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.