008270676 0.471481916666 y[1] (closed_form) = 3.30096554518 0.471006440353 absolute error = 0.001003 relative error = 0.03007 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.147 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = 3.30254961691 0.473110992089 y[1] (closed_form) = 3.30343714466 0.472635188707 absolute error = 0.001007 relative error = 0.03018 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.149 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4073 1.399 h = 0.001 0.001 y[1] (numeric) = 3.3040488078 0.474068501816 y[1] (closed_form) = 3.3049380218 0.473592535454 absolute error = 0.001009 relative error = 0.03021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5430.2MB, alloc=52.3MB, time=66.83 x[1] = 2.4083 1.4 h = 0.003 0.006 y[1] (numeric) = 3.30487386626 0.473914210322 y[1] (closed_form) = 3.30576306898 0.473437868041 absolute error = 0.001009 relative error = 0.03021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = 3.3088190923 0.474454068906 y[1] (closed_form) = 3.30971316446 0.473970802162 absolute error = 0.001016 relative error = 0.0304 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.156 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = 3.31131377762 0.476073834997 y[1] (closed_form) = 3.31221254741 0.475590233552 absolute error = 0.001021 relative error = 0.0305 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.158 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5475.6MB, alloc=52.3MB, time=67.39 x[1] = 2.4115 1.414 h = 0.001 0.001 y[1] (numeric) = 3.31282957345 0.477025526229 y[1] (closed_form) = 3.31373003241 0.476541758966 absolute error = 0.001022 relative error = 0.03053 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.159 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4125 1.415 h = 0.001 0.003 y[1] (numeric) = 3.31365847245 0.476863884436 y[1] (closed_form) = 3.31455891955 0.476379740566 absolute error = 0.001022 relative error = 0.03053 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.161 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = 3.31547861779 0.47736796953 y[1] (closed_form) = 3.31638053559 0.476882647338 absolute error = 0.001024 relative error = 0.03057 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.162 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5521.1MB, alloc=52.3MB, time=67.95 x[1] = 2.4136 1.422 h = 0.003 0.006 y[1] (numeric) = 3.31749891309 0.478649602579 y[1] (closed_form) = 3.3184038393 0.478164032529 absolute error = 0.001027 relative error = 0.03063 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.164 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = 3.32148669208 0.479151267579 y[1] (closed_form) = 3.32239648744 0.478658743982 absolute error = 0.001035 relative error = 0.03082 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.169 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = 3.32402226968 0.480758893657 y[1] (closed_form) = 3.32493677517 0.480266024502 absolute error = 0.001039 relative error = 0.03092 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.171 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5566.4MB, alloc=52.3MB, time=68.51 x[1] = 2.4168 1.436 h = 0.001 0.001 y[1] (numeric) = 3.32556252517 0.481702958697 y[1] (closed_form) = 3.32647872423 0.481209919678 absolute error = 0.00104 relative error = 0.03096 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.172 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4178 1.437 h = 0.001 0.003 y[1] (numeric) = 3.32639738563 0.481530814704 y[1] (closed_form) = 3.327313572 0.481037398041 absolute error = 0.001041 relative error = 0.03095 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.173 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = 3.32823995484 0.482019851056 y[1] (closed_form) = 3.32915761355 0.481525249627 absolute error = 0.001042 relative error = 0.03099 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.175 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5611.8MB, alloc=52.3MB, time=69.06 x[1] = 2.4189 1.444 h = 0.003 0.006 y[1] (numeric) = 3.33029295979 0.483291557572 y[1] (closed_form) = 3.33121363486 0.482796701174 absolute error = 0.001045 relative error = 0.03105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.176 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = 3.33432333128 0.48375483208 y[1] (closed_form) = 3.33524887436 0.483252992095 absolute error = 0.001053 relative error = 0.03124 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.181 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.422 1.455 h = 0.0001 0.003 y[1] (numeric) = 3.33689989046 0.485350196956 y[1] (closed_form) = 3.3378301562 0.484848000291 absolute error = 0.001057 relative error = 0.03134 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.183 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5657.2MB, alloc=52.3MB, time=69.62 x[1] = 2.4221 1.458 h = 0.001 0.001 y[1] (numeric) = 3.33846465826 0.48628656204 y[1] (closed_form) = 3.339396622 0.485784191372 absolute error = 0.001059 relative error = 0.03137 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.184 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4231 1.459 h = 0.001 0.003 y[1] (numeric) = 3.33930547453 0.48610387344 y[1] (closed_form) = 3.34023742472 0.485601124088 absolute error = 0.001059 relative error = 0.03137 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.186 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = 3.3411704986 0.486577770505 y[1] (closed_form) = 3.34210392273 0.486073829845 absolute error = 0.001061 relative error = 0.03141 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.188 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5702.5MB, alloc=52.3MB, time=70.18 x[1] = 2.4242 1.466 h = 0.003 0.006 y[1] (numeric) = 3.34325628417 0.48783945213 y[1] (closed_form) = 3.34419273263 0.487335249221 absolute error = 0.001064 relative error = 0.03147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.189 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = 3.3473292857 0.488264135769 y[1] (closed_form) = 3.34827060071 0.487752918869 absolute error = 0.001071 relative error = 0.03166 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.194 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = 3.34994691565 0.489847115844 y[1] (closed_form) = 3.35089296592 0.489335530882 absolute error = 0.001076 relative error = 0.03176 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.196 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5747.9MB, alloc=52.3MB, time=70.73 x[1] = 2.4274 1.48 h = 0.001 0.001 y[1] (numeric) = 3.35153624839 0.490775705766 y[1] (closed_form) = 3.35248400109 0.490263942566 absolute error = 0.001077 relative error = 0.03179 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.197 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = 3.35238301428 0.490582429678 y[1] (closed_form) = 3.35333075256 0.490070286748 absolute error = 0.001077 relative error = 0.03179 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.198 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4285 1.485 h = 0.003 0.006 y[1] (numeric) = 3.35449719434 0.49183579378 y[1] (closed_form) = 3.35544796373 0.491323382125 absolute error = 0.00108 relative error = 0.03185 % Correct digits = 3 memory used=5793.4MB, alloc=52.3MB, time=71.29 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = 3.35860738231 0.492227605438 y[1] (closed_form) = 3.35956301709 0.491708153312 absolute error = 0.001088 relative error = 0.03203 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.205 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = 3.36126058554 0.493800314962 y[1] (closed_form) = 3.3622209666 0.493280484918 absolute error = 0.001092 relative error = 0.03214 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.207 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5838.9MB, alloc=52.3MB, time=71.85 x[1] = 2.4317 1.499 h = 0.001 0.001 y[1] (numeric) = 3.36287119886 0.49472244443 y[1] (closed_form) = 3.36383328623 0.49420243248 absolute error = 0.001094 relative error = 0.03217 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.208 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4327 1.5 h = 0.001 0.003 y[1] (numeric) = 3.36372320752 0.494520091054 y[1] (closed_form) = 3.36468527972 0.493999698461 absolute error = 0.001094 relative error = 0.03216 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.209 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = 3.36563027856 0.494965839871 y[1] (closed_form) = 3.36659382763 0.494444243561 absolute error = 0.001096 relative error = 0.0322 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.211 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5884.2MB, alloc=52.3MB, time=72.41 x[1] = 2.4338 1.507 h = 0.003 0.006 y[1] (numeric) = 3.36777737208 0.496208991622 y[1] (closed_form) = 3.36874396049 0.495687119165 absolute error = 0.001098 relative error = 0.03226 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = 3.37193025838 0.496561832387 y[1] (closed_form) = 3.37290171014 0.496032888387 absolute error = 0.001106 relative error = 0.03245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.218 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = 3.37462469962 0.498121921808 y[1] (closed_form) = 3.37560091033 0.497592588024 absolute error = 0.00111 relative error = 0.03255 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.219 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5929.6MB, alloc=52.3MB, time=72.96 x[1] = 2.437 1.521 h = 0.001 0.001 y[1] (numeric) = 3.37625997645 0.499036132974 y[1] (closed_form) = 3.37723789793 0.498506612874 absolute error = 0.001112 relative error = 0.03258 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.221 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.438 1.522 h = 0.001 0.003 y[1] (numeric) = 3.37711792249 0.498823110997 y[1] (closed_form) = 3.37809582789 0.4982932092 absolute error = 0.001112 relative error = 0.03257 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.222 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.439 1.525 h = 0.0001 0.004 y[1] (numeric) = 3.37904753536 0.499253453961 y[1] (closed_form) = 3.38002691909 0.498722341632 absolute error = 0.001114 relative error = 0.03261 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.224 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5975.0MB, alloc=52.3MB, time=73.52 x[1] = 2.4391 1.529 h = 0.003 0.006 y[1] (numeric) = 3.38122761324 0.500486289693 y[1] (closed_form) = 3.38221004436 0.499954893457 absolute error = 0.001117 relative error = 0.03267 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.225 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = 3.38542323107 0.500799951078 y[1] (closed_form) = 3.38641052319 0.50026145188 absolute error = 0.001125 relative error = 0.03285 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = 3.38815899918 0.502347289966 y[1] (closed_form) = 3.38915106296 0.501808388856 absolute error = 0.001129 relative error = 0.03295 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.232 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6020.4MB, alloc=52.3MB, time=74.08 x[1] = 2.4423 1.543 h = 0.001 0.001 y[1] (numeric) = 3.38981899184 0.503253503528 y[1] (closed_form) = 3.39081277086 0.502714411597 absolute error = 0.001131 relative error = 0.03298 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.234 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4433 1.544 h = 0.001 0.003 y[1] (numeric) = 3.3906828677 0.50302976875 y[1] (closed_form) = 3.3916766297 0.502490294066 absolute error = 0.001131 relative error = 0.03298 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.235 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = 3.39263505137 0.50344460983 y[1] (closed_form) = 3.39363029312 0.502903917704 absolute error = 0.001133 relative error = 0.03301 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.237 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6065.7MB, alloc=52.3MB, time=74.63 x[1] = 2.4444 1.551 h = 0.003 0.006 y[1] (numeric) = 3.39484818417 0.504667023807 y[1] (closed_form) = 3.39584648139 0.504126039849 absolute error = 0.001135 relative error = 0.03307 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.238 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = 3.39908656515 0.504941294556 y[1] (closed_form) = 3.40008972068 0.504393175869 absolute error = 0.001143 relative error = 0.03326 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.243 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = 3.40186374881 0.50647575011 y[1] (closed_form) = 3.40287168875 0.505927217125 absolute error = 0.001148 relative error = 0.03336 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.245 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6111.1MB, alloc=52.3MB, time=75.19 x[1] = 2.4476 1.565 h = 0.001 0.001 y[1] (numeric) = 3.4035485095 0.507373885346 y[1] (closed_form) = 3.40455816916 0.506825156942 absolute error = 0.001149 relative error = 0.03338 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.247 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4486 1.566 h = 0.001 0.003 y[1] (numeric) = 3.40441830709 0.507139393122 y[1] (closed_form) = 3.40542794878 0.506590280905 absolute error = 0.001149 relative error = 0.03338 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.248 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = 3.40639308998 0.507538634898 y[1] (closed_form) = 3.40740421279 0.506988298237 absolute error = 0.001151 relative error = 0.03342 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6156.5MB, alloc=52.3MB, time=75.75 x[1] = 2.4497 1.573 h = 0.003 0.006 y[1] (numeric) = 3.40863934807 0.508750519494 y[1] (closed_form) = 3.40965353445 0.508199882909 absolute error = 0.001154 relative error = 0.03348 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.251 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = 3.41292052222 0.508985185604 y[1] (closed_form) = 3.41393956389 0.508427382185 absolute error = 0.001162 relative error = 0.03366 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.256 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = 3.41573920989 0.510506622669 y[1] (closed_form) = 3.41676304876 0.509948392306 absolute error = 0.001166 relative