Rational function certification of multisum/integral/“𝑞” identities

DOI10.1090/S0273-0979-1992-00297-5zbMath0759.05007arXivmath/9207218OpenAlexW1976761604MaRDI QIDQ4016745

Herbert S. Wilf, Doron Zeilberger

Publication date: 16 January 1993

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9207218

zbMATH Keywords

identitiesrecurrence relationLaguerre polynomialsspecial functionshypergeometricholonomic\(q\)-hypergeometric identities\(q\)-sums

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Additive difference equations (39A10) Classical hypergeometric functions, ({}_2F_1) (33C05) Other special functions (33E99)

Related Items (12)

q-Analogues of some supercongruences related to Euler numbers ⋮ Binomial identities -- combinatorial and algorithmic aspects ⋮ A \(q\)-analogue of the (L.2) supercongruence of van Hamme ⋮ A \(q\)-analogue of the (J.2) supercongruence of van Hamme ⋮ Proof of conjectures of Sun on double basic hypergeometric sums ⋮ Telescopers for differential forms with one parameter ⋮ How to Generate All Possible Rational Wilf-Zeilberger Pairs? ⋮ On the existence of telescopers for mixed hypergeometric terms ⋮ A q-analogue of a curious supercongruence of Guillera and Zudilin ⋮ Some variations of a ‘divergent’ Ramanujan-type q-supercongruence ⋮ Linear differential equations as a data structure ⋮ A characterization of inverse relations.

Cites Work

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• The method of differentiating under the integral sign
• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• A fast algorithm for proving terminating hypergeometric identities
• A proof of the Bieberbach conjecture
• A holonomic systems approach to special functions identities
• Generalized Euler integrals and \(A\)-hypergeometric functions
• The method of creative telescoping
• A generalization of Selberg’s beta integral
• Rational Functions Certify Combinatorial Identities
• Algorithms for the Solution of Systems of Linear Diophantine Equations
• A q-Beta Integral Associated with $BC_1 $
• Macdonald’s constant term conjectures for exceptional root systems
• Towards computerized proofs of identities
• Some generalized hypergeometric polynomials

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