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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,
Publishing Free Software Manuals --- http://www.network-theory.co.uk/