Generalizations of Milne's \(\mathrm{U}(n+1)q\)-binomial theorems

DOI10.1016/J.CAMWA.2009.03.086zbMath1189.33030OpenAlexW2053817293MaRDI QIDQ980090

Mingjin Wang

Publication date: 28 June 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2009.03.086

zbMATH Keywords

Andrews-Askey integral\(q\)-Chu-Vandermonde sums\(q\)-Pfaff-Saalschütz formulaMilne's \(\mathrm{U}(n+1)\) refinement of the \(q\)-binomial theorems

Mathematics Subject Classification ID

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

Related Items (12)

\(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials ⋮ An expectation formula based on a Maclaurin expansion ⋮ Multiple expansion formulas over root systems ⋮ A note on q-difference equations for Cigler’s polynomials ⋮ An expectation formula with applications ⋮ Generalized \(q\)-difference equations for \((q, c)\)-hypergeometric polynomials and some applications ⋮ Some iterated fractional \(q\)-integrals and their applications ⋮ Generalizations of Milne’s U(n + 1) q-Chu-Vandermonde summation ⋮ A new discrete probability space with applications ⋮ An extension of the \(q\)-beta integral with applications ⋮ Homogeneous \(q\)-partial difference equations and some applications ⋮ q-Difference equations for the generalized Cigler’s polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Operator identities and several \(U(n+1)\) generalizations of the Kalnins--Miller transformations
• Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple \(q\)-series identities
• Balanced \(_ 3\phi_ 2\) summation theorems for \(U(n)\) basic hypergeometric series
• Parameter augmentation for basic hypergeometric series. II
• Some operator identities and \(q\)-series transformation formulas
• An expansion formula for \(q\)-series and applications
• A remark on Andrews-Askey integral
• Applications of operator identities to the multiple \(q\)-binomial theorem and \(q\)-Gauss summation theorem
• Another q-Extension of the Beta Function

This page was built for publication: Generalizations of Milne's \(\mathrm{U}(n+1)q\)-binomial theorems