Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple \(q\)-series identities

zbMath1148.33015MaRDI QIDQ924226

Tianze Wang, Zhizheng Zhang

Publication date: 15 May 2008

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

zbMATH Keywords

Mehler's formulaoperator identitybivariate Rogers-Szegö polynomialMilne's fundamental theorem for \(A_n\) or \(U(n+1)\) basic hypergeometric seriesmultiple \(q\)-series identityRogers's formula

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items

\(q\)-difference equations for Askey-Wilson type integrals via \(q\)-polynomials ⋮ Bivariate generating functions for Rogers-Szegö polynomials ⋮ On Carlitz's trilinear generating functions ⋮ A \(U(n + 1)\) Bailey lattice ⋮ Generalizations of Milne's \(\mathrm{U}(n+1)q\)-binomial theorems ⋮ New proofs of generating functions for Rogers-Szegö polynomials

Cites Work

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• On certain q-orthogonal polynomials
• Operator identities and several \(U(n+1)\) generalizations of the Kalnins--Miller transformations
• An elementary proof of the Macdonald identities for \(A_{\ell}^{(1)}\)
• Basic hypergeometric series very well-poised in U(n)
• Convergence of Padé approximants of partial theta functions and the Rogers-Szegö polynomials
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
• Convergence of Padé approximants for a \(q\)-hypergeometric series (Wynn's power series I)
• Balanced \(_ 3\phi_ 2\) summation theorems for \(U(n)\) basic hypergeometric series
• Parameter augmentation for basic hypergeometric series. II
• A new \(A_n\) extension of Ramanujan's \(_1\psi_1\) summation with applications to multilateral \(A_n\) series.
• Continued fractions for Rogers--Szegö polynomials
• Some operator identities and \(q\)-series transformation formulas
• On a general \(q\)-Fourier transformation with nonsymmetric kernels
• The homogeneous \(q\)-difference operator
• 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
• On the Askey-Wilson and Rogers Polynomials
• Positivity preserving transformations for 𝑞-binomial coefficients
• The bivariate Rogers–Szegö polynomials
• On the Foundations of Combinatorial Theory IV Finite Vector Spaces and Eulerian Generating Functions