A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by Fasenmyer, Gosper, Zeilberger, Wilf, and Petkovšek, the problem of determining whether a given hypergeometric sum is expressible in simple closed form and, if so, finding the form, is now (subject to a mild restriction) completely solved. The algorithm which does so has been implemented in several computer algebra packages and is called Zeilberger's algorithm.

binomial sums | generalized hypergeometric function | Gosper's algorithm | hypergeometric series | Sister Celine's method | Wilf-Zeilberger pair | Zeilberger's algorithm