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 Petkovsek, 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.

**References**

Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. *A=B.* Wellesley, MA: A. K. Peters, p. 18, 1996.

© 1996-9

1999-05-25