Hello Barton,
> Except for pure numerical evaluation, automatic expansion of the
> rising factorial (pochhammer) isn't all that useful, I think. There
> is a question about what to do with pochhammer(x,10^9); and what about
> pochhammer(x,10^9 + 1) / pochhammer(x,10^9))?
>
> I propose that user should have to call to expand to force expansion. I
> know how to
> do this with expand, but not ratexpand:
I have used pochhammer a lot to expand special functions for special
values and in the integration routines for the power functions.
All this code assumes that pochhammer expands automatically. One problem
is indeed that there is no upper limit for a useful integer. By the way
that is a problem with the functions $sum and $product too.
What is your reason that the automatic expansion is not useful?
The simplifier of the factorial and the gamma functions have build in
the variables factlim and gammalim. Setting the values of this variables
the expansion can be controlled.
When setting factlim to zero no evaluation of the factorial function is
done. Setting it no -1 the factorial function does not check the integer
and tries to evaluate for every integer.
Dieter Kaiser