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MathGroup Archive 1998

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Re: Computing my own function efficiently


  • To: mathgroup@smc.vnet.net
  • Subject: [mg11126] Re: Computing my own function efficiently
  • From: mike johnson <mike_johnson@llnl.gov>
  • Date: Mon, 23 Feb 1998 21:40:45 -0500
  • Organization: LLNL
  • References: <6cgg8n$sg1@smc.vnet.net>

Tommy Nordgren wrote:
> 
> I have a function that is defined by: f[k_,b_] := Integrate[
>         Cos[b x] Exp[-x^2]/(k^2+x^2),{x,-Infinity,Infinity}] Since Mathematica
> can't solve the integral...

Gradshteyn & Ryzhik, Table of Integrals, Series & Products, 4th ed. Sec
3.954 gives the following algebraic answer (after some change in
notation) in terms of error functions:

Pi^(3/2) Exp[k^2]/(4k)*
   (2 Cosh[b k] - Exp[-b k] Erf[k-b/2] - Exp[bk] Erf[k+b/2])

Sometimes the old ways are still useful. -- 
Michael A. Johnson, Mail Stop L-463
Lawrence Livermore Nat'l Lab
7000 East Ave., P. O. Box 808
Livermore, CA 94551
Fax: (510) 422-6007
mike-johnson@llnl.gov



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