hello,
i wonder if anyone has some advice about the numerical
evaluation of the hypergeometric function 2F1.
i'm willing to consider pretty much any method
(even if not particularly fast or accurate), since the
alternative is numerical evaluation of an integral.
that's not the end of the world, but i'd rather avoid it.
if i'm not mistaken hgfred is maxima's hypergeometric function.
hgfred ([a, b], [c], z), numer; yields numerical values for
some values of a, b, c, and z but not for all.
so i'm looking for a way to evaluate it when the built-in
method returns a noun expression.
2F1 is defined by an infinite series which converges
only for |z| < 1. however i want to evaluate it for -100 < z < 0
(real values of z only). i guess the function has an
analytic continuation, however i don't know how to
exploit that to get numerical values.
thanks in advance for any advice.
robert dodier