Evaluating complicated integral numerically

*To*: mathgroup at smc.vnet.net*Subject*: [mg127338] Evaluating complicated integral numerically*From*: Niles <niels.martinsen at gmail.com>*Date*: Wed, 18 Jul 2012 01:38:11 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Hi I am trying to evaluate a complicated integral numerically, but when my limits are > +/-5, then Mathematica fails: ClearAll["Global`*"] sigma = 1; gaussian[x_, y_, z_] := 1/(Sqrt[2 \[Pi]] \[Sigma])^3 Exp[-((x^2 + y^2 + z^2)/(2 sigma^2))]; gamma = 10^4; lorentzian[f_, f0_] := gamma/(2 \[Pi]) 1/((f - f0)^2 + gamma^2/4); f = 1000; NIntegrate[ lorentzian[ f, Sqrt[x^2 + y^2 + 4 z^2]]*gaussian[x, y, z] Sqrt[ x^2 + y^2]/Sqrt[x^2 + y^2 + 4 z^2], {x, -500, 500}, {y, -500, 500}, {z, -500, 500}] I don't see what goes wrong here? Is it really true that NIntegrate can't handle this?! Thanks in advance. Best, Niles.