Bug in Gosper (simpler version)? (was: Symbolic summation)



On 12/30/06, Michel Van den Bergh <michel.vandenbergh at uhasselt.be> wrote:
> (%i1) display2d:false;
>
> (%o1) false
> (%i2) load(zeilberger);
>
> (%o2)
> ?\/usr\/share\/maxima\/5\.11\.0\/share\/contrib\/Zeilberger\/zeilberger\.mac
> (%i3) AntiDifference(-(1/(n+1)-1/n),n);
>
> (%o3) (-n-1)*(1/n-1/(n+1))
> (%i4) AntiDifference((1/(n+1)-1/n),n);
>
> Unknown operator :  -
> 1/(n+1)-1/n  is not hypergeometric in  n
> (%o4) NON_HYPERGEOMETRIC

This is indeed a bug in AntiDifference. GosperSum also has some other
little bugs. There is another implementation of the Gosper algorithm
in nusum (closed_form uses nusum not GosperSum).

(%i2) nusum(1/n-1/(n+1), n, 1, k);
(%o2) k/(k+1)
(%i3) nusum(1/(n+1)-1/n, n, 1, k);
(%o3) -k/(k+1)

HTH,
Andrej