\(q\)-integral representation of the Al-Salam-Carlitz polynomials

DOI10.1016/j.aml.2009.01.002zbMath1173.33305OpenAlexW2081951511MaRDI QIDQ1023086

Mingjin Wang

Publication date: 10 June 2009

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2009.01.002

zbMATH Keywords

Hermite polynomialsAndrews-Askey integralAl-Salam-Carlitz polynomialsRogers-Szegö polynomials\(q\)-integral representationLeibniz rule for the \(q\)-difference operator

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items

Homogeneous \(q\)-difference equations and generating functions for \(q\)-hypergeometric polynomials ⋮ A note on generalized \(q\)-difference equations for general Al-Salam-Carlitz polynomials ⋮ Generalized q-Laguerre type polynomials and q-partial differential equations ⋮ An expectation formula based on a Maclaurin expansion ⋮ A \(q\)-extension of a partial differential equation and the Hahn polynomials ⋮ Two \(q\)-operational equations and Hahn polynomials ⋮ A multiple \(q\)-translation formula and its implications ⋮ An expectation formula with applications ⋮ Two Ramanujan’s formulas and normal distribution ⋮ Moments for generating functions of Al-Salam-Carlitz polynomials ⋮ Some iterated fractional \(q\)-integrals and their applications ⋮ A probabilistic version of Mehler's formula ⋮ A new discrete probability space with applications ⋮ Unnamed Item ⋮ q-Laguerre polynomials and related q-partial differential equations ⋮ q-Difference equations for the generalized Cigler’s polynomials

Cites Work

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• Some families of hypergeometric polynomials and associated integral representations
• The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
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• Parameter augmentation for basic hypergeometric series. II
• On the Askey-Wilson and Rogers Polynomials
• Another q-Extension of the Beta Function
• ON q-DIFFERENCE EQUATIONS FOR CERTAIN WELL-POISED BASIC HYPERGEOMETRIC SERIES