error = 0.03376 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.258 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6201.8MB, alloc=52.3MB, time=76.31 x[1] = 2.4529 1.587 h = 0.001 0.001 y[1] (numeric) = 3.41744879066 0.511396597444 y[1] (closed_form) = 3.41847435373 0.51083816697 absolute error = 0.001168 relative error = 0.03378 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = 3.41832450141 0.511151302693 y[1] (closed_form) = 3.41935004553 0.510592487341 absolute error = 0.001168 relative error = 0.03378 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.261 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.454 1.592 h = 0.003 0.006 y[1] (numeric) = 3.42059945629 0.512354432217 y[1] (closed_form) = 3.42162807084 0.511795309777 absolute error = 0.001171 relative error = 0.03384 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.262 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6247.3MB, alloc=52.3MB, time=76.87 x[1] = 2.457 1.598 h = 0.0001 0.005 y[1] (numeric) = 3.42491796344 0.512555344739 y[1] (closed_form) = 3.42595143082 0.511989027521 absolute error = 0.001178 relative error = 0.03402 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.267 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = 3.42777260436 0.514065961726 y[1] (closed_form) = 3.4288108801 0.513499206624 absolute error = 0.001183 relative error = 0.03412 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.269 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4572 1.606 h = 0.001 0.001 y[1] (numeric) = 3.42950368954 0.5149491419 y[1] (closed_form) = 3.43054369342 0.514382182627 absolute error = 0.001185 relative error = 0.03415 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.271 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6292.8MB, alloc=52.3MB, time=77.43 x[1] = 2.4582 1.607 h = 0.001 0.003 y[1] (numeric) = 3.43038461229 0.514694582555 y[1] (closed_form) = 3.43142459637 0.514127237474 absolute error = 0.001185 relative error = 0.03414 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.272 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = 3.43240170932 0.515064803634 y[1] (closed_form) = 3.43344317704 0.51449622085 absolute error = 0.001187 relative error = 0.03418 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.274 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4593 1.614 h = 0.003 0.006 y[1] (numeric) = 3.43470992106 0.51625719918 y[1] (closed_form) = 3.43575446755 0.515688301072 absolute error = 0.001189 relative error = 0.03424 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.276 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6338.2MB, alloc=52.3MB, time=77.99 x[1] = 2.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = 3.43907127548 0.51641810196 y[1] (closed_form) = 3.44012067118 0.515841976346 absolute error = 0.001197 relative error = 0.03441 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.281 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = 3.44196758606 0.517915443775 y[1] (closed_form) = 3.44302180295 0.51733886715 absolute error = 0.001202 relative error = 0.03451 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.283 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4625 1.628 h = 0.001 0.001 y[1] (numeric) = 3.44372358873 0.518790307535 y[1] (closed_form) = 3.44477953826 0.518213521874 absolute error = 0.001203 relative error = 0.03454 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.284 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6383.6MB, alloc=52.3MB, time=78.54 x[1] = 2.4635 1.629 h = 0.001 0.003 y[1] (numeric) = 3.44461040785 0.518524860522 y[1] (closed_form) = 3.44566633657 0.517947687984 absolute error = 0.001203 relative error = 0.03454 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.285 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = 3.44665018338 0.518879196336 y[1] (closed_form) = 3.44770759697 0.518300778831 absolute error = 0.001205 relative error = 0.03457 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.287 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4646 1.636 h = 0.003 0.006 y[1] (numeric) = 3.448991722 0.520060745084 y[1] (closed_form) = 3.4500522225 0.519482003689 absolute error = 0.001208 relative error = 0.03463 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.289 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6429.0MB, alloc=52.3MB, time=79.10 x[1] = 2.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = 3.45339594899 0.520181416406 y[1] (closed_form) = 3.45446129475 0.519595414453 absolute error = 0.001216 relative error = 0.03481 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.294 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = 3.45633401698 0.521665341207 y[1] (closed_form) = 3.45740419679 0.521078874859 absolute error = 0.00122 relative error = 0.0349 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.296 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4678 1.65 h = 0.001 0.001 y[1] (numeric) = 3.4581149887 0.522531802415 y[1] (closed_form) = 3.45918690565 0.521945122072 absolute error = 0.001222 relative error = 0.03493 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.297 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6474.5MB, alloc=52.3MB, time=79.66 x[1] = 2.4688 1.651 h = 0.001 0.003 y[1] (numeric) = 3.45900769414 0.522255421438 y[1] (closed_form) = 3.46007958925 0.521668353146 absolute error = 0.001222 relative error = 0.03493 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.299 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = 3.4610701743 0.522593769297 y[1] (closed_form) = 3.46214355545 0.522005448686 absolute error = 0.001224 relative error = 0.03496 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.301 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4699 1.658 h = 0.003 0.006 y[1] (numeric) = 3.46344510935 0.523764356407 y[1] (closed_form) = 3.46452158557 0.523175703175 absolute error = 0.001227 relative error = 0.03502 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.302 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6519.9MB, alloc=52.3MB, time=80.22 x[1] = 2.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = 3.46789223252 0.523844571923 y[1] (closed_form) = 3.46897354971 0.523248624759 absolute error = 0.001235 relative error = 0.03519 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.307 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.473 1.669 h = 0.0001 0.003 y[1] (numeric) = 3.47087214535 0.525314935556 y[1] (closed_form) = 3.47195830947 0.524718510356 absolute error = 0.001239 relative error = 0.03529 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.309 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4731 1.672 h = 0.001 0.001 y[1] (numeric) = 3.47267813746 0.526172906688 y[1] (closed_form) = 3.47376604323 0.525576262443 absolute error = 0.001241 relative error = 0.03532 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.311 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6565.2MB, alloc=52.3MB, time=80.77 x[1] = 2.4741 1.673 h = 0.001 0.003 y[1] (numeric) = 3.47357671866 0.525885545041 y[1] (closed_form) = 3.47466460154 0.525288511773 absolute error = 0.001241 relative error = 0.03531 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.312 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = 3.47566192896 0.526207800923 y[1] (closed_form) = 3.476751299 0.525609507893 absolute error = 0.001243 relative error = 0.03535 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.314 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4752 1.68 h = 0.003 0.006 y[1] (numeric) = 3.47807032973 0.527367309709 y[1] (closed_form) = 3.47916280301 0.526768675165 absolute error = 0.001246 relative error = 0.0354 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.316 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6610.6MB, alloc=52.3MB, time=81.33 x[1] = 2.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = 3.48256037095 0.527406842466 y[1] (closed_form) = 3.48365768057 0.526800880299 absolute error = 0.001254 relative error = 0.03558 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.321 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = 3.48558221573 0.528863498473 y[1] (closed_form) = 3.48668438516 0.528257044375 absolute error = 0.001258 relative error = 0.03567 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.323 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4784 1.694 h = 0.001 0.001 y[1] (numeric) = 3.48741327933 0.529712890628 y[1] (closed_form) = 3.48851719494 0.529106212341 absolute error = 0.00126 relative error = 0.0357 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.324 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6656.0MB, alloc=52.3MB, time=81.89 x[1] = 2.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = 3.48831772522 0.529414501205 y[1] (closed_form) = 3.48942161686 0.528807432819 absolute error = 0.00126 relative error = 0.0357 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.325 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4795 1.699 h = 0.003 0.006 y[1] (numeric) = 3.49075512155 0.530564779216 y[1] (closed_form) = 3.49186212333 0.52995736147 absolute error = 0.001263 relative error = 0.03575 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.327 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = 3.49528260971 0.530569621464 y[1] (closed_form) = 3.496394444 0.529954846788 absolute error = 0.00127 relative error = 0.03593 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.332 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6701.4MB, alloc=52.3MB, time=82.44 x[1] = 2.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = 3.49834078328 0.532014860275 y[1] (closed_form) = 3.49945748865 0.531399581655 absolute error = 0.001275 relative error = 0.03602 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.334 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4827 1.713 h = 0.001 0.001 y[1] (numeric) = 3.50019357201 0.532857095171 y[1] (closed_form) = 3.50131202751 0.532241587914 absolute error = 0.001277 relative error = 0.03605 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.335 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4837 1.714 h = 0.001 0.003 y[1] (numeric) = 3.50110318888 0.532549245054 y[1] (closed_form) = 3.50222161948 0.531933346757 absolute error = 0.001277 relative error = 0.03604 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.337 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6746.8MB, alloc=52.3MB, time=83.00 x[1] = 2.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = 3.50323095499 0.532841547585 y[1] (closed_form) = 3.50435087481 0.532224375458 absolute error = 0.001279 relative error = 0.03608 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.339 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4848 1.721 h = 0.003 0.006 y[1] (numeric) = 3.5057019464 0.533980525932 y[1] (closed_form) = 3.50682498476 0.533362995401 absolute error = 0.001282 relative error = 0.03613 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.341 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = 3.51027239141 0.53394425649 y[1] (closed_form) = 3.51140025701 0.533319334763 absolute error = 0.001289 relative error = 0.0363 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.346 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6792.2MB, alloc=52.3MB, time=83.56 x[1] = 2.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = 3.51337265982 0.535375510096 y[1] (closed_form) = 3.51450540943 0.534750070053 absolute error = 0.001294 relative error = 0.0364 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.348 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.488 1.735 h = 0.001 0.001 y[1] (numeric) = 3.51525061563 0.53620899755 y[1] (closed_form) = 3.51638511988 0.535583323556 absolute error = 0.001296 relative error = 0.03642 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.349 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.489 1.736 h = 0.001 0.003 y[1] (numeric) = 3.51616607573 0.535890030813 y[1] (closed_form) = 3.51730055397 0.535263964699 absolute error = 0.001296 relative error = 0.03642 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6837.7MB, alloc=52.3MB, time=84.12 x[1] = 2.49 1.739 h = 0.0001 0.004 y[1] (numeric) = 3.51831664264 0.536165936797 y[1] (closed_form) = 3.51945261107 0.535538589161 absolute error = 0.001298 relative error = 0.03645 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.352 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4901 1.743 h = 0.003 0.006 y[1] (numeric) = 3.52082129778 0.53729349372 y[1] (closed_form) = 3.52196039294 0.53666577832 absolute error = 0.001301 relative error = 0.03651 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.354 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = 3.52543471647 0.537215878321 y[1] (closed_form) = 3.52657863327 0.536580737156 absolute error = 0.001308 relative error = 0.03668 % Correct digits = 3 memory used=6883.1MB, alloc=52.3MB, time=84.67 Radius of convergence (given) for eq 1 = 4.359 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = 3.52857716575 0.538632993742 y[1] (closed_form) = 3.52972597948 0.537997319637 absolute error = 0.001313 relative error = 0.03677 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.361 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4933 1.757 h = 0.001 0.001 y[1] (numeric) = 3.53048033905 0.539457640948 y[1] (closed_form) = 3.53163091193 0.538821727486 absolute error = 0.001315 relative error = 0.0368 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.363 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6928.5MB, alloc=52.3MB, time=85.23 x[1] = 2.4943 1.758 h = 0.001 0.003 y[1] (numeric) = 3.5314016298 0.539127509372 y[1] (closed_form) = 3.53255217554 0.538491202708 absolute error = 0.001315 relative error = 0.03679 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.364 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = 3.53357502047 0.539386909738 y[1] (closed_form) = 3.53472705733 0.538749313776 absolute error = 0.001317 relative error = 0.03683 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.366 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4954 1.765 h = 0.003 0.006 y[1] (numeric) = 3.53611340743 0.540502921515 y[1] (closed_form) = 3.5372685792 0.539864948265 absolute error = 0.00132 relative error = 0.03688 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.368 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6973.8MB, alloc=52.3MB, time=85.78 x[1] = 2.