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Re: Bug in definite integral over Gamma function?


In Mathematica 8.0.0, result is 21/8.

On 2/24/2011 6:24 AM, H Hogreve wrote:
> 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
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
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University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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