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Zbl 0759.05007
Wilf, Herbert S.; Zeilberger, Doron
Rational function certification of multisum/integral/``q'' identities. (English)
[J] Bull. Am. Math. Soc., New Ser. 27, No.1, 148-153 (1992). ISSN 0273-0979; ISSN 1088-9485/e

The authors develop interesting algorithms for such type of identities that involve multiple sums and integrals of products of special functions of hypergeometric type. The ideas of rational function certification, WZ- pair, and companion identity introduced by the authors in their earlier works [J. Am. Math. Soc. 3, No. 1, 147-158 (1990; Zbl 0695.05004); Bull. Am. Math. Soc., New Ser. 23, No. 1, 77-83 (1990; Zbl 0718.05010)] are extended to multiple sums and integrals. The algorithm provability is also stated for the $q$-hypergeometric identities. An explicit example of the algorithm depicts the computer proof of the well-known Hille-Hardy bilinear formula for Laguerre polynomials.
[R.K.Raina (Udaipur)]

MSC 2000:: *05A19 Combinatorial identities
05A10 Combinatorial functions
33C45 Orthogonal polynomials and functions of hypergeometric type
05A30 q-calculus and related topics
11B65 Binomial coefficients, etc.
33C05 Classical hypergeometric functions
39A10 Difference equations
33E99 Special functions

Keywords: $q$-hypergeometric identities; identities; hypergeometric; holonomic; recurrence relation; $q$-sums; special functions; Laguerre polynomials

Citations: Zbl 0695.05004; Zbl 0718.05010

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