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Re: [Help-gsl] Does GSL or IMSL or GMP or MPFR have high precision hyper

From: Jordi Gutierrez Hermoso
Subject: Re: [Help-gsl] Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1?
Date: Sat, 7 Jul 2007 20:05:12 -0500

On 04/07/07, Michael <address@hidden> wrote:
More specifically, I hope I will be able to looking into the multiple
precision implementation of the hypergeometric function 2F1(a, b, c,
z) and change the power series

Your best bet is probably to look at the GSL code for 2F1 (which is
declared in gsl_sf_hyperg.h) and try to adapt that for higher
precision. If you need help, try consulting the suggested references
in the GSL manual:

    MISCFUN: A software package to compute uncommon special functions.
    `ACM Trans. Math. Soft.', vol. 22, 1996, 288-301

    G.N. Watson, A Treatise on the Theory of Bessel Functions, 2nd
    Edition (Cambridge University Press, 1944).

    G. Nemeth, Mathematical Approximations of Special Functions, Nova
    Science Publishers, ISBN 1-56072-052-2

    B.C. Carlson, Special Functions of Applied Mathematics (1977)

    W.J. Thompson, Atlas for Computing Mathematical Functions, John
    Wiley & Sons, New York (1997).

    Y.Y. Luke, Algorithms for the Computation of Mathematical
    Functions, Academic Press, New York (1977).

Alternatively, consult Abramowitz & Stegun, a standard reference for the GSL:

Good luck,
- Jordi G. H.

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