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Zbl 0739.05007
Wilf, Herbert S.; Zeilberger, Doron
An algorithmic proof theory for hypergeometric (ordinary and ``$q$") multisum/integral identities. (English)
[J] Invent. Math. 103, No.3, 575-634 (1991). ISSN 0020-9910; ISSN 1432-1297/e

It is shown that every `proper-hypergeometric' multisum/integral identity, or $q$-identity, with fixed number of summation and/or integration signs, possesses a short, computer-constructible proof. We give a fast algorithm for finding such proofs. Most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here. We give many examples of the method, including computer-generated proofs of identities of Mehta-Dyson, Selberg, Hille-Hardy, $q$-Saalschütz, and others. The prospect of using the method for proving multivariate identities that involve an arbitrary number of summations/integrations is discussed.
[H.S.Wilf]

MSC 2000:: *05A19 Combinatorial identities
05A10 Combinatorial functions
11B65 Binomial coefficients, etc.
05A30 q-calculus and related topics
33C99 Hypergeometric functions
39A10 Difference equations

Keywords: holonomic; recurrence relation; Mehta-Dyson integrals; hypergeometric; multisum; identity

Cited in: Zbl 1250.11023 Zbl 1241.57008 Zbl 1170.33005 Zbl 1057.33018 Zbl 1015.33013 Zbl 0968.11011 Zbl 0912.33010 Zbl 0901.33008 Zbl 1016.33006 Zbl 0903.33008 Zbl 0863.05009 Zbl 0894.30013

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