Subject: Version 2.0 of my symbolic summation package
From: Fabrizio Caruso
Date: Wed, 17 Mar 2004 14:08:48 +0100
Hi!
I have updated and improved my Maxima package
for definite hypergeometric summation.
The package implements Zeilberger's algorithm
with Axel Riese's optimization (Filtering).
The new version has fewer bugs and is much faster.
------------------------------------------------------------
DESCRIPTION OF THE PROBLEM
A term t_k is hypergeometric in k iff t_(k+1)/t_k is
a rational function in k.
For example Binomial(n,k) is hypergeometric in n and k.
Given a proper hypergeometric term (in n and k) F_n,k and a
positive integer d we want to find a d-th order linear
recurrence with polynomial coefficients (in n) for F_n,k
and a rational function R in n and k such that:
a_0 F_n,k + ... + a_d F_(n+d),k = Delta_K(R(n,k) F(n,k)),
where
Delta_k is the k-forward difference operator, i.e.,
Delta_k(t_k) := t_(k+1) - t_k.
-----------------------------------------------------------
The package can be found at
http://www.risc.uni-linz.ac.at/research/combinat/risc/software/
You can get the package for free but should first
ask either Peter Paule:
ppaule@risc.uni-linz.ac.at
or Axel Riese:
ariese@risc.uni-linz.ac.at
for the password.
Best Regards
Fabrizio Caruso