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?
>>
>
>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}]]

```

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