Two operator identities and their applications to terminating basic hypergeometric series and \(q\)-integrals

DOI10.1016/j.jmaa.2005.03.064zbMath1081.33032OpenAlexW2024373272MaRDI QIDQ2575047

Zhizheng Zhang, Jun Wang

Publication date: 5 December 2005

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.2005.03.064

zbMATH Keywords

\(q\)-integralsBasic hypergeometric seriesoperator idenities

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Related Items (13)

Operator identities and several \(U(n+1)\) generalizations of the Kalnins--Miller transformations ⋮ Expansions in Askey-Wilson polynomials via Bailey transform ⋮ 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 ⋮ Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple \(q\)-series identities ⋮ The Cauchy operator for basic hypergeometric series ⋮ Two new \(q\)-exponential operator identities and their applications ⋮ Some integrals involving \(q\)-Laguerre polynomials and applications ⋮ Twoq-difference equations andq-operator identities ⋮ Two generalized \(q\)-exponential operators and their applications ⋮ New proofs of generating functions for Rogers-Szegö polynomials ⋮ An operator approach to the Al-Salam–Carlitz polynomials

Cites Work

• An elementary evaluation of a beta type integral
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• Parameter augmentation for basic hypergeometric series. II
• Some operator identities and \(q\)-series transformation formulas
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Barnes and Ramanujan-Type Integrals on the q-Linear Lattice
• Transformations of Basic Hypergeometric Functions of Special Type
• Transformations of Basic Hypergeometric Functions of any Order
• On the Transformation Theory of Basic Hypergeometric Functions
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