# [Maxima] again on Zeilberger package behaviour

Andrej Vodopivec andrej.vodopivec at gmail.com
Sun Jan 7 08:38:51 CST 2007

```This is cause by the same bug as was discussed on the list in recent
days. With my patch your example works.

> *****************************************************
> (%i7) AntiDifference(DeltaF(n,k),k);
> (%o7)                         NON_HYPERGEOMETRIC
> *****************************************************

(%i6) AntiDifference(DeltaF(n,k),k);
Dependent equations eliminated:  (1)
(%o6) (k*(n-2*k+1)*binom(n,k))/(2*(-n/2+k-1/2)*(2*n-2*k+2)*2^n)

> But the function IS hypergeometric! The expected
> G(n,k) = - binomial(n,k-1)/2^(n+1) or any equivalent
> expression.
>
> *****************************************************
> (%i8) Gosper(DeltaF(n,k),k);
> (%o8)                         NON_HYPERGEOMETRIC
> *****************************************************

(%i7) Gosper(DeltaF(n,k),k);
Dependent equations eliminated:  (1)
(%o7) -k/(2*(-n/2+k-1/2))
(%i8) ratsimp(%);
(%o8) k/(n-2*k+1)

> Gosper(f_k, k) should find the WZ certificate, in
> this case
> R(n,k) = -k/(2*(n-k+1)), but it doesn't.
>
> *****************************************************
> (%i9) GosperSum(DeltaF(n,k),k,0,k);
> (%o9)                        NON_HYPERGEOMETRIC
> *****************************************************

(%i9) GosperSum(DeltaF(n,k),k,0,k)\$
Dependent equations eliminated:  (1)
(%i10) ratsimp(%);
(%o10) -((k+1)*binom(n,k+1))/((2*n-2*k)*2^n)

> And nusum happily finds the solution. What went wrong
> with Zeilberger package?

There was a bug in Zeilberger. I will commit the patch to cvs soon.

Andrej
```