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Re: Bug in definite integral over Gamma function?

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  • Subject: [mg116830] Re: Bug in definite integral over Gamma function?
  • From: Peter Pein <petsie at>
  • Date: Wed, 2 Mar 2011 04:31:47 -0500 (EST)
  • References: <ik5f76$sif$>

Am 24.02.2011 12:25, schrieb H Hogreve:
> 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


entering an additional "bus stop" at the route to infinity helps:

In[1]:= $Version

Out[1]= 7.0 for Microsoft Windows (64-bit) (February 18, 2009)
Out[2]= 21/8


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