From: Andrej Bauer <andrej@gs2.sp.cs.cmu.edu>
Newsgroups: sci.math.research
Subject: Re: Q: Hypergeometric functions
Date: 20 Dec 1998 17:17:57 -0500

edgar@math.ohio-state.edu (G. A. Edgar) writes:

> There is a decision procedure for such sums, I believe.  See, for
> example, the book "A=B" by Petkovsek, Wilf, & Zilberger.
                                                ^^^^^^^^^
                                                Zeilberger

The relevant URL is "http://www.cis.upenn.edu/~wilf/AeqB.html"

The algorithms described in the book can find closed forms and prove
equality of indefinite and definite hypergeometric sums. It seems
like in this case you are dealing with quadruple hypergeometric
summations so the implementations of algorithms on the A=B web page
might not be directly applicable. Nevertheless, the book contains
exactly what you asked for---a theory of "symbolic summation",
analogous to a theory of "symbolic integration".

Andrej