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Abstract: This paper presents a general method for proving and discovering combinatorial identities: to prove an identity one can present a certificate that consists of a pair of functions of two integer variables. To prove the identity, take the two functions that are given, check that condition (1) below is satisfied (a simple mechanical task), and check the equally simple fact that the boundary conditions (F1), (G1), (G2) below are satisfied. The identity is then proved. Alternatively, one can present ... (Update)
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BibTeX entry: (Update)
H.S. Wilf, D. Zeilberger, Rational functions certify combinatorial identities, Jour. Amer. Math. Soc. 3 (1990), 147-158. http://citeseer.ist.psu.edu/wilf89rational.html More
@misc{ wilf90rational,
author = "H. Wilf and D. Zeilberger",
title = "Rational functions certify combinatorial identities",
text = "H.S. Wilf, D. Zeilberger, Rational functions certify combinatorial identities,
Jour. Amer. Math. Soc. 3 (1990), 147-158.",
year = "1990",
url = "citeseer.ist.psu.edu/wilf89rational.html" }
Citations (may not include all citations):442 Concrete mathematics (context) - Graham, Knuth et al. - 1989
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51 A holonomic systems approach to special function identities (context) - Zeilberger
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15 Strange evaluations of hypergeometric series (context) - Gessel, Stanton - 1982
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