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Integrate product of Gaussian*Sin

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


	Can anyone suggest a good change of variables to carry out the

	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

	Integrate[Exp[-alpha*(x-a)^2*Sin[n Pi x/L],{x,-c,c}]
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

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