Bug in definite integral over Gamma function?

*To*: mathgroup at smc.vnet.net*Subject*: [mg116704] Bug in definite integral over Gamma function?*From*: "H Hogreve" <hogreve at ifisr.org>*Date*: Thu, 24 Feb 2011 06:24:19 -0500 (EST)

When getting weired results after a large chain of symbolic calculations, I spotted the reason to something that appears to be a bug in an integration, i.e., in Integrate[x^4*Exp[-x]*Gamma[2, x], {x, 0, Infinity}] The two 7.0 versions of Mathematica (32-bit Windows and 64-bit Linux) available for checking this integral yield the result -363/8 which is obviously incorrect; a correct results can be obtained by computing the indefinite integral and taking the limits x->0 and x->Infinity. Moreover, the 6.0 version of Mathematica also gives the correct result for the definite integral. Now I am wondering how Mathematica 8 is handling this integral, and whether there are possibilities in Mathematica 7 to get the correct definite integral (other than via the indefinite one and boundary values) ? Many thanks in advance for any hints, H. Hogreve