[Maxima] List of undocumented functions

[Barton Willis]

-----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