faster factorial



Robert Dodier wrote on 04/13/2006 09:38:34 AM:

> i'm in favor of replacing the existing factorial with this one

I think, but haven't proved, that Richard's 'k' function
can be used to speed up at least some cases of genfact 
(the double factorial, for one case). This reminds me:

The Maxima user documentation for genfact doesn't mention
that it applies entier to the middle argument. (I'll
file a report.) I think commercial macsyma changed this
from entier to ceiling. Do we want ceiling too?  The
Maxima documentation says that x !! may differ from 
standards for non-integer x. What is the canonical
reference for  the double factorial function?

Maxima:    (2/3) !! --> 1 
Macsyma:   (2/3) !! --> 2/3.

Barton