Zeilberger's Algorithm
An Algorithm which finds a Polynomial recurrence for terminating Hypergeometric Identities of the form
where
is a Binomial Coefficient, 
, 
, 
, 
, 
, 
are constantintegers and 
, 
, 
, 
, 
, 
, and 
are complex numbers (Zeilberger 1990). The methodwas called Creative Telescoping by van der Poorten (1979), and led to the development of the amazing machinery ofWilf-Zeilberger Pairs.See also Binomial Series, Gosper's Algorithm, Hypergeometric Identity, Sister Celine's Method,Wilf-Zeilberger Pair
References
Krattenthaler, C. ``HYP and HYPQ: The Mathematica Package HYP.'' http://radon.mat.univie.ac.at/People/kratt/hyp_hypq/hyp.html. Paule, P. and Riese, A. ``A Mathematica Paule, P. and Schorn, M. ``A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities.'' J. Symb. Comput. 20, 673-698, 1995. Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. ``Zeilberger's Algorithm.'' Ch. 6 in A=B. Wellesley, MA: A. K. Peters, pp. 101-119, 1996. Riese, A. ``A Generalization of Gosper's Algorithm to Bibasic Hypergeometric Summation.'' Electronic J. Combinatorics 1, R19 1-16, 1996.http://www.combinatorics.org/Volume_1/volume1.html#R19. van der Poorten, A. ``A Proof that Euler Missed... Apéry's Proof of the Irrationality of Wegschaider, K. Computer Generated Proofs of Binomial Multi-Sum Identities. Diploma Thesis, RISC. Linz, Austria: J. Kepler University, May 1997. Zeilberger, D. ``Doron Zeilberger's Maple Packages and Programs: EKHAD.'' http://www.math.temple.edu/~zeilberg/programs.html. Zeilberger, D. ``A Fast Algorithm for Proving Terminating Hypergeometric Series Identities.'' Discrete Math. 80, 207-211, 1990. Zeilberger, D. ``A Holonomic Systems Approach to Special Function Identities.'' J. Comput. Appl. Math. 32, 321-368, 1990. Zeilberger, D. ``The Method of Creative Telescoping.'' J. Symb. Comput. 11, 195-204, 1991.
-Analogue of Zeilberger's Algorithm Based on an Algebraically Motivated Approach to -Hypergeometric Telescoping.'' In Special Functions, -Series and Related Topics, Fields Institute Communications 14, 179-210, 1997.
.'' Math. Intel. 1, 196-203, 1979.
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