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Re: [Help-gsl] gsl_sf_bessel_il_scaled

From: Brian Gough
Subject: Re: [Help-gsl] gsl_sf_bessel_il_scaled
Date: Sat, 20 Nov 2010 12:50:37 +0000
User-agent: Wanderlust/2.15.6 (Almost Unreal) Emacs/23.2 Mule/6.0 (HANACHIRUSATO)

At Tue, 16 Nov 2010 17:59:01 +0100,
Torquil Macdonald Sørensen wrote:
> The problem manifests itself with the error message:
> gsl: gamma.c:1454: ERROR: underflow
> Default GSL error handler invoked.
> Aborted
> 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?

Hello.  The value of il(100,0.01) is 8.45272785e-389 which is below
the limit of double-precision (1e-308) so underflow is the correct
result in this case.

If you find any values of (l,x) which give an underflow error when the
result should be in the range of double precision, please can you
submit them as a bug report to address@hidden  Thanks

Brian Gough

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