Subject: Symbolic summation (was: levin versus ratsum)
From: Andrej Vodopivec
Date: Sat, 30 Dec 2006 01:09:55 +0100
> I'm new in this type of summation, and i know that bill Gosper has dedicated a
> lot to this type of stuff in macsyma, etc, but closeform look not very
> powerfull. For example it can't do (or give up very quickly) the following
>
>
> load(closed_form);
> a(n):=(n^3+2*n+7*n+5)/(n^8+8*n^5+6*n^4+2*n^3+n^2+n+11);
> b(n):=a(n)-a(n+20);
> sum(rat(b(n)),n,1,inf)$
> closed_form(%);
As I said closed_form simplifies using Gosper and Zeilberger
algorithms. In this case Gosper algorithm does not compute the
antidifference.
Still I think closed_form is quite powerful. Do load(closed_form_test)
to see some sums which can be simplified.
Andrej