       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:= h[Abs, #^2 &, 1]

Out= 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
>
>

```

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