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Re: integral inside an integral

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  • Subject: [mg113611] Re: integral inside an integral
  • From: Bob Hanlon <hanlonr at>
  • 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] //


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]


% // N


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]


I want to put arbitrary  functions f and g into h and get an answer.


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