Re: The integrand has evaluated to non-numerical values for all

*To*: mathgroup at smc.vnet.net*Subject*: [mg83880] Re: The integrand has evaluated to non-numerical values for all*From*: "Steve Luttrell" <steve at _removemefirst_luttrell.org.uk>*Date*: Mon, 3 Dec 2007 05:50:10 -0500 (EST)*References*: <fitstp$69s$1@smc.vnet.net>

Here is a way of approximating your integral by doing a series expansion about a functional form that Mathematica DOES know how to integrate: First of all define a series expansion of your f[x,y]. f20[x_,y_,n_]:=(Series[\[ExponentialE]^-(\[Epsilon]+y)^2,{\[Epsilon],0,n}] Sin[x y])/(x y)//Normal//Simplify Now compute the first 10 approximations to your integral. This takes a minute or so to compute on my PC. fapprox=Table[f2[x_,y_,i]=f20[x,y,i]/.\[Epsilon]->-1;Integrate[f2[x,y,i],{y,0,\[Infinity]}]//FullSimplify//PowerExpand,{i,10}] You can then plot the differences between successive approximations. Plot[Map[#[[2]]-#[[1]]&,Partition[fapprox,2,1]]//Evaluate,{x,0.01,10},PlotStyle->Table[Hue[0.8(i-1)/10],{i,1,10}]] You don't need to go too far out in the sequence of series approximations before these differences become quite small. Steve Luttrell West Malvern, UK "Kreig Hucson" <kreig.hucson at yahoo.com> wrote in message news:fitstp$69s$1 at smc.vnet.net... > Hi all, > > Being given the function: > > f[x_,y_]:= Sin[x*y]*Exp[-(y-1)^2]/(x*y) , > > I want to integrate it with respect to y, from 0 to Infinity, and to > obtain a function of x only, F[x]. > > I typed the command: > > F[x_]:= Assuming[x>0, Integrate[f[x,y],{y,0,Infinity}]] > > but the integral remained unevaluated by Mathematica 6. > > After this, I typed the command: > > F[x_]:= Assuming[x>0, NIntegrate[f[x,y],{y,0,Infinity}]] > > but I received the error message: "The integrand f[x,y] has evaluated to > non-numerical values for all sampling points in the region with boundaries > {{Infinity,0.}}". > I looked at the explanations of the error message and there it was > suggested to give a particular value to x and to compute the integral for > that particular value. I gived one particular value and I obtained the > expected result. Anyway I need to obtain an analytical expression for all > x>0. > > My question is, how can be performed the integral and to obtain the > analytical function F[x]? > > Thank You in advance, > > Kreig >