On 5/3/07, Kostas Oikonomou <ko at research.att.com> wrote:
>
> Why not have all three? Pochhammer, rising_factorial, falling_factorial.
> The first two would be synonyms for the same thing.
>
Well, there's actually a good argument for avoiding synonyms. Poch should
simplify to rising (or vice versa), so that poch(x)-rising(x) simplifies to
0. You'd get even more simplifications "for free"if you canonicalize
rising/falling to poch via falling(x,n)=(-1)^n*poch(-x,n). But that might
make expressions harder to read. Poch also needs to be added to makefact,
so that minfactorial can be used to simplify it.
-s