Inventiones mathematicae

, Volume 108, Issue 1, pp 575–633 | Cite as

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

  • Herbert S. Wilf
  • Doron Zeilberger


It is shown that every ‘proper-hypergeometric’ multisum/integral identity, orq-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.


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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Herbert S. Wilf
    • 1
    • 2
  • Doron Zeilberger
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Department of MathematicsTemple UniversityPhiladelphiaUSA

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