MathGroup Archive 1997

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Integrate product of Gaussian*Sin

  • To: mathgroup at
  • Subject: [mg6916] Re: [mg6855] Integrate product of Gaussian*Sin
  • From: seanross at
  • Date: Fri, 25 Apr 1997 14:00:44 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

James Perry 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

Re-write the Sin as a complex exponential.  You will then have two 
integrals both of which are quadratic in the exponent, but with a 
complex coefficient.  The problem here will not be to get a result, but 
to interpret it.  ie. what exactly is the error function for complex 

  • Prev by Date: Re: Gaussian Matrix Elimination
  • Next by Date: Re: Integrate product of Gaussian*Sin
  • Previous by thread: Integrate product of Gaussian*Sin
  • Next by thread: Re: Integrate product of Gaussian*Sin