Generalized \(q\)-difference equations for \((q, c)\)-hypergeometric polynomials and some applications

DOI10.1007/s11139-022-00634-9OpenAlexW4297494480MaRDI QIDQ2696319

Hong-Li Zhou, Sama Arjika, Jian Cao

Publication date: 11 April 2023

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-022-00634-9

zbMATH Keywords

generating function\(q\)-difference equation\((q, c)\)-hypergeometric polynomials\(U(n+1)\) type \(q\)-binomial formulasAndrews-Askey integrals

Mathematics Subject Classification ID

Umbral calculus (05A40) (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)

Cites Work

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• \(q\)-difference equation and \(q\)-polynomials
• A \(q\)-extension of a partial differential equation and the Hahn polynomials
• Generalizations of Milne's \(\mathrm{U}(n+1)q\)-binomial theorems
• The theory of the umbral calculus. I
• Balanced \(_ 3\phi_ 2\) summation theorems for \(U(n)\) basic hypergeometric series
• Parameter augmentation for basic hypergeometric series. II
• Some iterated fractional \(q\)-integrals and their applications
• A note on \(q\)-difference equations for Ramanujan's integrals
• Some operator identities and \(q\)-series transformation formulas
• Generating functions for some families of the generalized Al-Salam-Carlitz \(q\)-polynomials
• A note on generalized \(q\)-difference equations for general Al-Salam-Carlitz polynomials
• \((q,c)\)-derivative operator and its applications
• Notes on Askey-Roy integral and certain generating functions for \(q\)-polynomials
• A note on moment integrals and some applications
• Lectures on the theory of functions of several complex variables. Notes by Raghavan Narasimhan. Reprint
• New forms of the Cauchy operator and some of their applications
• A note on q-difference equations for Cigler’s polynomials
• Twoq-difference equations andq-operator identities
• Certain q-Polynomial Expansions for Functions of Several Variables. II
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Another q-Extension of the Beta Function
• Certain q-Polynomial Expansions for Functions of Several Variables
• Some Orthogonal q‐Polynomials
• BASIC INTEGRATION