
(* f1=Integrate[x^n*Sin[x]*Exp[-x^2],{x,0,Infinity}] *)

Clear[x]
n=20
mydata=Table[0,{i,1,n}]
For[i=1, i<=n, i++,
  ci=Integrate[x^(i-1)*Sin[x]*Exp[-x^2],{x,0,Infinity}];
  Print["i-1=",i-1,",  ci=",ci];
  mydata[[i]]=ci
]
Print[InputForm[mydata]]
Print["iv="]
Print[N[mydata,20]]

(* DawsonF *)
(*

/*
  mydata --> Dawson
  xij in resin_series is the local coordinate at (-1,0,-1)
*/

def std2val(Std) {
  if (type(Std)>3) return map(std2val,Std);
  Dawson=number_float_to_rational(
   [0.42443638350202229593, 0.34509711176078574369, 0.35610909587550557398, 0.43137138970098217962, 0.58902727396887639350, 0.88431134888701346821, 
 
    1.4350386267412079504, 2.4857776331519098100, 4.5512868623659767388, 8.7366186770377047065, 17.457575840142396790, 36.069725365864391955, 76.536197958225090470, 
 
    165.52739674743753006, 361.46842226355826420, 786.51871763483598708, 1668.5280101564636485, 3304.2221146907784747, 5425.4748292290384355, 3514.5586792470815677]);
   K11=deg(Std,dx11);
   K12=deg(Std,dx12);
   K22=deg(Std,dx22);
   return 2^K12*Dawson[2*K11+K12]*Dawson[K12+2*K22];  /* bug fixed on 10/10 */
}
setprec(30);;
std2val(Std=[1,dx11,dx12,dx22,dx11^2,dx12^2,dx22^2,dx11*dx12*dx22]);

def resin_series(Approx) {
  F=(1+dx11+dx12+dx22)^Approx;
  F=dp_ptod(F,V=[dx11,dx12,dx22]);
  G=0;
  while (F != 0) {
    E=dp_etov(F);
    S=dp_dtop(dp_ht(F),V);
    G += std2val(S)*x11^E[0]*x12^E[1]*x22^E[2]/(fac(E[0])*fac(E[1])*fac(E[2]));
    F=dp_rest(F);
  }
  return G;
}
F=resin_series(5);;
F_iv=base_replace(map(poly_dact,Std,F,[x11,x12,x22]),[[x11,0],[x12,-1/100],[x22,0]]);

number_eval(F_iv);
*)

(*
F_iv2=base_replace(map(poly_dact,Std,F,[x11,x12,x22]),[[x11,0],[x12,1/100],[x22,0]]);

number_eval(F_iv2);
*)
