New proofs of generating functions for Rogers-Szegö polynomials

DOI10.1016/j.amc.2008.11.003zbMath1160.33312OpenAlexW2095717613MaRDI QIDQ1002307

Jian Cao

Publication date: 25 February 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2008.11.003

zbMATH Keywords

generating function\(q\)-difference operator\(q\)-exponential operatorRogers-Szegö polynomialsoperator identity

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (18)

A Note onq-Integrals and Certain Generating Functions ⋮ Bivariate generating functions for Rogers-Szegö polynomials ⋮ q-Difference equations of moment integrals for transformational identities and generating functions ⋮ On Carlitz's trilinear generating functions ⋮ Moments for generating functions of Al-Salam-Carlitz polynomials ⋮ Generalizations of certain Carlitz's trilinear and Srivastava-Agarwal type generating functions ⋮ \((q,c)\)-derivative operator and its applications ⋮ Some \(q\)-generating functions of the Carlitz and Srivastava-Agarwal types associated with the generalized Hahn polynomials and the generalized Rogers-Szegö polynomials ⋮ Notes on Askey-Roy integral and certain generating functions for \(q\)-polynomials ⋮ A note on moment integrals and some applications ⋮ Some integrals involving \(q\)-Laguerre polynomials and applications ⋮ \(q\)-difference equation and the Cauchy operator identities ⋮ A note on \(q\)-partial differential equations for generalized \(q\)-2D Hermite polynomials ⋮ Unnamed Item ⋮ q-Difference equations for generalized homogeneousq-operators and certain generating functions ⋮ ALTERNATIVE PROOFS OF GENERATING FUNCTIONS FOR HAHN POLYNOMIALS AND SOME APPLICATIONS ⋮ An operator approach to the Al-Salam–Carlitz polynomials ⋮ Some new generating functions for \(q\)-Hahn polynomials

Cites Work

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• \(q\)-differential operator identities and applications
• Poisson kernel and multilinear generating functions of some orthogonal polynomials
• Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple \(q\)-series identities
• The Cauchy operator for basic hypergeometric series
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• q-beta integrals and the q-Hermite polynomials
• Some multilinear generating functions for q-Hermite polynomials
• Parameter augmentation for basic hypergeometric series. II
• Some operator identities and \(q\)-series transformation formulas
• Generating functions for certain q-orthogonal polynomials
• Applications of operator identities to the multiple \(q\)-binomial theorem and \(q\)-Gauss summation theorem
• Two operator identities and their applications to terminating basic hypergeometric series and \(q\)-integrals
• 𝑞-difference operators, orthogonal polynomials, and symmetric expansions
• On the Askey-Wilson and Rogers Polynomials
• Some Orthogonal q‐Polynomials
• Some polynomials related to theta functions

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