Subject: Symbolic summation (was: levin versus ratsum)
From: miguel lopez
Date: Fri, 29 Dec 2006 23:35:46 +0000 (UTC)
Andrej Vodopivec <andrej.vodopivec <at> gmail.com> writes:
>
> There is a closed_form function for sum simplification in maxima. It
> uses Gosper and Zeilberger algorithms.
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(%);
And i see that maxima can factor the denominator of b(n),
so that factor(denominantor b(n)) = c1*c2 so it should be able
to determine in simple cases like this that c1 = c2(n-20), form here the
solution seems not very far.
Best regards.
-M