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.
Hypergeometric Identity
See also
Binomial Sums, Generalized Hypergeometric Function, Gosper's Algorithm, Hypergeometric Series, Sister Celine's Method, Wilf-Zeilberger Pair, Zeilberger's AlgorithmExplore with Wolfram|Alpha
References
Koepf, W. "Hypergeometric Identities." Ch. 2 in Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, pp. 11-30, 1998.Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, p. 18, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.Referenced on Wolfram|Alpha
Hypergeometric IdentityCite this as:
Weisstein, Eric W. "Hypergeometric Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HypergeometricIdentity.html