An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities

Herbert S. Wilf, Doron Zeilberger

Research output: Contribution to journalArticlepeer-review

220 Scopus citations


It is shown that every 'proper-hypergeometric' multisum/integral identity, or q-identity, with a fixed number of summations 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.

Original languageEnglish (US)
Pages (from-to)575-633
Number of pages59
JournalInventiones Mathematicae
Issue number1
StatePublished - Dec 1992

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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