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Re: [Help-gsl] integration w/ qagp, bessel_Jnu

From: Brian Gough
Subject: Re: [Help-gsl] integration w/ qagp, bessel_Jnu
Date: Tue, 15 Nov 2005 17:01:51 +0000

Jorge Talamantes writes:
 > Dear all,
 > I am trying to integrate the following function:
 > I = \int_0^{x1} M (D, alpha, x, n) dx,
 > where D, alpha and n are parameters to be passed to M, and
 > M = x^(D-alpha-1) * [ j(x,n+0.5) ]^2.
 > Here, j is the Bessel function of order (n + 0.5).
 > For some combinations of D and alpha, the integrand M diverges at the
 > origin. So, I am trying to use gsl_integration_qagp -- adaptive
 > integration with known singular points.
 > The problem I am having is that, for a given x, there is a maximum n for
 > which I can compute j(x,n+0.5) --  increasing n leads to an underflow
 > error from gsl_sf_bessel_Jnu.

Split up the integral (or integrand) to compute the part near x=0
using the asymptotic form of j(x,n) for small x to avoid underflow.
Or disable the underflow error if it doesn't affect the final results.

Brian Gough

Network Theory Ltd,
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