An operator approach to the Al-Salam–Carlitz polynomials

DOI10.1063/1.3321603zbMath1310.33006arXiv0910.1746OpenAlexW3100331121MaRDI QIDQ5249149

Husam L. Saad, William Y. C. Chen, Lisa Hui Sun

Publication date: 29 April 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.1746

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (10)

New forms of the Cauchy operator and some of their applications ⋮ Two operator representations for the trivariate \(q\)-polynomials and Hahn polynomials ⋮ Two \(q\)-operational equations and Hahn polynomials ⋮ On Carlitz's trilinear generating functions ⋮ Moments for generating functions of Al-Salam-Carlitz polynomials ⋮ Generalizations of certain Carlitz's trilinear and Srivastava-Agarwal type generating functions ⋮ Some \(q\)-generating functions of the Carlitz and Srivastava-Agarwal types associated with the generalized Hahn polynomials and the generalized Rogers-Szegö polynomials ⋮ New application of the Cauchy operator on the homogeneous Rogers-Szegö polynomials ⋮ Notes on Askey-Roy integral and certain generating functions for \(q\)-polynomials ⋮ Unnamed Item

Cites Work

• Unnamed Item
• \(q\)-differential operator identities and applications
• The Cauchy operator for basic hypergeometric series
• New proofs of generating functions for Rogers-Szegö polynomials
• More on the umbral calculus, with emphasis on the \(q\)-umbral calculus
• The \(q\)-harmonic oscillator and the Al-Salam and Carlitz polynomials
• On combinatorics of Al-Salam Carlitz polynomials
• Parameter augmentation for basic hypergeometric series. II
• Generating functions for certain q-orthogonal polynomials
• The homogeneous \(q\)-difference operator
• Two operator identities and their applications to terminating basic hypergeometric series and \(q\)-integrals
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• On the Rogers-Szego polynomials
• Multivariable Al-Salam & Carlitz Polynomials Associated with the TypeA q-Dunkl Kernel
• The bivariate Rogers–Szegö polynomials
• Some Orthogonal q‐Polynomials
• A basic analogue of the bessel polynomial
• On the Foundations of Combinatorial Theory V, Eulerian Differential Operators

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