       # Computing my own function efficiently

• To: mathgroup@smc.vnet.net
• Subject: [mg11073] Computing my own function efficiently
• Date: Wed, 18 Feb 1998 20:32:24 -0500
• Organization: Royal Institute of Technology (KTH)

```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, I'm looking for ways to  efficiently perform
the integration. I don't think a Gaussian quadrature formula based on
hermite polynomials would do the trick, since Cos[b x]/(k^2+x^2) can't
be well fiited to a  polynomial globally.
Using simpsons formula will be inefficient for large b, since for
highorder accuracy it's necessary to use steps shorter than the period
of the cosine.
The approach I'm considering is to derive the integral of  Cos[b x]
times a second-order polynomial, and approximate the integral
as the sum of several such segments. What I'm wondering about now, is
how to get a good error estimate of this method.
--
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Tommy Nordgren                    "Home is not where you are born,
Royal Institute of Technology      but where your heart finds peace."
Stockholm                         Tommy Nordgren - The dying old crone