Re: Incorrect integral in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg91428] Re: Incorrect integral in Mathematica*From*: Thomas Dickens <lonelyz at att.net>*Date*: Thu, 21 Aug 2008 04:16:15 -0400 (EDT)*References*: <g8b8t8$8pq$1@smc.vnet.net> <g8ea2p$4el$1@smc.vnet.net>

On Tue, 19 Aug 2008 11:16:41 +0000 (UTC), amzoti <amzoti at gmail.com> wrote: >On Aug 18, 12:38 am, Eran Mukamel <emuka... at stanford.edu> wrote: >> Hi All, >> >> I'm getting a nonsensical answer of 0 for the following integral in Mathe= >matica 5.0 (Mac OSX): >> >> Integrate[Exp[-x^2/(2w^2)]Exp[-(y - y0)^2/(2z^2)], >> {x, -Infinity, Infinity}, {y, -Infinity, Infinity}] >> >> The result should be (2 Pi w z). Any ideas why this fails? >> >> Thanks in advance, Eran > >I tried this integral in version 4 on a PC and got the correct answer >(although in a slightly different form).: > >(2*Pi)/(Sqrt[1/w^2]*Sqrt[1/z^2]) I tried it in Mathematica 3.0 on Windows XP and obtained If[Re[z^2] > 0 && Re[y0/z^2] < 0 && Re[w^2] > 0, 2*Pi*Sqrt[w^2]*Sqrt[z^2], Integrate[Integrate[E^ (-(x^2/(2*w^2)) - (y - y0)^2/(2*z^2)), {y, -Infinity, Infinity}], {x, -Infinity, Infinity}]]