Re: Approximation to Bessel Function in Integrand

On Jul 27, 3:34 pm, "mbtrawicki" <mbtrawi...@xxxxxxxxx> wrote:
Hello Clay,

I verified your results and have very similar numbers. I am using Maple to
compute those integrals. Is there no closed-form solution? I still have not
found one in any of my references for the integral. Do you know of a faster
implementation of Maple in Matlab? I am using Maple functions in Matlab
since the integration is a major component of a bigger program, but my
Matlab is running so slowly this way. I am not sure whether there is any
way around it. I welcome all suggestions.

Thank you again,

Marek

Hello Marek,

An obvious closed form solution does not pop into my head. I'm using
MathCad but not using Maple.

A chunk of 'c' code to generate the Gaussian Quad coefs is not too
hard to come up with. I.e., the integrand can be sampled at about 100
to 200 points, and from that you would get a very precise result and
should execute in fractions of a second. If -1 < p < 20, then you
will only need to integrate from 0 to 8. The product I0(2x)*e^-(x*x)
acts alot like e^-(x/1.7)^3, so unless p is big, the exponential term
crushes x^p to 0.

Look up how to calculate the Gaussian Quadrature coefs and code that
up. The integral becomes trivial to do from there.

IHTH,
Clay






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