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = 3.54076981481 0.540383723399 y[1] (closed_form) = 3.54192980227 0.539738289518 absolute error = 0.001327 relative error = 0.03705 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.373 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = 3.54395453056 0.5417865454 y[1] (closed_form) = 3.54511942788 0.541140563701 absolute error = 0.001332 relative error = 0.03714 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.375 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4986 1.779 h = 0.001 0.001 y[1] (numeric) = 3.54588297147 0.542602258204 y[1] (closed_form) = 3.54704963247 0.541956031651 absolute error = 0.001334 relative error = 0.03717 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.376 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7019.2MB, alloc=52.3MB, time=86.34 x[1] = 2.4996 1.78 h = 0.001 0.003 y[1] (numeric) = 3.54681007976 0.542260913196 y[1] (closed_form) = 3.54797671246 0.541614292358 absolute error = 0.001334 relative error = 0.03716 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.378 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = 3.54900631649 0.542503697596 y[1] (closed_form) = 3.55017444116 0.5418557796 absolute error = 0.001336 relative error = 0.0372 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5007 1.787 h = 0.003 0.006 y[1] (numeric) = 3.55157850298 0.543608038709 y[1] (closed_form) = 3.55274977075 0.542959733739 absolute error = 0.001339 relative error = 0.03725 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.382 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7064.7MB, alloc=52.3MB, time=86.90 x[1] = 2.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = 3.55627791223 0.543447018648 y[1] (closed_form) = 3.5574539894 0.542791217891 absolute error = 0.001347 relative error = 0.03742 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.387 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = 3.55950497959 0.544835389752 y[1] (closed_form) = 3.56068597955 0.544179026046 absolute error = 0.001351 relative error = 0.03751 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.389 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5039 1.801 h = 0.001 0.001 y[1] (numeric) = 3.56145873796 0.54564207266 y[1] (closed_form) = 3.56264150611 0.544985458511 absolute error = 0.001353 relative error = 0.03754 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7110.1MB, alloc=52.3MB, time=87.46 x[1] = 2.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = 3.56239165013 0.545289465259 y[1] (closed_form) = 3.56357438882 0.544632455743 absolute error = 0.001353 relative error = 0.03753 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.392 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.505 1.806 h = 0.003 0.006 y[1] (numeric) = 3.56499312538 0.546384062632 y[1] (closed_form) = 3.56617901411 0.545726657625 absolute error = 0.001356 relative error = 0.03758 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.393 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.508 1.812 h = 0.0001 0.005 y[1] (numeric) = 3.56973006045 0.546187362628 y[1] (closed_form) = 3.57092075329 0.545522431261 absolute error = 0.001364 relative error = 0.03775 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.399 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7155.6MB, alloc=52.3MB, time=88.02 x[1] = 2.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = 3.57299382521 0.547563672937 y[1] (closed_form) = 3.57418945215 0.54689816555 absolute error = 0.001368 relative error = 0.03784 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.401 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5082 1.82 h = 0.001 0.001 y[1] (numeric) = 3.57496952481 0.548362808104 y[1] (closed_form) = 3.57616692391 0.547697045446 absolute error = 0.00137 relative error = 0.03787 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.402 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5092 1.821 h = 0.001 0.003 y[1] (numeric) = 3.57590755639 0.548000535838 y[1] (closed_form) = 3.57710492501 0.547334376865 absolute error = 0.00137 relative error = 0.03786 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.403 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7201.1MB, alloc=52.3MB, time=88.58 x[1] = 2.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = 3.57814656228 0.548212376528 y[1] (closed_form) = 3.57934542442 0.547544905556 absolute error = 0.001372 relative error = 0.03789 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.406 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5103 1.828 h = 0.003 0.006 y[1] (numeric) = 3.58078196336 0.54929506557 y[1] (closed_form) = 3.58198398395 0.548627189271 absolute error = 0.001375 relative error = 0.03795 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.407 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = 3.58556192277 0.549056092122 y[1] (closed_form) = 3.58676874052 0.548380653772 absolute error = 0.001383 relative error = 0.03811 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.412 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7246.5MB, alloc=52.3MB, time=89.14 x[1] = 2.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = 3.58886819822 0.550417653581 y[1] (closed_form) = 3.59007996301 0.549741623613 absolute error = 0.001388 relative error = 0.03821 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.415 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5135 1.842 h = 0.001 0.001 y[1] (numeric) = 3.59086930836 0.551207578198 y[1] (closed_form) = 3.59208284981 0.550531287202 absolute error = 0.001389 relative error = 0.03823 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.416 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5145 1.843 h = 0.001 0.003 y[1] (numeric) = 3.59181311759 0.550833951312 y[1] (closed_form) = 3.59302662736 0.550157262917 absolute error = 0.001389 relative error = 0.03822 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.417 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7292.0MB, alloc=52.3MB, time=89.69 x[1] = 2.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = 3.59407503074 0.551028853658 y[1] (closed_form) = 3.59529003472 0.550350845167 absolute error = 0.001391 relative error = 0.03825 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.419 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5156 1.85 h = 0.003 0.006 y[1] (numeric) = 3.59674442447 0.552099503908 y[1] (closed_form) = 3.59796259507 0.551421079943 absolute error = 0.001394 relative error = 0.03831 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.421 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = 3.60156741605 0.551818010876 y[1] (closed_form) = 3.60279037653 0.551131988893 absolute error = 0.001402 relative error = 0.03847 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.426 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7337.4MB, alloc=52.3MB, time=90.25 x[1] = 2.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = 3.60491628593 0.553164659657 y[1] (closed_form) = 3.60614420636 0.552478030206 absolute error = 0.001407 relative error = 0.03856 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.429 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5188 1.864 h = 0.001 0.001 y[1] (numeric) = 3.60694285554 0.553945274431 y[1] (closed_form) = 3.60817255715 0.553258378106 absolute error = 0.001409 relative error = 0.03859 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5198 1.865 h = 0.001 0.003 y[1] (numeric) = 3.60789242724 0.553560242953 y[1] (closed_form) = 3.60912209594 0.552872948144 absolute error = 0.001409 relative error = 0.03858 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.431 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7382.8MB, alloc=52.3MB, time=90.81 x[1] = 2.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = 3.61017726717 0.553738091786 y[1] (closed_form) = 3.61140843072 0.553049468703 absolute error = 0.001411 relative error = 0.03861 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.434 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5209 1.872 h = 0.003 0.006 y[1] (numeric) = 3.6128807197 0.554796570875 y[1] (closed_form) = 3.61411505805 0.554107522012 absolute error = 0.001414 relative error = 0.03866 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.435 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = 3.61774674938 0.554472309766 y[1] (closed_form) = 3.61898586994 0.553775626643 absolute error = 0.001422 relative error = 0.03883 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.441 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7428.2MB, alloc=52.3MB, time=91.36 x[1] = 2.524 1.883 h = 0.0001 0.003 y[1] (numeric) = 3.62113829688 0.555803879846 y[1] (closed_form) = 3.62238239032 0.555106573159 absolute error = 0.001426 relative error = 0.03892 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.443 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5241 1.886 h = 0.001 0.001 y[1] (numeric) = 3.62319037456 0.556575084174 y[1] (closed_form) = 3.62443625367 0.555877504677 absolute error = 0.001428 relative error = 0.03894 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.444 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5251 1.887 h = 0.001 0.003 y[1] (numeric) = 3.624145693 0.556178597792 y[1] (closed_form) = 3.62539153795 0.555480618726 absolute error = 0.001428 relative error = 0.03894 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.445 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7473.6MB, alloc=52.3MB, time=91.92 x[1] = 2.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = 3.6264534785 0.556339276726 y[1] (closed_form) = 3.62770081889 0.555639961127 absolute error = 0.00143 relative error = 0.03896 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.448 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5262 1.894 h = 0.003 0.006 y[1] (numeric) = 3.62919105554 0.557385450537 y[1] (closed_form) = 3.63044157889 0.556685698695 absolute error = 0.001433 relative error = 0.03902 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.449 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = 3.6341001273 0.557018170532 y[1] (closed_form) = 3.63535542484 0.55631074792 absolute error = 0.001441 relative error = 0.03918 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.455 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7519.0MB, alloc=52.3MB, time=92.48 x[1] = 2.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = 3.63753443505 0.558334493711 y[1] (closed_form) = 3.63879471837 0.557626431189 absolute error = 0.001446 relative error = 0.03927 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.457 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5294 1.908 h = 0.001 0.001 y[1] (numeric) = 3.63961206902 0.559096185687 y[1] (closed_form) = 3.64087414251 0.55838784433 absolute error = 0.001447 relative error = 0.03929 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.458 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = 3.64057311794 0.558688193759 y[1] (closed_form) = 3.641835156 0.557979451747 absolute error = 0.001447 relative error = 0.03929 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7564.6MB, alloc=52.3MB, time=93.04 x[1] = 2.5305 1.913 h = 0.003 0.006 y[1] (numeric) = 3.6433402695 0.559724074563 y[1] (closed_form) = 3.64460549744 0.559014887129 absolute error = 0.00145 relative error = 0.03934 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.461 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = 3.64828690868 0.559320075468 y[1] (closed_form) = 3.64955690406 0.558603185525 absolute error = 0.001458 relative error = 0.0395 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.467 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = 3.65175827314 0.560623648964 y[1] (closed_form) = 3.6530332656 0.559906104997 absolute error = 0.001463 relative error = 0.03959 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.469 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7610.0MB, alloc=52.3MB, time=93.60 x[1] = 2.5337 1.927 h = 0.001 0.001 y[1] (numeric) = 3.65385805844 0.561377375633 y[1] (closed_form) = 3.65513484501 0.560659547626 absolute error = 0.001465 relative error = 0.03961 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5347 1.928 h = 0.001 0.003 y[1] (numeric) = 3.6548241644 0.560959507301 y[1] (closed_form) = 3.65610091445 0.56024127769 absolute error = 0.001465 relative error = 0.03961 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.472 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = 3.65717490149 0.561088196988 y[1] (closed_form) = 3.658453148 0.560368615276 absolute error = 0.001467 relative error = 0.03963 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.474 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7655.4MB, alloc=52.3MB, time=94.15 x[1] = 2.5358 1.935 h = 0.003 0.006 y[1] (numeric) = 3.65997629997 0.562111518972 y[1] (closed_form) = 3.66125774474 0.561391481219 absolute error = 0.00147 relative error = 0.03968 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.476 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = 3.66496598646 0.561664028168 y[1] (closed_form) = 3.66625218998 0.560936250906 absolute error = 0.001478 relative error = 0.03985 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.481 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = 3.66848026542 0.562952036991 y[1] (closed_form) = 3.6697714789 0.5622235889 absolute error = 0.001483 relative error = 0.03993 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.483 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7700.8MB, alloc=52.3MB, time=94.71 x[1] = 2.539 1.949 h = 0.001 0.001 y[1] (numeric) = 3.670605697 0.563696058808 y[1] (closed_form) = 3.67189870908 0.562967320486 absolute error = 0.001484 relative error = 0.03995 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.485 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.54 1.95 h = 0.001 0.003 y[1] (numeric) = 3.67157750233 0.563266589628 