Re: Bug in definite integral over Gamma function?

*To*: mathgroup at smc.vnet.net*Subject*: [mg116745] Re: Bug in definite integral over Gamma function?*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Fri, 25 Feb 2011 06:38:52 -0500 (EST)

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. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305