q-Difference equations for generalized homogeneousq-operators and certain generating functions

DOI10.1080/10236198.2013.823955zbMath1350.39004OpenAlexW2019304097MaRDI QIDQ4979810

Jian Cao

Publication date: 19 June 2014

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2013.823955

zbMATH Keywords

generating function\(q\)-difference equationJackson \(q\)-integralVerma-Jain polynomial\(q\)-integral operatorsRamanujan identities\(U(n+1)\) generating functionhomogeneous \(q\)-operatortransformational identity

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Difference equations, scaling ((q)-differences) (39A13)

Related Items (6)

Homogeneous \(q\)-difference equations and generating functions for \(q\)-hypergeometric polynomials ⋮ \(q\)-difference equation and \(q\)-polynomials ⋮ A note on q-difference equations for Cigler’s polynomials ⋮ An expansion of \((q, \lambda)\)-derivative operator ⋮ 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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• Generalizations of certain Carlitz's trilinear and Srivastava-Agarwal type generating functions
• Bivariate generating functions for Rogers-Szegö polynomials
• Operator identities and several \(U(n+1)\) generalizations of the Kalnins--Miller transformations
• \(q\)-differential operator identities and applications
• Poisson kernel and multilinear generating functions of some orthogonal polynomials
• The Cauchy operator for basic hypergeometric series
• Another homogeneous \(q\)-difference operator
• New proofs of generating functions for Rogers-Szegö polynomials
• Generating functions for a class of \(q\)-polynomials
• Some multilinear generating functions for q-Hermite polynomials
• Balanced \(_ 3\phi_ 2\) summation theorems for \(U(n)\) basic hypergeometric series
• Parameter augmentation for basic hypergeometric series. II
• Some operator identities and \(q\)-series transformation formulas
• \(q\)-difference equation and the Cauchy operator identities
• The homogeneous \(q\)-difference operator
• Twoq-difference equations andq-operator identities
• An extension of the non-terminating₆φ₅summation and the Askey–Wilson polynomials
• Complex Analysis: A Brief Tour into Higher Dimensions
• Some Orthogonal q‐Polynomials

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