From sources-request at octave dot org Wed May  5 01:51:29 2004
Subject: Re: GSL special functions
From: Gert  Van den Eynde <gvdeynde at SCKCEN dot BE>
To: sources at octave dot org
Cc: Teemu Ikonen <tpikonen at pcu dot helsinki dot fi>
Date: Wed, 5 May 2004 08:48:33 +0200

Hi,

> The binding code is mostly trivial, but there's still a possibility of bugs
> present, perhaps even in the underlying GSL code. Therefore, I'd eventually
> like to have some tests to check for correct values in a few well selected
> points in the functions. Does anyone know of an accurate source of such
> values for a good number of special functions?

Have a look at this compendium by Lozier and Olver:

http://math.nist.gov/mcsd/Reports/2001/nesf/

It has a huge bibliography for special functions.

I've used some tables in Abramovitz & Stegun, some in 


S. Zhang and J. Jin, Computation of special functions, John Wiley & Sons Inc., 
New York, 1996

and I believe

W. J. Thompson, Atlas for computing mathematical functions: an illustrated 
guide for practitioners, with programs in C and Mathematica, John Wiley & 
Sons Inc., New York, 1997

also has some tables with reference values.


What you also could do, if you have access to a symbolic package like 
Mathematica, Maple or MuPAD and the function is implemented, make some 
evaluations with high accuracy fixed precision and compare with your results. 
However, the simplest thing is to compare to raw GSL calls. What I know from 
the GSL is that their special functions section is quite good, if not very 
good. Just one side note: they warn the user for the confluent hypergeometric 
function since the main author of those routines still has some doubts 
himself.


I hope this helps,

gert


>
> Teemu