We are representing the hypergeometric function as %f[m,n](l1,l2,x),
where m is the length of l1 and n is the length of l2.
I do know that 2F1 etc. are the usual names for these functions in the
literature, but I don't see the point of following that convention in
Maxima, unless we're going to do something useful with it. Currently,
we don't even check that the indexes are consistent with the lengths!:
%f[0,0]([a],[b],x) => no error
I also don't understand why hgfred works the way it does. It would be
more consistent with Maxima conventions in general if %f simplified
the simplest cases (e.g. %f([a],[a],x) => exp(x)) and if there were a
separate simplification function (along the lines of trigsimp or
whatever) which performed the more radical transformations; or
alternatively a simplification flag like halfangles, etc.
Writing hgfred as a simplifier would also let substitutions etc. work
correctly. Currently there are no simplifications on %f at all.
On a somewhat different topic, it would be nice if ?? hyperg and ? %f
gave information about %f and hgfred.
-s