> "Richard Fateman" <fateman at cs.berkeley.edu> writes:
>
> > nusum in commercial macsyma gives
> >
> > ((cos((b/2)))/(2 * sin((b/2)))) - ((cos(b * (k + (1/2))))/(2 * sin((b/2))))
Hmm, that's interesting. I'm inclined to think nusum was
extended with non-hypergeometric stuff, or maybe an
identity was applied to the summand before applying
Gosper's algorithm.
Maxima nusum(sin(b*n), n, 0, N);
complains "non-rational term ratio to nusum".
Current version of GosperSum complains
"sin(b n) is not hypergeometric in n".
> GosperSum(cos(b*k), k, D,N);
> GosperSum(sin(b*k), k, D,N);
> GosperSum(a^k*sin(b*k), k, D,N);
I don't think any of these can be solved by Gosper's
or Zeilberger's algorithms. Maybe you can contact
Fabrizio Caruso about that, he would know for sure.
As to other methods -- I guess that these should be
solvable by trigonometric identities, but I don't have
any suggestions about where to start.
HTH
Robert Dodier