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Re: Bug in definite integral over Gamma function?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116727] Re: Bug in definite integral over Gamma function?
  • From: Just A Stranger <forpeopleidontknow at gmail.com>
  • Date: Fri, 25 Feb 2011 06:35:37 -0500 (EST)

This is what I got in Mathematica 8:

In[1]:= Integrate[x4*Exp[-x]*Gamma[2, x], {x, 0, Infinity}]

Out[1]= (3 x4)/4

(The extent of my knowledge of the Gamma function is "factorial function 
generalized to the reals or something", so can't help you beyond this)

On 02/24/2011 03:24 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
>



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