The power collection method for connection relations: Meixner polynomials

DOI10.7153/jca-2017-11-08zbMath1424.33020arXiv1509.01027OpenAlexW2963464070MaRDI QIDQ4627848

Howard S. Cohl, Michael A. Baeder, Roberto S. Costas-Santos, Wen-Qing Xu

Publication date: 5 March 2019

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.01027

zbMATH Keywords

generating functionsinfinite serieseigenfunction expansionsconnection coefficientsdefinite integralsconnection-type relations

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Generalized hypergeometric series, ({}_pF_q) (33C20)

Uses Software

• DLMF

Cites Work

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• Coefficients of multiplication formulas for classical orthogonal polynomials
• Formulas and identities involving the Askey-Wilson operator
• Representations of \(q\)-orthogonal polynomials
• Expansions in the Askey-Wilson polynomials
• Connection relations and expansions
• Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme
• Extensions of discrete classical orthogonal polynomials beyond the orthogonality
• Representations of orthogonal polynomials
• Projection formulas for orthogonal polynomials of a discrete variable
• Connection and linearization coefficients of the Askey-Wilson polynomials
• Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Duplication coefficients via generating functions