       Re: integral inside an integral

• To: mathgroup at smc.vnet.net
• Subject: [mg113611] Re: integral inside an integral
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 4 Nov 2010 04:01:39 -0500 (EST)

```In your definition of h, alpha must be a pattern, and since you are using numerical techniques alpha should be restricted to a numeric value.

Clear[h, h2]

k[x_] := Exp[-x^2/3]

h[f_, g_, alpha_?NumericQ] :=
NIntegrate[f[alpha - x]*k[x]/
NIntegrate[g[alpha - x - y]*k[y],
{y, -Infinity, Infinity}],
{x, -Infinity, Infinity}]

h[Exp[-3 #^2/4] &, Exp[-5 #^2/6] &, 6] //
Quiet

0.00081979

Checking this:

h2[f_, g_, alpha_] :=
Integrate[f[alpha - x]*k[x]/
Integrate[g[alpha - x - y]*k[y],
{y, -Infinity, Infinity}],
{x, -Infinity, Infinity}]

h2[Exp[-3 #^2/4] &, Exp[-5 #^2/6] &, 6]

(7*Sqrt[2/71])/E^(516/71)

% // N

0.00081979

Bob Hanlon

---- "Hagwood 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

```

• Prev by Date: Re: Graphics: How to get values corresponding to Automatic?
• Next by Date: Re: integral inside an integral
• Previous by thread: integral inside an integral
• Next by thread: Re: integral inside an integral