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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.
See also Generalized Hypergeometric Function, Gosper's Algorithm, Hypergeometric Series, Sister Celine's Method, Wilf-Zeilberger Pair, Zeilberger's Algorithm
References
Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, p. 18, 1996.