Applications of operator identities to the multiple \(q\)-binomial theorem and \(q\)-Gauss summation theorem

DOI10.1016/j.disc.2006.01.025zbMath1095.05002OpenAlexW1985459651MaRDI QIDQ2497480

Maixue Liu, Zhizheng Zhang

Publication date: 4 August 2006

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2006.01.025

zbMATH Keywords

summation formulamultiple basic hypergeometric seriestransformation formulaoperator identity\(U(n+1)\) \(q\)-binomial theorem\(U(n+1)\) \(q\)-Gauss theorem

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30)

Related Items (12)

Operator identities and several \(U(n+1)\) generalizations of the Kalnins--Miller transformations ⋮ \(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials ⋮ Bivariate generating functions for Rogers-Szegö polynomials ⋮ A note on q-difference equations for Cigler’s polynomials ⋮ On Carlitz's trilinear generating functions ⋮ Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple \(q\)-series identities ⋮ Notes on Askey-Roy integral and certain generating functions for \(q\)-polynomials ⋮ Generalizations of Milne's \(\mathrm{U}(n+1)q\)-binomial theorems ⋮ New proofs of generating functions for Rogers-Szegö polynomials ⋮ Unnamed Item ⋮ A note on $q$-partial difference equations and some applications to generating functions and $q$-integrals ⋮ q-Difference equations for the generalized Cigler’s polynomials

Cites Work

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• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• Balanced \(_ 3\phi_ 2\) summation theorems for \(U(n)\) basic hypergeometric series
• Parameter augmentation for basic hypergeometric series. II
• On the Askey-Wilson and Rogers Polynomials
• q-Series and Orthogonal Polynomials Associated with Barnes’ First Lemma
• Transformations of Basic Hypergeometric Functions of Special Type
• Transformations of Basic Hypergeometric Functions of any Order
• On the Transformation Theory of Basic Hypergeometric Functions

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