Operator identities and several \(U(n+1)\) generalizations of the Kalnins--Miller transformations

DOI10.1016/j.jmaa.2005.12.073zbMath1113.33020OpenAlexW2071753892MaRDI QIDQ852833

Zhizheng Zhang

Publication date: 15 November 2006

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.2005.12.073

zbMATH Keywords

basic hypergeometric seriesmultiple basic hypergeometric seriesChu-Vandermonde summationKalnins-Miller transformation

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic hypergeometric functions associated with root systems (33D67)

Related Items (8)

Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple \(q\)-series identities ⋮ Generalizations of Milne’s U(n + 1) q-Chu-Vandermonde summation ⋮ A note on moment integrals and some applications ⋮ A \(U(n + 1)\) Bailey lattice ⋮ Generalizations of Milne's \(\mathrm{U}(n+1)q\)-binomial theorems ⋮ \(q\)-difference equation and the Cauchy operator identities ⋮ q-Difference equations for generalized homogeneousq-operators and certain generating functions ⋮ The \(C_n\) WP-Bailey chain

Cites Work

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• 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
• Applications of operator identities to the multiple \(q\)-binomial theorem and \(q\)-Gauss summation theorem
• Two operator identities and their applications to terminating basic hypergeometric series and \(q\)-integrals
• q-Series and Orthogonal Polynomials Associated with Barnes’ First Lemma

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