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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


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