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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}]]


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