y[1] (closed_form) = 3.67287047658 0.562537448618 absolute error = 0.001484 relative error = 0.03995 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.486 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.541 1.953 h = 0.0001 0.004 y[1] (numeric) = 3.67395123594 0.563377770037 y[1] (closed_form) = 3.67524570705 0.562647268444 absolute error = 0.001486 relative error = 0.03998 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.488 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7746.2MB, alloc=52.3MB, time=95.27 x[1] = 2.5411 1.957 h = 0.003 0.006 y[1] (numeric) = 3.67678694591 0.564388394281 y[1] (closed_form) = 3.67808462342 0.56365742573 absolute error = 0.001489 relative error = 0.04003 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = 3.68181967808 0.563897154432 y[1] (closed_form) = 3.68312210529 0.563158409117 absolute error = 0.001497 relative error = 0.04019 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.495 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = 3.68537695245 0.56516942421 y[1] (closed_form) = 3.68668440249 0.564429991016 absolute error = 0.001502 relative error = 0.04027 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.498 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7791.6MB, alloc=52.3MB, time=95.82 x[1] = 2.5443 1.971 h = 0.001 0.001 y[1] (numeric) = 3.68752807746 0.565903635585 y[1] (closed_form) = 3.68883733057 0.565163905881 absolute error = 0.001504 relative error = 0.0403 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.499 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5453 1.972 h = 0.001 0.003 y[1] (numeric) = 3.68850556433 0.565462513998 y[1] (closed_form) = 3.68981477828 0.564722380522 absolute error = 0.001504 relative error = 0.04029 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = 3.69090231029 0.565556064145 y[1] (closed_form) = 3.69221302145 0.564814561528 absolute error = 0.001506 relative error = 0.04032 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.503 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7837.0MB, alloc=52.3MB, time=96.38 x[1] = 2.5464 1.979 h = 0.003 0.006 y[1] (numeric) = 3.69377239556 0.566553849882 y[1] (closed_form) = 3.69508632123 0.565811869233 absolute error = 0.001509 relative error = 0.04037 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.504 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = 3.69884816976 0.566018601439 y[1] (closed_form) = 3.70016683573 0.565268806521 absolute error = 0.001517 relative error = 0.04053 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = 3.70244851982 0.567274955673 y[1] (closed_form) = 3.70377222146 0.566524455581 absolute error = 0.001522 relative error = 0.04061 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.512 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7882.5MB, alloc=52.3MB, time=96.95 x[1] = 2.5496 1.993 h = 0.001 0.001 y[1] (numeric) = 3.70462538499 0.567999249742 y[1] (closed_form) = 3.70595089417 0.567248446773 absolute error = 0.001523 relative error = 0.04063 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.513 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5506 1.994 h = 0.001 0.003 y[1] (numeric) = 3.70560853502 0.567546423884 y[1] (closed_form) = 3.70693400369 0.566795216061 absolute error = 0.001524 relative error = 0.04063 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.515 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = 3.70802830834 0.567622221628 y[1] (closed_form) = 3.70935527451 0.566869636029 absolute error = 0.001526 relative error = 0.04065 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.517 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7927.9MB, alloc=52.3MB, time=97.51 x[1] = 2.5517 2.001 h = 0.003 0.006 y[1] (numeric) = 3.71093283219 0.568607026396 y[1] (closed_form) = 3.71226302098 0.567853951537 absolute error = 0.001529 relative error = 0.0407 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.519 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = 3.71605164276 0.568027507621 y[1] (closed_form) = 3.71738656206 0.567266580742 absolute error = 0.001537 relative error = 0.04086 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.524 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = 3.71969514811 0.569267767698 y[1] (closed_form) = 3.7210351159 0.568506118106 absolute error = 0.001541 relative error = 0.04095 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.527 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7973.3MB, alloc=52.3MB, time=98.06 x[1] = 2.5549 2.015 h = 0.001 0.001 y[1] (numeric) = 3.72189779977 0.569982036335 y[1] (closed_form) = 3.72323957954 0.569220077413 absolute error = 0.001543 relative error = 0.04097 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.528 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = 3.72288659402 0.569517454045 y[1] (closed_form) = 3.72422833192 0.568755089186 absolute error = 0.001543 relative error = 0.04096 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.529 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.556 2.02 h = 0.003 0.006 y[1] (numeric) = 3.7258209689 0.570491381243 y[1] (closed_form) = 3.72716593629 0.569728517296 absolute error = 0.001546 relative error = 0.04101 % Correct digits = 3 memory used=8018.8MB, alloc=52.3MB, time=98.62 Radius of convergence (given) for eq 1 = 4.531 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.559 2.026 h = 0.0001 0.005 y[1] (numeric) = 3.73097734928 0.569874057321 y[1] (closed_form) = 3.73232703892 0.569103308545 absolute error = 0.001554 relative error = 0.04117 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.537 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = 3.73465825913 0.571100834791 y[1] (closed_form) = 3.73601300848 0.570329348163 absolute error = 0.001559 relative error = 0.04125 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.539 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8064.3MB, alloc=52.3MB, time=99.18 x[1] = 2.5592 2.034 h = 0.001 0.001 y[1] (numeric) = 3.73688326488 0.57180669424 y[1] (closed_form) = 3.73823983012 0.571034892709 absolute error = 0.001561 relative error = 0.04127 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5602 2.035 h = 0.001 0.003 y[1] (numeric) = 3.73787704281 0.571332017329 y[1] (closed_form) = 3.739233565 0.570559808915 absolute error = 0.001561 relative error = 0.04127 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.542 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = 3.74033991687 0.571374727673 y[1] (closed_form) = 3.74169793703 0.570601125223 absolute error = 0.001563 relative error = 0.04129 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.544 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8109.6MB, alloc=52.3MB, time=99.74 x[1] = 2.5613 2.042 h = 0.003 0.006 y[1] (numeric) = 3.7433088481 0.572335404948 y[1] (closed_form) = 3.74467010606 0.571561292023 absolute error = 0.001566 relative error = 0.04134 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.546 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = 3.74850825203 0.571673317816 y[1] (closed_form) = 3.74987422177 0.570891281864 absolute error = 0.001574 relative error = 0.0415 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.551 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = 3.75223246563 0.572883664117 y[1] (closed_form) = 3.75360350786 0.572100872324 absolute error = 0.001579 relative error = 0.04158 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.553 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8155.1MB, alloc=52.3MB, time=100.30 x[1] = 2.5645 2.056 h = 0.001 0.001 y[1] (numeric) = 3.7544833442 0.573579294147 y[1] (closed_form) = 3.75585620675 0.572796180834 absolute error = 0.001581 relative error = 0.0416 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.555 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5655 2.057 h = 0.001 0.003 y[1] (numeric) = 3.75548273029 0.573092762731 y[1] (closed_form) = 3.75685554839 0.572309241456 absolute error = 0.001581 relative error = 0.04159 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.556 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = 3.75796867173 0.573117365106 y[1] (closed_form) = 3.75934298789 0.57233244095 absolute error = 0.001583 relative error = 0.04162 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.559 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8200.5MB, alloc=52.3MB, time=100.86 x[1] = 2.5666 2.064 h = 0.003 0.006 y[1] (numeric) = 3.76097222122 0.574064645335 y[1] (closed_form) = 3.76234978323 0.573279199032 absolute error = 0.001586 relative error = 0.04167 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = 3.76621463717 0.573357527136 y[1] (closed_form) = 3.76759690014 0.572564119374 absolute error = 0.001594 relative error = 0.04182 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.566 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = 3.76998223213 0.574551257671 y[1] (closed_form) = 3.77136958033 0.573757075839 absolute error = 0.001599 relative error = 0.04191 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.568 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8245.9MB, alloc=52.3MB, time=101.42 x[1] = 2.5698 2.078 h = 0.001 0.001 y[1] (numeric) = 3.77225902858 0.575236546585 y[1] (closed_form) = 3.77364820151 0.574442036531 absolute error = 0.0016 relative error = 0.04192 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.57 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5708 2.079 h = 0.001 0.003 y[1] (numeric) = 3.77326400231 0.574738107681 y[1] (closed_form) = 3.77465312937 0.573943188587 absolute error = 0.0016 relative error = 0.04192 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.571 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = 3.775773023 0.574744475576 y[1] (closed_form) = 3.77716364816 0.573948144683 absolute error = 0.001602 relative error = 0.04194 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.573 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8291.4MB, alloc=52.3MB, time=101.97 x[1] = 2.5719 2.086 h = 0.003 0.006 y[1] (numeric) = 3.77881125183 0.575678209851 y[1] (closed_form) = 3.78020513087 0.574881344985 absolute error = 0.001606 relative error = 0.04199 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.575 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = 3.7840966662 0.574925790647 y[1] (closed_form) = 3.785495235 0.574120925664 absolute error = 0.001614 relative error = 0.04214 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.581 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.575 2.097 h = 0.0001 0.003 y[1] (numeric) = 3.78790771936 0.57610271876 y[1] (closed_form) = 3.7893113861 0.575297061236 absolute error = 0.001618 relative error = 0.04223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.583 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8336.8MB, alloc=52.3MB, time=102.54 x[1] = 2.5751 2.1 h = 0.001 0.001 y[1] (numeric) = 3.79021047828 0.576777553632 y[1] (closed_form) = 3.79161597416 0.575971561098 absolute error = 0.00162 relative error = 0.04225 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.584 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5761 2.101 h = 0.001 0.003 y[1] (numeric) = 3.79122101859 0.576267153983 y[1] (closed_form) = 3.79262646715 0.575460751334 absolute error = 0.00162 relative error = 0.04224 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.586 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = 3.79375312956 0.576255159786 y[1] (closed_form) = 3.7951600762 0.57544733635 absolute error = 0.001622 relative error = 0.04227 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.588 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8382.2MB, alloc=52.3MB, time=103.09 x[1] = 2.5772 2.108 h = 0.003 0.006 y[1] (numeric) = 3.79682609819 0.57717519756 y[1] (closed_form) = 3.79823630672 0.576366828171 absolute error = 0.001625 relative error = 0.04231 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = 3.80215449525 0.576377205365 y[1] (closed_form) = 3.80356938196 0.575560796978 absolute error = 0.001634 relative error = 0.04246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.595 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = 3.80600908273 0.577537142351 y[1] (closed_form) = 3.80742908004 0.576719922714 absolute error = 0.001638 relative error = 0.04255 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.598 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8427.6MB, alloc=52.3MB, time=103.65 x[1] = 2.5804 2.122 h = 0.001 0.001 y[1] (numeric) = 3.80833784823 0.578201409034 y[1] (closed_form) = 3.80975967907 0.577383847513 absolute error = 0.00164 relative error = 0.04256 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.599 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = 3.80935393349 0.57767899512 y[1] (closed_form) = 3.81077571556 0.576861022412 absolute error = 0.00164 relative error = 0.04256 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.601 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5815 2.127 h = 0.003 0.006 y[1] (numeric) = 3.81245701878 0.578587536515 y[1] (closed_form) = 3.81388206952 0.577769007392 absolute error = 0.001643 relative error = 0.0426 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.602 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8473.1MB, alloc=52.3MB, time=104.21 x[1] = 2.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = 3.81782294702 0.577750608982 y[1] (closed_form) = 3.81925266614 0.576924007073 absolute error = 0.001651 relative error = 0.04276 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.608 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = 3.82171527321 0.578896287707 y[1] (closed_form) = 3.82315011404 0.578068858405 absolute error = 0.001656 relative error = 0.04284 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5847 2.141 h = 0.001 0.001 y[1] (numeric) = 3.82406658702 0.579551675809 y[1] (closed_form) = 3.82550326522 0.57872389869 absolute error = 0.001658 relative error = 0.04286 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.612 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8518.5MB, alloc=52.3MB, time=104.76 x[1] = 2.5857 2.142 h = 0.001 0.003 y[1] (numeric) = 3.82508757142 0.57901894305 y[1] (closed_form) = 3.8265241996 0.578190753804 absolute error = 0.001658 relative error = 0.04285 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.613 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = 3.82766289684 0.578972713243 y[1] (closed_form) = 3.82910102297 0.578143086295 absolute error = 0.00166 relative error = 0.04287 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.615 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5868 2.149 h = 0.003 0.006 y[1] (numeric) = 3.83080083435 0.579867274251 y[1] (closed_form) = 3.83224223736 0.579037078751 absolute error = 0.001663 relative error = 0.04292 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.617 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8563.9MB, alloc=52.3MB, time=105.32 x[1] = 2.