Re: Incorrect integral in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg91436] Re: Incorrect integral in Mathematica
• From: Bhuvanesh <BhuvaneshBhatt at gmail.com>
• Date: Thu, 21 Aug 2008 05:56:44 -0400 (EDT)

This was a bug. Essentially, the following should have Sqrt[Pi]/Sqrt[a], but it was incorrectly giving zero in version 5.0.x:

Integrate[Exp[-a*(y - y0)^2], {y, -Infinity, Infinity}, GenerateConditions->False]

Here are a couple of workarounds:

\$Version      = 5.0.1 for Linux (November 18, 2003)

In[1]:= Integrate[Exp[-x^2/(2w^2)]Exp[-(y - y0)^2/(2z^2)],
{x, -Infinity, Infinity}, {y, -Infinity, Infinity}, GenerateConditions->True] /. If[_,res_,_]:>res        //InputForm

Integrate::gener: Unable to check convergence.

Out[1]//InputForm=
Sqrt[2*Pi]*Sqrt[z^2]*If[Re[w^2] > 0, Sqrt[2*Pi]*Sqrt[w^2],
Integrate[E^(-x^2/(2*w^2)), {x, -Infinity, Infinity},
Assumptions -> Re[w^2] <= 0]]

In[2]:= Integrate[Exp[-x^2/(2w^2)]Exp[-(y - y0)^2/(2z^2)], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}, Assumptions->z>0] //InputForm

Out[2]//InputForm=
Sqrt[2*Pi]*z*If[Re[w^2] > 0, Sqrt[2*Pi]*Sqrt[w^2],
Integrate[E^(-x^2/(2*w^2)), {x, -Infinity, Infinity},
Assumptions -> z > 0 && Re[w^2] <= 0]]

The integral works correctly in version 5.1 and newer versions. Sorry for the inconvenience.

Bhuvanesh,
Wolfram Research

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