\((q,c)\)-derivative operator and its applications

DOI10.1016/j.aam.2020.102081zbMath1456.05019OpenAlexW3045325811MaRDI QIDQ2221756

Helen W. J. Zhang

Publication date: 2 February 2021

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2020.102081

zbMATH Keywords

exponential operatorsRogers-Szegö polynomials\((q,c)\)-derivative operatorexpanded theorem

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Fractional derivatives and integrals (26A33) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Difference equations, scaling ((q)-differences) (39A13)

Related Items (4)

Two \(q\)-operational equations and Hahn polynomials ⋮ A \(q\)-operational equation and the Rogers-Szegő polynomials ⋮ Generalized \(q\)-difference equations for \((q, c)\)-hypergeometric polynomials and some applications ⋮ An expansion of \((q, \lambda)\)-derivative operator

Cites Work

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• Homogeneous \(q\)-partial difference equations and some applications
• \(q\)-differential operator identities and applications
• The Cauchy operator for basic hypergeometric series
• Another homogeneous \(q\)-difference operator
• New proofs of generating functions for Rogers-Szegö polynomials
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• More on the umbral calculus, with emphasis on the \(q\)-umbral calculus
• q-beta integrals and the q-Hermite polynomials
• Parameter augmentation for basic hypergeometric series. II
• Some operator identities and \(q\)-series transformation formulas
• A \(q\)-series expansion formula and the Askey-Wilson polynomials
• Generating functions for certain q-orthogonal polynomials
• Lectures on the theory of functions of several complex variables. Notes by Raghavan Narasimhan. Reprint
• \(q\)-difference equation and the Cauchy operator identities
• \(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials
• The homogeneous \(q\)-difference operator
• On the $q$-partial differential equations and $q$-series
• Twoq-difference equations andq-operator identities
• An extension of the non-terminating₆φ₅summation and the Askey–Wilson polynomials
• On the Askey-Wilson and Rogers Polynomials
• On the Rogers-Szego polynomials
• The bivariate Rogers–Szegö polynomials
• Some polynomials related to theta functions

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