>>>>> "Robert" == Robert Dodier <robert.dodier at gmail.com> writes:
Robert> if i'm not mistaken hgfred is maxima's hypergeometric function.
Robert> hgfred ([a, b], [c], z), numer; yields numerical values for
Robert> some values of a, b, c, and z but not for all.
Robert> so i'm looking for a way to evaluate it when the built-in
Robert> method returns a noun expression.
Actually, hgfred is really a simplifier for hypergeometric functions
where it tries to simplify a hypergeometric function in terms of
other, simpler, functions. That hgfred yields numerical values at all
is just chance that it simplified pFq to something that maxima knew
how to evaluate.
Robert> 2F1 is defined by an infinite series which converges
Robert> only for |z| < 1. however i want to evaluate it for -100 < z < 0
Robert> (real values of z only). i guess the function has an
Robert> analytic continuation, however i don't know how to
Robert> exploit that to get numerical values.
http://www.math.sfu.ca/~cbm/aands/page_559.htm has some formulas that
might be useful to you.
However, as far as I know, the only way to evaluate 2F1 in general is
from the series. I have a couple of books (at home) that do that.
They don't give any other method than that with some simple
relationships thrown in to help the convergence of the series.
Ray