Re: [Help-gsl] Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1?

[Jordi Gutierrez Hermoso]

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:

    http://www.cimat.mx/~jordi/books/HandbookMathFunction.djvu

Good luck,
- Jordi G. H.