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = 3.8362097137 0.57898426202 y[1] (closed_form) = 3.83765577281 0.578145954446 absolute error = 0.001671 relative error = 0.04307 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.623 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = 3.84014571599 0.580112593966 y[1] (closed_form) = 3.84159690942 0.579273439849 absolute error = 0.001676 relative error = 0.04315 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.625 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.59 2.163 h = 0.001 0.001 y[1] (numeric) = 3.84252311854 0.580757198768 y[1] (closed_form) = 3.84397615371 0.579917689802 absolute error = 0.001678 relative error = 0.04317 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.627 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8609.4MB, alloc=52.3MB, time=105.88 x[1] = 2.591 2.164 h = 0.001 0.003 y[1] (numeric) = 3.84354960681 0.580212351196 y[1] (closed_form) = 3.84500259045 0.579372429033 absolute error = 0.001678 relative error = 0.04316 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.628 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.592 2.167 h = 0.0001 0.004 y[1] (numeric) = 3.84614805092 0.580147388358 y[1] (closed_form) = 3.8476025323 0.579306019306 absolute error = 0.00168 relative error = 0.04318 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5921 2.171 h = 0.003 0.006 y[1] (numeric) = 3.84932089954 0.581027813916 y[1] (closed_form) = 3.85077866572 0.5801858639 absolute error = 0.001683 relative error = 0.04323 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.632 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8654.9MB, alloc=52.3MB, time=106.44 x[1] = 2.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = 3.85477270819 0.58009843927 y[1] (closed_form) = 3.85623511784 0.57924833768 absolute error = 0.001692 relative error = 0.04338 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.638 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = 3.85875246041 0.581209229942 y[1] (closed_form) = 3.86022001693 0.580358262424 absolute error = 0.001696 relative error = 0.04346 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.64 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5953 2.185 h = 0.001 0.001 y[1] (numeric) = 3.86115599441 0.581842933844 y[1] (closed_form) = 3.86262539701 0.580991604361 absolute error = 0.001698 relative error = 0.04348 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.642 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8700.3MB, alloc=52.3MB, time=107.00 x[1] = 2.5963 2.186 h = 0.001 0.003 y[1] (numeric) = 3.86218796331 0.581285917208 y[1] (closed_form) = 3.86365731287 0.580434173462 absolute error = 0.001698 relative error = 0.04347 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.643 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = 3.86480953383 0.581202089583 y[1] (closed_form) = 3.86628038084 0.580348889692 absolute error = 0.0017 relative error = 0.04349 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.645 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5974 2.193 h = 0.003 0.006 y[1] (numeric) = 3.86801735152 0.582068222909 y[1] (closed_form) = 3.86949149125 0.58121442949 absolute error = 0.001704 relative error = 0.04354 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.647 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8745.6MB, alloc=52.3MB, time=107.55 x[1] = 2.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = 3.87351206554 0.581092206186 y[1] (closed_form) = 3.8749908357 0.58023022149 absolute error = 0.001712 relative error = 0.04368 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.653 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = 3.87753564067 0.582185259097 y[1] (closed_form) = 3.87901957023 0.581322388854 absolute error = 0.001717 relative error = 0.04376 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.655 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6006 2.207 h = 0.001 0.001 y[1] (numeric) = 3.8799653483 0.582807943313 y[1] (closed_form) = 3.88145112825 0.581944703903 absolute error = 0.001718 relative error = 0.04378 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.657 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8791.0MB, alloc=52.3MB, time=108.11 x[1] = 2.6016 2.208 h = 0.001 0.003 y[1] (numeric) = 3.88100277404 0.582238703121 y[1] (closed_form) = 3.88248849942 0.581375048385 absolute error = 0.001719 relative error = 0.04378 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.658 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = 3.8836474778 0.58213587791 y[1] (closed_form) = 3.88513470028 0.581270757708 absolute error = 0.001721 relative error = 0.0438 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.66 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6027 2.215 h = 0.003 0.006 y[1] (numeric) = 3.88689032186 0.582987560634 y[1] (closed_form) = 3.88838084493 0.582121834192 absolute error = 0.001724 relative error = 0.04384 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.662 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8836.5MB, alloc=52.3MB, time=108.67 x[1] = 2.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = 3.89242791511 0.58196462026 y[1] (closed_form) = 3.89392305521 0.581090662634 absolute error = 0.001732 relative error = 0.04399 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.668 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = 3.8964953853 0.583039736945 y[1] (closed_form) = 3.89799569726 0.58216487392 absolute error = 0.001737 relative error = 0.04407 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6059 2.229 h = 0.001 0.001 y[1] (numeric) = 3.89895130819 0.583651281507 y[1] (closed_form) = 3.90045347486 0.582776042031 absolute error = 0.001739 relative error = 0.04408 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.672 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8881.7MB, alloc=52.3MB, time=109.22 x[1] = 2.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = 3.89999416642 0.583069763034 y[1] (closed_form) = 3.90149627697 0.582194107171 absolute error = 0.001739 relative error = 0.04408 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.673 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.607 2.234 h = 0.003 0.006 y[1] (numeric) = 3.90326738033 0.583909297407 y[1] (closed_form) = 3.90477279813 0.583033024218 absolute error = 0.001742 relative error = 0.04412 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.675 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.61 2.24 h = 0.0001 0.005 y[1] (numeric) = 3.90884242357 0.582846250111 y[1] (closed_form) = 3.91035244703 0.581961711066 absolute error = 0.00175 relative error = 0.04427 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.681 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8927.1MB, alloc=52.3MB, time=109.78 x[1] = 2.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = 3.91294795116 0.583906291495 y[1] (closed_form) = 3.91446315743 0.583020829924 absolute error = 0.001755 relative error = 0.04434 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.683 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6102 2.248 h = 0.001 0.001 y[1] (numeric) = 3.91542660688 0.584508463394 y[1] (closed_form) = 3.91694367162 0.583622619087 absolute error = 0.001757 relative error = 0.04436 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.685 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6112 2.249 h = 0.001 0.003 y[1] (numeric) = 3.91647426844 0.583916396497 y[1] (closed_form) = 3.91799127572 0.583030134873 absolute error = 0.001757 relative error = 0.04435 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.686 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8972.6MB, alloc=52.3MB, time=110.34 x[1] = 2.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = 3.91916226296 0.583778139961 y[1] (closed_form) = 3.92068076662 0.582890395345 absolute error = 0.001759 relative error = 0.04438 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.688 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6123 2.256 h = 0.003 0.006 y[1] (numeric) = 3.92247060965 0.584602925409 y[1] (closed_form) = 3.92399242862 0.583714550595 absolute error = 0.001762 relative error = 0.04442 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.69 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = 3.9280884811 0.583492425144 y[1] (closed_form) = 3.92961489163 0.582595744201 absolute error = 0.00177 relative error = 0.04456 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.696 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9018.1MB, alloc=52.3MB, time=110.90 x[1] = 2.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = 3.93223803805 0.584534156622 y[1] (closed_form) = 3.93376964377 0.583636532868 absolute error = 0.001775 relative error = 0.04464 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.698 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6155 2.27 h = 0.001 0.001 y[1] (numeric) = 3.93474298655 0.585124963008 y[1] (closed_form) = 3.936276455 0.58422694908 absolute error = 0.001777 relative error = 0.04466 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6165 2.271 h = 0.001 0.003 y[1] (numeric) = 3.93579603444 0.584520515091 y[1] (closed_form) = 3.93732944385 0.583622082792 absolute error = 0.001777 relative error = 0.04465 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.701 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9063.6MB, alloc=52.3MB, time=111.46 x[1] = 2.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = 3.93850717843 0.584362875467 y[1] (closed_form) = 3.94004208366 0.583462950666 absolute error = 0.001779 relative error = 0.04467 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.704 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6176 2.278 h = 0.003 0.006 y[1] (numeric) = 3.9418507134 0.585172749257 y[1] (closed_form) = 3.94338894173 0.584272181123 absolute error = 0.001782 relative error = 0.04471 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.706 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = 3.94751138068 0.584014509097 y[1] (closed_form) = 3.94905418608 0.583105594372 absolute error = 0.001791 relative error = 0.04486 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.711 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9109.0MB, alloc=52.3MB, time=112.02 x[1] = 2.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = 3.95170503661 0.585037726611 y[1] (closed_form) = 3.95325304952 0.584127848561 absolute error = 0.001796 relative error = 0.04493 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.714 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6208 2.292 h = 0.001 0.001 y[1] (numeric) = 3.95423631796 0.585617044185 y[1] (closed_form) = 3.95578619786 0.58470676844 absolute error = 0.001797 relative error = 0.04495 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.715 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6218 2.293 h = 0.001 0.003 y[1] (numeric) = 3.95529472623 0.585000159884 y[1] (closed_form) = 3.95684454548 0.584089464716 absolute error = 0.001798 relative error = 0.04494 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.717 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9154.5MB, alloc=52.3MB, time=112.58 x[1] = 2.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = 3.95802902303 0.584823000452 y[1] (closed_form) = 3.95958033749 0.583910803211 absolute error = 0.0018 relative error = 0.04496 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.719 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6229 2.3 h = 0.003 0.006 y[1] (numeric) = 3.96140780083 0.585617798194 y[1] (closed_form) = 3.96296244612 0.584704944337 absolute error = 0.001803 relative error = 0.045 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.721 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9199.9MB, alloc=52.3MB, time=113.14 x[1] = 2.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = 3.96711122932 0.584411529406 y[1] (closed_form) = 3.96867043682 0.583490288312 absolute error = 0.001811 relative error = 0.04515 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.727 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.626 2.311 h = 0.0001 0.003 y[1] (numeric) = 3.97134905293 0.585416026975 y[1] (closed_form) = 3.97291348021 0.584493801812 absolute error = 0.001816 relative error = 0.04522 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.729 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6261 2.314 h = 0.001 0.001 y[1] (numeric) = 3.97390670664 0.585983731293 y[1] (closed_form) = 3.97547300513 0.585061100833 absolute error = 0.001818 relative error = 0.04524 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.731 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9245.3MB, alloc=52.3MB, time=113.70 x[1] = 2.6271 2.315 h = 0.001 0.003 y[1] (numeric) = 3.97497044876 0.58535435503 y[1] (closed_form) = 3.97653668498 0.5844313041 absolute error = 0.001818 relative error = 0.04523 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.732 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = 3.97772790082 0.58515753809 y[1] (closed_form) = 3.97929563155 0.584232975451 absolute error = 0.00182 relative error = 0.04525 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.734 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6282 2.322 h = 0.003 0.006 y[1] (numeric) = 3.98114197522 0.585937093862 y[1] (closed_form) = 3.9827130445 0.58501186118 absolute error = 0.001823 relative error = 0.04529 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.736 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9290.8MB, alloc=52.3MB, time=114.26 x[1] = 2.