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“Automatic” proof of hypergeometric identities and functions (after D. Zeilberger). (Démonstration “automatique” d’identités et fonctions hypergéometriques (d’après D. Zeilberger).) (French) Zbl 0796.33014

Séminaire Bourbaki, Vol. 1991/92. Exposés 745-759 (avec table par noms d’auteurs de 1948/49 à 1991/92). Paris: Société Mathématique de France, Astérisque. 206, 41-91 (Exp. No. 746) (1992).
A standard technique for proving identities for hypergeometric series is to find a recursion satisfied by each of the identities. The difficulty is usually contained in the problem of finding the right recursion. This paper is an exposition of a mechanical technique for finding such recursions. It was developed principally by Doron Zeilberger, and it enables the user to discover and prove a wide variety of hypergeometric series identities.
For the entire collection see [Zbl 0772.00016].

MSC:

33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33C20 Generalized hypergeometric series, \({}_pF_q\)
11B65 Binomial coefficients; factorials; \(q\)-identities

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