[Maxima] ratexpand + pochhammer

[Barton Willis]

-----maxima-bounces at math.utexas.edu wrote: -----

>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.

Does this code need things like pochhammer(a,2) --> a (a + 1) or
do you need expressions to be fully expanded: pochhammer(a,2) --> a^2 + a?
Does the code need to expand pochhammer(x,n) when x is both symbolic
and numeric?

>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.

There is an option variable pochhammer_max_index, but it works
differently than does factlim. Setting pochhammer_max_index to -1 keeps
pochhammer(x,n) from expanding:

(%i6) pochhammer(x,1), pochhammer_max_index :-1;
(%o6) pochhammer(x,1)

Not so good:

(%i8) pochhammer(x,1), pochhammer_max_index : 'inf;
Maxima encountered a Lisp error:
 Error in <= [or a callee]: $INF is not of type (OR RATIONAL LISP:FLOAT).

Barton