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = 3.98688812808 0.584682505931 y[1] (closed_form) = 3.98846374431 0.583748845185 absolute error = 0.001831 relative error = 0.04544 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.742 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = 3.99117018712 0.585668075665 y[1] (closed_form) = 3.99275103535 0.58473340988 absolute error = 0.001836 relative error = 0.04551 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.745 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6314 2.336 h = 0.001 0.001 y[1] (numeric) = 3.99375425213 0.586224041145 y[1] (closed_form) = 3.99533697577 0.585288962379 absolute error = 0.001838 relative error = 0.04553 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.746 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9336.2MB, alloc=52.3MB, time=114.83 x[1] = 2.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = 3.994823301 0.585582117141 y[1] (closed_form) = 3.99640596072 0.584646616862 absolute error = 0.001838 relative error = 0.04552 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.747 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6325 2.341 h = 0.003 0.006 y[1] (numeric) = 3.99826798454 0.586348840529 y[1] (closed_form) = 3.99985398933 0.585412658515 absolute error = 0.001842 relative error = 0.04556 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = 4.00405146222 0.585052935406 y[1] (closed_form) = 4.00564200102 0.584108289858 absolute error = 0.00185 relative error = 0.0457 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.755 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9381.7MB, alloc=52.3MB, time=115.38 x[1] = 2.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = 4.00837188005 0.586022572782 y[1] (closed_form) = 4.00996766156 0.585076904107 absolute error = 0.001855 relative error = 0.04577 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.758 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6357 2.355 h = 0.001 0.001 y[1] (numeric) = 4.01097885163 0.586568647669 y[1] (closed_form) = 4.01257651224 0.585622559383 absolute error = 0.001857 relative error = 0.04579 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.759 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6367 2.356 h = 0.001 0.003 y[1] (numeric) = 4.01205259663 0.585915940935 y[1] (closed_form) = 4.01365019191 0.584969430222 absolute error = 0.001857 relative error = 0.04578 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.761 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9427.1MB, alloc=52.3MB, time=115.94 x[1] = 2.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = 4.0148533766 0.585682451989 y[1] (closed_form) = 4.01645246505 0.584734411465 absolute error = 0.001859 relative error = 0.0458 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.763 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6378 2.363 h = 0.003 0.006 y[1] (numeric) = 4.01833345653 0.58643362115 y[1] (closed_form) = 4.01993589793 0.5854848853 absolute error = 0.001862 relative error = 0.04584 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.765 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = 4.02415958755 0.585088851152 y[1] (closed_form) = 4.02576654699 0.584131610613 absolute error = 0.00187 relative error = 0.04598 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.771 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9472.5MB, alloc=52.3MB, time=116.50 x[1] = 2.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = 4.02852436688 0.586039169606 y[1] (closed_form) = 4.03013658114 0.58508088455 absolute error = 0.001876 relative error = 0.04605 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.773 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.641 2.377 h = 0.001 0.001 y[1] (numeric) = 4.03115782215 0.586573269429 y[1] (closed_form) = 4.03277191966 0.585614556927 absolute error = 0.001877 relative error = 0.04607 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.775 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.642 2.378 h = 0.001 0.003 y[1] (numeric) = 4.03223682264 0.585907910303 y[1] (closed_form) = 4.03385085315 0.584948774337 absolute error = 0.001878 relative error = 0.04606 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.776 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9518.0MB, alloc=52.3MB, time=117.06 x[1] = 2.643 2.381 h = 0.0001 0.004 y[1] (numeric) = 4.03506076138 0.58565436458 y[1] (closed_form) = 4.03667628416 0.584693688994 absolute error = 0.00188 relative error = 0.04608 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.778 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6431 2.385 h = 0.003 0.006 y[1] (numeric) = 4.03857628952 0.586389809381 y[1] (closed_form) = 4.04019517284 0.585428424628 absolute error = 0.001883 relative error = 0.04612 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.781 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = 4.0444450306 0.584995879018 y[1] (closed_form) = 4.04606841562 0.584025948254 absolute error = 0.001891 relative error = 0.04626 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.786 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9563.4MB, alloc=52.3MB, time=117.62 x[1] = 2.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = 4.04885423642 0.585926665268 y[1] (closed_form) = 4.05048288831 0.58495566837 absolute error = 0.001896 relative error = 0.04633 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.789 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6463 2.399 h = 0.001 0.001 y[1] (numeric) = 4.05151421261 0.586448661236 y[1] (closed_form) = 4.05314475188 0.585477228977 absolute error = 0.001898 relative error = 0.04635 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.79 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6473 2.4 h = 0.001 0.003 y[1] (numeric) = 4.05259843989 0.585770593383 y[1] (closed_form) = 4.05422891046 0.584798736629 absolute error = 0.001898 relative error = 0.04634 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.792 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9608.8MB, alloc=52.3MB, time=118.18 x[1] = 2.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = 4.05544553622 0.585496849482 y[1] (closed_form) = 4.0570774981 0.584523443238 absolute error = 0.0019 relative error = 0.04636 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.794 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6484 2.407 h = 0.003 0.006 y[1] (numeric) = 4.05899656333 0.586216398198 y[1] (closed_form) = 4.06063189331 0.585242268804 absolute error = 0.001903 relative error = 0.0464 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.796 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = 4.06490786893 0.584773010304 y[1] (closed_form) = 4.06654768387 0.583790293412 absolute error = 0.001912 relative error = 0.04653 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.802 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9654.3MB, alloc=52.3MB, time=118.73 x[1] = 2.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = 4.06936156526 0.585684049213 y[1] (closed_form) = 4.07100665904 0.584700244347 absolute error = 0.001917 relative error = 0.04661 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.804 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6516 2.421 h = 0.001 0.001 y[1] (numeric) = 4.07204809898 0.586193811429 y[1] (closed_form) = 4.07369508425 0.58520956321 absolute error = 0.001919 relative error = 0.04662 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.806 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6526 2.422 h = 0.001 0.003 y[1] (numeric) = 4.07313752377 0.585502978335 y[1] (closed_form) = 4.07478443863 0.584518304593 absolute error = 0.001919 relative error = 0.04661 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.807 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9699.7MB, alloc=52.3MB, time=119.29 x[1] = 2.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = 4.07600777555 0.58520889393 y[1] (closed_form) = 4.07765618069 0.58422266077 absolute error = 0.001921 relative error = 0.04663 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6537 2.429 h = 0.003 0.006 y[1] (numeric) = 4.0795943516 0.585912373364 y[1] (closed_form) = 4.08124613234 0.584925402928 absolute error = 0.001924 relative error = 0.04667 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.812 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = 4.08554817387 0.584419229118 y[1] (closed_form) = 4.08720442246 0.583423629539 absolute error = 0.001932 relative error = 0.04681 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.817 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9745.1MB, alloc=52.3MB, time=119.85 x[1] = 2.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = 4.0900464237 0.585310303711 y[1] (closed_form) = 4.09170796304 0.584313594097 absolute error = 0.001938 relative error = 0.04688 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.82 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6569 2.443 h = 0.001 0.001 y[1] (numeric) = 4.09275955093 0.585807701188 y[1] (closed_form) = 4.09442298583 0.584810540146 absolute error = 0.001939 relative error = 0.04689 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.822 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = 4.09385414338 0.585104046165 y[1] (closed_form) = 4.09551750614 0.584106458578 absolute error = 0.00194 relative error = 0.04688 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.823 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9790.4MB, alloc=52.3MB, time=120.41 x[1] = 2.658 2.448 h = 0.003 0.006 y[1] (numeric) = 4.09747155263 0.58579397824 y[1] (closed_form) = 4.09913829735 0.584795641093 absolute error = 0.001943 relative error = 0.04692 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.825 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.661 2.454 h = 0.0001 0.005 y[1] (numeric) = 4.10346252934 0.584258270498 y[1] (closed_form) = 4.10513372736 0.583251268025 absolute error = 0.001951 relative error = 0.04706 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.831 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = 4.10799942036 0.585132517054 y[1] (closed_form) = 4.10967591959 0.584124385522 absolute error = 0.001956 relative error = 0.04713 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.833 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9835.9MB, alloc=52.3MB, time=120.97 x[1] = 2.6612 2.462 h = 0.001 0.001 y[1] (numeric) = 4.11073561616 0.585619483008 y[1] (closed_form) = 4.11241401455 0.584610893083 absolute error = 0.001958 relative error = 0.04714 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.835 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6622 2.463 h = 0.001 0.003 y[1] (numeric) = 4.11183478608 0.584904806835 y[1] (closed_form) = 4.11351311084 0.583895789468 absolute error = 0.001958 relative error = 0.04713 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.836 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = 4.11474836216 0.584572767284 y[1] (closed_form) = 4.11642817519 0.58356217186 absolute error = 0.00196 relative error = 0.04715 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.839 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9881.3MB, alloc=52.3MB, time=121.53 x[1] = 2.6633 2.47 h = 0.003 0.006 y[1] (numeric) = 4.11840141294 0.585246304388 y[1] (closed_form) = 4.1200846156 0.584234945116 absolute error = 0.001964 relative error = 0.04719 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.841 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = 4.12443481479 0.583660279323 y[1] (closed_form) = 4.12612245292 0.582640212788 absolute error = 0.001972 relative error = 0.04732 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.847 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = 4.12901637641 0.5845141537 y[1] (closed_form) = 4.13070932752 0.583492935634 absolute error = 0.001977 relative error = 0.04739 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.849 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9926.8MB, alloc=52.3MB, time=122.09 x[1] = 2.6665 2.484 h = 0.001 0.001 y[1] (numeric) = 4.13177923258 0.584988508705 y[1] (closed_form) = 4.13347408688 0.583966824026 absolute error = 0.001979 relative error = 0.04741 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.851 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6675 2.485 h = 0.001 0.003 y[1] (numeric) = 4.13288351378 0.584260904304 y[1] (closed_form) = 4.13457829269 0.583238791169 absolute error = 0.001979 relative error = 0.0474 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.852 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = 4.13582023563 0.583908112006 y[1] (closed_form) = 4.13751650157 0.582884410725 absolute error = 0.001981 relative error = 0.04742 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.855 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9972.1MB, alloc=52.3MB, time=122.64 x[1] = 2.6686 2.492 h = 0.003 0.006 y[1] (numeric) = 4.13950897578 0.584565076882 y[1] (closed_form) = 4.14120863872 0.583540597224 absolute error = 0.001985 relative error = 0.04745 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.857 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = 4.14558474834 0.582928431069 y[1] (closed_form) = 4.14728882853 0.581895202064 absolute error = 0.001993 relative error = 0.04759 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.862 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = 4.15021104058 0.583761711099 y[1] (closed_form) = 4.15192044546 0.582727307873 absolute error = 0.001998 relative error = 0.04766 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.865 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10017.4MB, alloc=52.3MB, time=123.20 x[1] = 2.6718 2.506 h = 0.001 0.001 y[1] (numeric) = 4.15300059127 0.584223321078 y[1] (closed_form) = 4.15471190335 0.58318844294 absolute error = 0.002 relative error = 0.04767 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.867 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6728 2.507 h = 0.001 0.003 y[1] (numeric) = 4.15410995229 0.583482731289 