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An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities. (English) Zbl 0739.05007
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.
Reviewer: H.S.Wilf

MSC:
05A19Combinatorial identities, bijective combinatorics
05A10Combinatorial functions
11B65Binomial coefficients, etc.
05A30q-calculus and related topics
33C99Hypergeometric functions
39A10Additive difference equations
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