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.