\(q\)-differential operator identities and applications

DOI10.1016/j.jmaa.2006.10.087zbMath1114.33023OpenAlexW1982180298MaRDI QIDQ884386

Jian-Ping Fang

Publication date: 6 June 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.10.087

zbMATH Keywords

\(q\)-exponential operatorbilateral basic hypergeometric seriestransformation formulaeJackson's summation formula\(q\)-differential operatorBasic hypergeometric series

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Applications of basic hypergeometric functions (33D90)

Related Items (23)

Remarks on a generalizedq-difference equation ⋮ \(q\)-difference equation and \(q\)-polynomials ⋮ 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 ⋮ Two \(q\)-operational equations and Hahn polynomials ⋮ A \(q\)-operational equation and the Rogers-Szegő polynomials ⋮ \((q,c)\)-derivative operator and its applications ⋮ Extensions of \(q\)-Chu-Vandermonde's identity ⋮ Applications of a generalized \(q\)-difference equation ⋮ Notes on Askey-Roy integral and certain generating functions for \(q\)-polynomials ⋮ Generalizations of Milne’s U(n + 1) q-Chu-Vandermonde summation ⋮ A note on generalized \(q\)-difference equations for \(q\)-beta and Andrews-Askey integral ⋮ \(q\)-difference equation and the Cauchy operator identities ⋮ Two generalized \(q\)-exponential operators and their applications ⋮ New proofs of generating functions for Rogers-Szegö polynomials ⋮ Unnamed Item ⋮ q-Difference equations for generalized homogeneousq-operators and certain generating functions ⋮ Note on a \(q\)-contour integral formula of Gasper-Rahman ⋮ q-Laguerre polynomials and related q-partial differential equations ⋮ An operator approach to the Al-Salam–Carlitz polynomials ⋮ Some new generating functions for \(q\)-Hahn polynomials ⋮ Contiguous relations and summation and transformation formulae for basic hypergeometric series

Cites Work

• Unnamed Item
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• More on the umbral calculus, with emphasis on the \(q\)-umbral calculus
• The theory of the umbral calculus. I
• Parameter augmentation for basic hypergeometric series. II
• Some operator identities and \(q\)-series transformation formulas
• An expansion formula for \(q\)-series and applications
• THE BAILEY TRANSFORM AND D.B. SEARS
• ON A CHARACTERIZATION OF MEIXNER'S POLYNOMIALS
• On the Foundations of Combinatorial Theory V, Eulerian Differential Operators

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