y[1] (closed_form) = 4.15582118719 0.582447423688 absolute error = 0.002 relative error = 0.04766 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.868 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = 4.15706981405 0.583109040437 y[1] (closed_form) = 4.15878253467 0.582072134544 absolute error = 0.002002 relative error = 0.04768 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.87 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10062.8MB, alloc=52.3MB, time=123.76 x[1] = 2.6739 2.514 h = 0.003 0.006 y[1] (numeric) = 4.16079429027 0.583749254301 y[1] (closed_form) = 4.16251041522 0.582711555363 absolute error = 0.002005 relative error = 0.04771 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.873 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = 4.1669123768 0.582061682764 y[1] (closed_form) = 4.16863290038 0.58101519225 absolute error = 0.002014 relative error = 0.04785 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.878 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.677 2.525 h = 0.0001 0.003 y[1] (numeric) = 4.17158345861 0.582874144497 y[1] (closed_form) = 4.17330931853 0.581826456856 absolute error = 0.002019 relative error = 0.04791 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.881 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10108.2MB, alloc=52.3MB, time=124.31 x[1] = 2.6771 2.528 h = 0.001 0.001 y[1] (numeric) = 4.17439973734 0.583322874312 y[1] (closed_form) = 4.17612750841 0.582274703384 absolute error = 0.002021 relative error = 0.04793 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.883 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6781 2.529 h = 0.001 0.003 y[1] (numeric) = 4.17551414612 0.582569241823 y[1] (closed_form) = 4.17724183823 0.581520640429 absolute error = 0.002021 relative error = 0.04792 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.884 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = 4.17849714095 0.58217450574 y[1] (closed_form) = 4.18022631737 0.581124295854 absolute error = 0.002023 relative error = 0.04794 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.886 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10153.6MB, alloc=52.3MB, time=124.87 x[1] = 2.6792 2.536 h = 0.003 0.006 y[1] (numeric) = 4.18225739908 0.582797788391 y[1] (closed_form) = 4.18398998712 0.581746770653 absolute error = 0.002026 relative error = 0.04797 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.888 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = 4.1884177405 0.58105898463 y[1] (closed_form) = 4.19015470817 0.579999132949 absolute error = 0.002035 relative error = 0.0481 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.894 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = 4.19313366976 0.581850402347 y[1] (closed_form) = 4.19487598532 0.580789330416 absolute error = 0.00204 relative error = 0.04817 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.897 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10199.0MB, alloc=52.3MB, time=125.42 x[1] = 2.6824 2.55 h = 0.001 0.001 y[1] (numeric) = 4.19597670933 0.582286115811 y[1] (closed_form) = 4.19772093999 0.581224552142 absolute error = 0.002042 relative error = 0.04818 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.898 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = 4.19709613328 0.581519383165 y[1] (closed_form) = 4.19884028316 0.580457388032 absolute error = 0.002042 relative error = 0.04818 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6835 2.555 h = 0.003 0.006 y[1] (numeric) = 4.20088743221 0.582128373671 y[1] (closed_form) = 4.20263499986 0.581065557827 absolute error = 0.002045 relative error = 0.04821 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.902 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10244.4MB, alloc=52.3MB, time=125.98 x[1] = 2.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = 4.20708471141 0.580345726676 y[1] (closed_form) = 4.20883664253 0.579274040078 absolute error = 0.002054 relative error = 0.04834 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.908 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = 4.21183954371 0.581119383456 y[1] (closed_form) = 4.21359683289 0.580046456669 absolute error = 0.002059 relative error = 0.04841 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.91 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10289.9MB, alloc=52.3MB, time=126.54 x[1] = 2.6867 2.569 h = 0.001 0.001 y[1] (numeric) = 4.21470580119 0.581544102322 y[1] (closed_form) = 4.21646500893 0.580470676505 absolute error = 0.002061 relative error = 0.04842 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.912 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6877 2.57 h = 0.001 0.003 y[1] (numeric) = 4.21582967246 0.580766106582 y[1] (closed_form) = 4.21758879786 0.579692248425 absolute error = 0.002061 relative error = 0.04841 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.913 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = 4.21885594574 0.580332092233 y[1] (closed_form) = 4.22061655279 0.579256606444 absolute error = 0.002063 relative error = 0.04843 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.916 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10335.3MB, alloc=52.3MB, time=127.11 x[1] = 2.6888 2.577 h = 0.003 0.006 y[1] (numeric) = 4.22268311146 0.580923812915 y[1] (closed_form) = 4.22444714372 0.579847491446 absolute error = 0.002066 relative error = 0.04846 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.918 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = 4.22892253307 0.579089358632 y[1] (closed_form) = 4.23069090908 0.578004123787 absolute error = 0.002075 relative error = 0.04859 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.924 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = 4.23372232028 0.579841547389 y[1] (closed_form) = 4.23549606576 0.578755048833 absolute error = 0.00208 relative error = 0.04866 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.926 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10380.8MB, alloc=52.3MB, time=127.67 x[1] = 2.692 2.591 h = 0.001 0.001 y[1] (numeric) = 4.23661539954 0.580252994095 y[1] (closed_form) = 4.23839106748 0.579165987914 absolute error = 0.002082 relative error = 0.04867 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.928 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.693 2.592 h = 0.001 0.003 y[1] (numeric) = 4.23774422447 0.579461790511 y[1] (closed_form) = 4.23951980822 0.578374351003 absolute error = 0.002082 relative error = 0.04866 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.929 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.694 2.595 h = 0.0001 0.004 y[1] (numeric) = 4.2407936075 0.579006306493 y[1] (closed_form) = 4.24257067129 0.577917229002 absolute error = 0.002084 relative error = 0.04868 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.932 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10426.1MB, alloc=52.3MB, time=128.22 x[1] = 2.6941 2.599 h = 0.003 0.006 y[1] (numeric) = 4.24465668357 0.579580573246 y[1] (closed_form) = 4.2464371797 0.578490644877 absolute error = 0.002088 relative error = 0.04871 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.934 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = 4.2509381818 0.577694000929 y[1] (closed_form) = 4.25272300157 0.576595116433 absolute error = 0.002096 relative error = 0.04884 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.94 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = 4.25578297863 0.578424490953 y[1] (closed_form) = 4.2575731792 0.577324319011 absolute error = 0.002101 relative error = 0.04891 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.943 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10471.5MB, alloc=52.3MB, time=128.78 x[1] = 2.6973 2.613 h = 0.001 0.001 y[1] (numeric) = 4.25870291055 0.578822526345 y[1] (closed_form) = 4.26049503743 0.577721838108 absolute error = 0.002103 relative error = 0.04892 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.944 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6983 2.614 h = 0.001 0.003 y[1] (numeric) = 4.25983665492 0.578018057067 y[1] (closed_form) = 4.26162869574 0.576916934523 absolute error = 0.002103 relative error = 0.04891 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.946 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = 4.26290913699 0.577540953438 y[1] (closed_form) = 4.26470265619 0.576438182508 absolute error = 0.002105 relative error = 0.04892 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.948 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10516.9MB, alloc=52.3MB, time=129.34 x[1] = 2.6994 2.621 h = 0.003 0.006 y[1] (numeric) = 4.2668081658 0.578097580692 y[1] (closed_form) = 4.26860512441 0.576993943552 absolute error = 0.002109 relative error = 0.04896 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = 4.2731316725 0.576158578168 y[1] (closed_form) = 4.27493293425 0.575045942026 absolute error = 0.002117 relative error = 0.04908 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.956 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = 4.2780215325 0.576867137037 y[1] (closed_form) = 4.2798281863 0.575753189503 absolute error = 0.002122 relative error = 0.04915 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.959 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10562.3MB, alloc=52.3MB, time=129.90 x[1] = 2.7026 2.635 h = 0.001 0.001 y[1] (numeric) = 4.28096834727 0.577251620944 y[1] (closed_form) = 4.2827769312 0.57613714837 absolute error = 0.002124 relative error = 0.04916 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.96 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7036 2.636 h = 0.001 0.003 y[1] (numeric) = 4.28210697626 0.576433828 y[1] (closed_form) = 4.28391547225 0.575318920143 absolute error = 0.002125 relative error = 0.04915 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.962 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = 4.28520254567 0.575934954002 y[1] (closed_form) = 4.28701251828 0.574818387306 absolute error = 0.002127 relative error = 0.04917 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.964 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10607.7MB, alloc=52.3MB, time=130.46 x[1] = 2.7047 2.643 h = 0.003 0.006 y[1] (numeric) = 4.28913756869 0.576473754829 y[1] (closed_form) = 4.29095098773 0.575356306456 absolute error = 0.00213 relative error = 0.0492 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.966 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = 4.29550301332 0.574482008525 y[1] (closed_form) = 4.29732071462 0.573355518156 absolute error = 0.002138 relative error = 0.04933 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.972 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = 4.3004379889 0.575168402119 y[1] (closed_form) = 4.30226109341 0.574040576201 absolute error = 0.002144 relative error = 0.04939 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.975 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10653.2MB, alloc=52.3MB, time=131.01 x[1] = 2.7079 2.657 h = 0.001 0.001 y[1] (numeric) = 4.30341171599 0.575539193363 y[1] (closed_form) = 4.30523675442 0.574410833585 absolute error = 0.002146 relative error = 0.0494 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.977 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = 4.30455519424 0.574708018661 y[1] (closed_form) = 4.30638014283 0.573579222631 absolute error = 0.002146 relative error = 0.04939 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.978 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.709 2.662 h = 0.003 0.006 y[1] (numeric) = 4.308521448 0.575231753877 y[1] (closed_form) = 4.31034984896 0.57410206275 absolute error = 0.002149 relative error = 0.04943 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.98 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10698.5MB, alloc=52.3MB, time=131.57 x[1] = 2.712 2.668 h = 0.0001 0.005 y[1] (numeric) = 4.31492356651 0.573194853711 y[1] (closed_form) = 4.31675623194 0.572056083229 absolute error = 0.002158 relative error = 0.04955 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.986 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = 4.31989768501 0.573862517655 y[1] (closed_form) = 4.32173576349 0.572722390798 absolute error = 0.002163 relative error = 0.04961 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.989 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7122 2.676 h = 0.001 0.001 y[1] (numeric) = 4.3228947658 0.574221729939 y[1] (closed_form) = 4.32473478154 0.573081061614 absolute error = 0.002165 relative error = 0.04962 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.99 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10743.8MB, alloc=52.3MB, time=132.13 x[1] = 2.7132 2.677 h = 0.001 0.003 y[1] (numeric) = 4.32404254971 0.573379047243 y[1] (closed_form) = 4.32588247397 0.572237941813 absolute error = 0.002165 relative error = 0.04962 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.992 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = 4.32718130822 0.572839534312 y[1] (closed_form) = 4.32902270576 0.57169675044 absolute error = 0.002167 relative error = 0.04963 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.994 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7143 2.684 h = 0.003 0.006 y[1] (numeric) = 4.33118363286 0.573345092077 y[1] (closed_form) = 4.33302848993 0.572201397478 absolute error = 0.002171 relative error = 0.04966 % Correct digits = 3 Radius of convergence (given) for eq 1 = 4.996 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10789.4MB, alloc=52.3MB, time=132.69 x[1] = 2.