TY - JOUR

T1 - An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities

AU - Wilf, Herbert S.

AU - Zeilberger, Doron

PY - 1992/12

Y1 - 1992/12

N2 - 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.

AB - 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.

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U2 - 10.1007/BF02100618

DO - 10.1007/BF02100618

M3 - Article

AN - SCOPUS:0001169022

VL - 108

SP - 575

EP - 633

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 1

ER -