Re: Integrate product of Gaussian*Sin

*To*: mathgroup at smc.vnet.net*Subject*: [mg6973] Re: [mg6855] Integrate product of Gaussian*Sin*From*: Richard Finley <trfin at fiona.umsmed.edu>*Date*: Wed, 30 Apr 1997 22:26:01 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

>Date: Thu, 24 Apr 1997 10:46:08 -0500 >To: James Perry <perryj at rpi.edu> >From: Richard Finley <trfin at fiona.umsmed.edu> >Subject: Re: [mg6855] Integrate product of Gaussian*Sin > Oops! Sorry!... when I wrote down this integral on paper I neglected to include the translation part of the argument in the Gaussian (a), and as several people pointed out, this Gaussian is not even except for a = 0. Thanks for keeping me honest. RF 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 >> >> >> >> >