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MathGroup Archive 2007

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Evaluating a convolution integral in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80223] Evaluating a convolution integral in Mathematica
  • From: rdbeer at indiana.edu
  • Date: Wed, 15 Aug 2007 04:15:13 -0400 (EDT)

I am having trouble evaluating a convolution integral in Mathematica.
Define B[x,{min,max}] to be a function that takes on the value 1 when
x is between min and max and 0 otherwise.  I need to find the
convolution of x^n B[x, {min1, max1}] with x^m B[x, {min2, max2}],
where x is Real, n and m are nonnegative integers, and the mins and
maxs are Real with the constraints that min1<=max1 and min2<=max2.

The resulting convolution integeral is Integrate[t^n B[t, {min1,
max1}] (x-t)^m B[x-t, {min2, max2}], {t, -Infinity, Infinity}].

Mathematica 6.0.1 has no problem evaluating this integral when
constant values are substituted for n, m, and the mins and maxs.
However, I need the general value of this integral.  Mathematica also
claims to be able to evaluate this general integral, returning a
complicated peicewise expression involving gamma functions and
hypergeometric functions.  However, when specific values for n, m and
the mins and maxs are then substituted into this general expression,
it always returns either 0 or Indeterminate.

Any help with evaluating this integral in general would be greatly
appreciated.



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