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.