Multivariate generating functions built from Chebyshev polynomials and some of their applications and generalizations

DOI10.4064/cm8417-6-2021zbMath1492.42033arXiv1706.00316OpenAlexW4210826895MaRDI QIDQ5090177

Paweł Jerzy Szabłowski

Publication date: 15 July 2022

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.00316

zbMATH Keywords

Chebyshev polynomials\(q\)-Hermite polynomialsKibble-Slepian formulamultivariate generating functionsinversion of Poisson-Mehler formula

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Other special orthogonal polynomials and functions (33C47) Multiple sequences and series (40B05) Special properties of functions of several variables, Hölder conditions, etc. (26B35)

Cites Work

• Unnamed Item
• Kibble-Slepian formula and generating functions for 2D polynomials
• On the structure and probabilistic interpretation of Askey-Wilson densities and polynomials with complex parameters
• Multidimensional \(q\)-normal and related distributions -- Markov case
• Towards a \(q\)-analogue of the Kibble-Slepian formula in 3 dimensions
• On probabilistic aspects of Chebyshev polynomials
• Generating functions for certain q-orthogonal polynomials
• Probabilistic aspects of Al-Salam–Chihara polynomials
• Poisson-Mehler summation formula Around Poisson-Mehler summation formula
• On q-Hermite polynomials and their relationship with some other families of orthogonal polynomials

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