Re: Bug in definite integral over Gamma function?
- To: mathgroup at smc.vnet.net
- Subject: [mg116746] Re: Bug in definite integral over Gamma function?
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 26 Feb 2011 06:05:51 -0500 (EST)
$Version "8.0 for Mac OS X x86 (64-bit) (November 6, 2010)" Integrate[x^4*Exp[-x]*Gamma[2, x], {x, 0, Infinity}] 21/8 $Version "7.0 for Mac OS X x86 (64-bit) (February 19, 2009)" Integrate[x^4*Exp[-x]*Gamma[2, x], {x, 0, Infinity}] -(363/8) Limit[Integrate[x^4*Exp[-x]*Gamma[2, x], {x, 0, a}], a -> Infinity] 21/8 Limit[Integrate[x^4*Exp[-x]*Gamma[2, x], {x, a, Infinity}], a -> 0] 21/8 Integrate[x^4*Exp[-x]*Gamma[2, x], {x, a, Infinity}] /. a -> 0 21/8 Integrate[x^n*Exp[-x]*Gamma[2, x], {x, 0, Infinity}] /. n -> 4 21/8 Integrate[x^4*Exp[-x]*Gamma[a, x], {x, 0, Infinity}] /. a -> 2 21/8 Bob Hanlon ---- H Hogreve <hogreve at ifisr.org> 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