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 >