[Maxima] More weird behaviour in Gosper and nusum (maxima does not know enough about factorials)

[Andrej Vodopivec]

On 1/7/07, Michel Van den Bergh <michel.vandenbergh at uhasselt.be> wrote:
> (%i1) load(zeilberger);
> (%o1)  /usr/share/maxima/5.11.0/share/contrib/Zeilberger/zeilberger.mac
> (%i2) AntiDifference((k+1)!-k!,k);
> (k + 1)! - k!  is not hypergeometric in  k
> (%o2)                         NON_HYPERGEOMETRIC
>
> nusum has a similar problem, and hence so does closed_form.
>
> I think maxima really needs some rules to work with factorials. At the
> minimum there
> should be some (optional) rules like

The function you want is minfactorial:

(%i1) load(zeilberger)$
(%i2) (k+1)! - k!$
(%i3) minfactorial(%);
(%o3) (k+1)*k!-k!
(%i4) AntiDifference(%, k);
Dependent equations eliminated:  (1)
(%o4) ((k+1)*k!-k!)/k
(%i5) ratsimp(%);
(%o5) k!

Andrej