-----maxima-bounces at math.utexas.edu wrote: -----
>There?is?hgfred,?but?that?is?primarily?meant?to?transform?hypergeometric
>functions?to?"simpler"?forms.??It's?not?really?meant?for?numerical
>evaluation.?Barton?has?done?some?work?in?this?area,?but?I?can't?remember
>what's?done.
Earlier this year, I played with numerical evaluation of the hypergeometic
functions. This code isn't even ready for share/contrib. I stopped working
on it for many reasons--mostly I was hoping that somebody else would
do it right.
My code uses a running error to sum the power series. When the running
error
bound is too large (subtractive cancellation), it tries again with a larger
value for fpprec. There are no special cases for 1F1, 2F1, etc --- all the
hypergeometrics use the same code. As I recall, the articles I located for
good methods for the hypergeometrics didn't seem all that great to me. But
obviously, somebody knows good fast ways. If you search our mailing list,
you'll find a recursion for 2F1 (I think)--as I recall, I found some ranges
where this code was inaccurate, but I forgotten the details.
For now, if you need numerical evaluation of the hypergeometrics, you are
on your own. One possibility might be GSL:
http://www.gnu.org/software/gsl/
Barton