Integrate product of Gaussian*Sin
- To: mathgroup at smc.vnet.net
- Subject: [mg6855] Integrate product of Gaussian*Sin
- From: James Perry <perryj at rpi.edu>
- Date: Thu, 24 Apr 1997 02:44:34 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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