Re: Integrate product of Gaussian*Sin
- To: mathgroup at smc.vnet.net
- Subject: [mg6907] Re: [mg6855] Integrate product of Gaussian*Sin
- From: Richard Finley <trfin at fiona.umsmed.edu>
- Date: Fri, 25 Apr 1997 14:00:38 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
James,
I am a little confused because there is an end bracket missing in your
equation. I presume that you mean the integral:
Integrate[Exp[-alpha*(x-a)^2]*Sin[n Pi x/L],{x,-Infinity,Infinity}]
If this is the integral you are interested in there is no need to change
variables because it is the integral of a product of odd and even functions
over the real line and is therefore identically zero for all values of the
parameters.
hope that helps.
regards, RF
At 02:44 AM 4/24/97 -0400, you wrote:
>Hi,
>
> Can anyone suggest a good change of variables to carry out the
>integration
>
> Integrate[Exp[-alpha*(x-a)^2*Sin[n Pi x/L],{x,-Infinity,Infinity}]
>
> I can't find this form in my integral tables (I'm going to check
>the library today for a more comprehensive list, I might find a form that I
>can convert my expression to), and Mathematica can't find a solution unless
>I take the limits of the integral {x,-c,c}. However, treated as an improper
>integral
>
> Integrate[Exp[-alpha*(x-a)^2*Sin[n Pi x/L],{x,-c,c}]
> Limit[%,c->Infinity]
>or Limit[%,c->-Infinity]
>
> Still does not give a solution, since the answer to the integral
>(with limits {x,-c,c}) is a combination of Erf[x] and Erfi[x], and the
>Limit[Erfi[x],x->+/- Infinity]->+/- Infinity. The Erf[x] has a limit of +/-
>1 as x->+/- Infinity.
> I'm not sure if there is a solution to this, anyone with
>Gaussian-type function experience?
>
>Thank you
>Jim
>
>
>
>