Re: integral inside an integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg113615] Re: integral inside an integral*From*: Leonid Shifrin <lshifr at gmail.com>*Date*: Thu, 4 Nov 2010 04:02:25 -0500 (EST)

Hi Charles, Not as easy as your code suggests, but something like this is possible. You have to make the parameter <alpha> numerical, and also define an auxiliary function to do the integration over y (at least, I could not see any other way to do this): Clear[h]; h[f_, g_, alpha_?NumericQ] := Module[{k, gint}, k[x_] := 1/(x^6 + 1); gint[x_?NumericQ] := NIntegrate[g[alpha - x - y]*k[y], {y, -Infinity, Infinity}]; NIntegrate[f[alpha - x]*k[x]/gint[x], {x, -Infinity, Infinity}]] Example (I hard-coded the k[x_] function for the sake of this example, since you mentioned that it is fixed): In[18]:= h[Abs, #^2 &, 1] Out[18]= 0.543665 Regards, Leonid On Wed, Nov 3, 2010 at 10:56 AM, Hagwood, Charles R. < charles.hagwood at nist.gov> wrote: > > Does anyone know how to make the following work using pure functions in > Mathematica? Given two functions f and g compute and for a fixed k[x] > > > h[f_,g_,alpha]:=NIntegrate[f[alpha-x]*k[x]/NIntegrate[g[alpha-x-y]*k[y],{y,-Infinity,Infinity}],{x,-Infinity,Infinity}] > > > I want to put arbitrary functions f and g into h and get an answer. > > Charles > >