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = 4.33762755549 0.571254860098 y[1] (closed_form) = 4.33947665543 0.570102042929 absolute error = 0.002179 relative error = 0.04979 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.002 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = 4.34264688681 0.571899919248 y[1] (closed_form) = 4.34450141079 0.570745721159 absolute error = 0.002184 relative error = 0.04985 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.005 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7175 2.698 h = 0.001 0.001 y[1] (numeric) = 4.34567093456 0.572245173845 y[1] (closed_form) = 4.34752739953 0.571090425329 absolute error = 0.002186 relative error = 0.04986 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.007 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10834.8MB, alloc=52.3MB, time=133.24 x[1] = 2.7185 2.699 h = 0.001 0.003 y[1] (numeric) = 4.3468235011 0.571389000564 y[1] (closed_form) = 4.34867987266 0.570233813987 absolute error = 0.002186 relative error = 0.04985 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.008 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = 4.34998530963 0.570827281399 y[1] (closed_form) = 4.35184315249 0.569670405785 absolute error = 0.002189 relative error = 0.04987 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7196 2.706 h = 0.003 0.006 y[1] (numeric) = 4.35402374417 0.571314471033 y[1] (closed_form) = 4.35588505343 0.570156668845 absolute error = 0.002192 relative error = 0.0499 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.013 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10880.3MB, alloc=52.3MB, time=133.80 x[1] = 2.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = 4.36050939358 0.569170589771 y[1] (closed_form) = 4.3623749237 0.56800362169 absolute error = 0.0022 relative error = 0.05002 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.018 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = 4.36557398676 0.569792805215 y[1] (closed_form) = 4.36744495184 0.568624431465 absolute error = 0.002206 relative error = 0.05008 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.021 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7228 2.72 h = 0.001 0.001 y[1] (numeric) = 4.36862502891 0.570123958102 y[1] (closed_form) = 4.37049793866 0.568955024893 absolute error = 0.002208 relative error = 0.05009 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.023 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10925.7MB, alloc=52.3MB, time=134.36 x[1] = 2.7238 2.721 h = 0.001 0.003 y[1] (numeric) = 4.36978234107 0.569254235831 y[1] (closed_form) = 4.37165515547 0.568084863609 absolute error = 0.002208 relative error = 0.05008 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.024 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = 4.37296718397 0.568670156618 y[1] (closed_form) = 4.37484146762 0.567499084721 absolute error = 0.00221 relative error = 0.0501 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.027 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7249 2.728 h = 0.003 0.006 y[1] (numeric) = 4.37704176621 0.569138786043 y[1] (closed_form) = 4.37891952306 0.567966771593 absolute error = 0.002214 relative error = 0.05013 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.029 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10971.2MB, alloc=52.3MB, time=134.92 x[1] = 2.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = 4.38356906265 0.566940936726 y[1] (closed_form) = 4.38545101796 0.565759712954 absolute error = 0.002222 relative error = 0.05025 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.035 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.728 2.739 h = 0.0001 0.003 y[1] (numeric) = 4.38867896556 0.567540067913 y[1] (closed_form) = 4.39056636665 0.566357413515 absolute error = 0.002227 relative error = 0.05031 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.038 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7281 2.742 h = 0.001 0.001 y[1] (numeric) = 4.39175702876 0.567856974093 y[1] (closed_form) = 4.39364637818 0.566673751132 absolute error = 0.002229 relative error = 0.05032 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.039 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11016.6MB, alloc=52.3MB, time=135.48 x[1] = 2.7291 2.743 h = 0.001 0.003 y[1] (numeric) = 4.392919049 0.566973644327 y[1] (closed_form) = 4.3948083011 0.56578998141 absolute error = 0.002229 relative error = 0.05031 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.041 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = 4.39612690956 0.566367050494 y[1] (closed_form) = 4.39801762879 0.565181677214 absolute error = 0.002232 relative error = 0.05033 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.043 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7302 2.75 h = 0.003 0.006 y[1] (numeric) = 4.40023767634 0.566816926328 y[1] (closed_form) = 4.40213187551 0.565630594388 absolute error = 0.002235 relative error = 0.05036 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.046 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11062.0MB, alloc=52.3MB, time=136.04 x[1] = 2.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = 4.40680653766 0.564564788905 y[1] (closed_form) = 4.4087049125 0.563369204109 absolute error = 0.002243 relative error = 0.05048 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.051 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = 4.41196179692 0.565140593653 y[1] (closed_form) = 4.41386562827 0.563943553074 absolute error = 0.002249 relative error = 0.05054 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.054 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7334 2.764 h = 0.001 0.001 y[1] (numeric) = 4.41506690712 0.565443107164 y[1] (closed_form) = 4.41697269043 0.564245488844 absolute error = 0.002251 relative error = 0.05055 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.056 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11107.5MB, alloc=52.3MB, time=136.60 x[1] = 2.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = 4.4162335973 0.564546111309 y[1] (closed_form) = 4.4181392813 0.563348052096 absolute error = 0.002251 relative error = 0.05054 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.057 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7345 2.769 h = 0.003 0.006 y[1] (numeric) = 4.42037576608 0.564980120518 y[1] (closed_form) = 4.42228493572 0.563781088682 absolute error = 0.002254 relative error = 0.05057 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.059 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = 4.42698098931 0.562681490198 y[1] (closed_form) = 4.42889431522 0.561473167678 absolute error = 0.002263 relative error = 0.05069 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.065 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11152.9MB, alloc=52.3MB, time=137.15 x[1] = 2.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = 4.43217560804 0.56323756218 y[1] (closed_form) = 4.43409439991 0.562027762185 absolute error = 0.002268 relative error = 0.05075 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.068 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7377 2.783 h = 0.001 0.001 y[1] (numeric) = 4.43530419343 0.563527891937 y[1] (closed_form) = 4.43722494045 0.562317506287 absolute error = 0.00227 relative error = 0.05076 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.07 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7387 2.784 h = 0.001 0.003 y[1] (numeric) = 4.43647503611 0.562619140781 y[1] (closed_form) = 4.43839568212 0.561408313412 absolute error = 0.00227 relative error = 0.05075 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.071 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11198.3MB, alloc=52.3MB, time=137.71 x[1] = 2.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = 4.43972595173 0.561970512196 y[1] (closed_form) = 4.44164806084 0.560757954431 absolute error = 0.002273 relative error = 0.05076 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.074 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7398 2.791 h = 0.003 0.006 y[1] (numeric) = 4.44390437306 0.562385404886 y[1] (closed_form) = 4.44582997468 0.561171858223 absolute error = 0.002276 relative error = 0.05079 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.076 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = 4.45055100569 0.560031886547 y[1] (closed_form) = 4.45248074007 0.558809005485 absolute error = 0.002285 relative error = 0.05091 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.082 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11243.7MB, alloc=52.3MB, time=138.27 x[1] = 2.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = 4.45579106721 0.560564177691 y[1] (closed_form) = 4.45772627811 0.559339793617 absolute error = 0.00229 relative error = 0.05097 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.085 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.743 2.805 h = 0.001 0.001 y[1] (numeric) = 4.45894674762 0.560839840925 y[1] (closed_form) = 4.46088391722 0.559614861885 absolute error = 0.002292 relative error = 0.05098 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.086 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.744 2.806 h = 0.001 0.003 y[1] (numeric) = 4.46012218849 0.559917313951 y[1] (closed_form) = 4.46205925507 0.558691892268 absolute error = 0.002292 relative error = 0.05097 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.088 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11289.2MB, alloc=52.3MB, time=138.83 x[1] = 2.745 2.809 h = 0.0001 0.004 y[1] (numeric) = 4.46339607011 0.559245724202 y[1] (closed_form) = 4.46533459744 0.558018561308 absolute error = 0.002294 relative error = 0.05098 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.09 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7451 2.813 h = 0.003 0.006 y[1] (numeric) = 4.46761077824 0.559641303391 y[1] (closed_form) = 4.46955280465 0.558413135121 absolute error = 0.002298 relative error = 0.05101 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.093 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = 4.47429873121 0.557232573429 y[1] (closed_form) = 4.47624486647 0.555995026952 absolute error = 0.002306 relative error = 0.05113 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.098 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11334.6MB, alloc=52.3MB, time=139.39 x[1] = 2.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = 4.47958427863 0.557740836963 y[1] (closed_form) = 4.48153590086 0.556501761739 absolute error = 0.002312 relative error = 0.05119 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.101 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7483 2.827 h = 0.001 0.001 y[1] (numeric) = 4.48276707785 0.558001684989 y[1] (closed_form) = 4.48472066229 0.556762005415 absolute error = 0.002314 relative error = 0.0512 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7493 2.828 h = 0.001 0.003 y[1] (numeric) = 4.48394707716 0.557065323362 y[1] (closed_form) = 4.48590055656 0.555825200229 absolute error = 0.002314 relative error = 0.05119 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.104 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11380.1MB, alloc=52.3MB, time=139.95 x[1] = 2.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = 4.48724390403 0.556370615028 y[1] (closed_form) = 4.48919884176 0.555128739825 absolute error = 0.002316 relative error = 0.0512 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.107 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7504 2.835 h = 0.003 0.006 y[1] (numeric) = 4.49149493197 0.5567466824 y[1] (closed_form) = 4.49345337527 0.555503785219 absolute error = 0.00232 relative error = 0.05123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.109 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11425.4MB, alloc=52.3MB, time=140.50 x[1] = 2.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = 4.49822411378 0.554282416023 y[1] (closed_form) = 4.50018664163 0.553030096738 absolute error = 0.002328 relative error = 0.05135 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.115 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = 4.50355518895 0.554766403605 y[1] (closed_form) = 4.50552321412 0.553512529638 absolute error = 0.002334 relative error = 0.05141 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.118 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7536 2.849 h = 0.001 0.001 y[1] (numeric) = 4.50676512997 0.555012286805 y[1] (closed_form) = 4.50873512084 0.553757799036 absolute error = 0.002336 relative error = 0.05141 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11470.8MB, alloc=52.3MB, time=141.06 x[1] = 2.7546 2.85 h = 0.001 0.003 y[1] (numeric) = 4.50794964741 0.554062031618 y[1] (closed_form) = 4.5099195312 0.55280709938 absolute error = 0.002336 relative error = 0.0514 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.121 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = 4.51126939775 0.553344046571 y[1] (closed_form) = 4.51324073736 0.55208735136 absolute error = 0.002338 relative error = 0.05142 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.123 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7557 2.857 h = 0.003 0.006 y[1] (numeric) = 4.51555677747 0.553700402566 y[1] (closed_form) = 4.51753162908 0.552442668647 absolute error = 0.002341 relative error = 0.05144 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.126 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11516.0MB, alloc=52.3MB, time=141.62 x[1] = 2.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = 4.52232709417 0.55118027382 y[1] (closed_form) = 4.52430600565 0.549913073818 absolute error = 0.00235 relative error = 0.05156 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = 4.52770373767 0.551639735549 y[1] (closed_form) = 4.52968815672 0.550370954733 absolute error = 0.002355 relative error = 0.05162 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.134 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7589 2.871 h = 0.001 0.001 y[1] (numeric) = 4.53094084273 0.551870503384 y[1] (closed_form) = 4.53292723092 0.550601099243 absolute error = 0.002357 relative error = 0.05163 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.136 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11561.4MB, alloc=52.3MB, time=142.18 x[1] = 2.7599 2.872 h = 0.001 0.003 y[1] (numeric) = 4.53212983742 0.550906295663 y[1] (closed_form) = 4.53411611647 0.549636446151 absolute error = 0.002358 relative error = 0.05162 % Correct digits = 3 Radius of convergence (given) for eq 1 = 5.138 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 754 Total Elapsed Time = 2 Minutes 22 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 2 Minutes 22 Seconds > quit memory used=11579.9MB, alloc=52.3MB, time=142.40