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[Help-gsl] gsl_sf_bessel_il_scaled

From: Torquil Macdonald Sørensen
Subject: [Help-gsl] gsl_sf_bessel_il_scaled
Date: Tue, 16 Nov 2010 17:59:01 +0100
User-agent: Mozilla/5.0 (X11; U; Linux x86_64; en-US; rv: Gecko/20101030 Icedove/3.0.10

Hi folks!

I'm having some trouble with gsl_sf_bessel_il_scaled(l,x) for large l / small x.

The problem manifests itself with the error message:

gsl: gamma.c:1454: ERROR: underflow
Default GSL error handler invoked.

This results e.g. from trying to compute gsl_sf_bessel_il_scaled(100, 0.01)

Thus my question:

Can I find documentation that describes for which values of (l,x) for which the function will compute a value successfully?

On wikipedia I found an asymptotic expression that works fine as long as
0 < x << sqrt(l+1), so I can use that instead if GSL only fails in cases when that approximation is OK to my accuracy.

But it would be nice if I don't have to experiment to determine for which (l,x) I can run the GSL function.

Or does anyone know of a more "robust" bessel function, e.g. in a different C / C++ library?

Torquil Sørensen

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