Certain results on generating functions related to the associated Meixner-Pollaczek polynomials

DOI10.1080/10652469.2021.1958214OpenAlexW3183907693MaRDI QIDQ5078306

Shu-Han Zhao, Min-Jie Luo, Ravinder Krishen Raina

Publication date: 23 May 2022

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2021.1958214

zbMATH Keywords

generating functionLagrange polynomialAppell functionMeixner-Pollaczek polynomial

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Appell, Horn and Lauricella functions (33C65)

Uses Software

• DLMF

Cites Work

• Linear birth and death models and associated Laguerre and Meixner polynomials
• Fourth-order difference equation for the associated Meixner and Charlier polynomials
• The third Appell function for one large variable
• Reduction formulas for the Appell and Humbert functions
• Some new results for the Lagrange polynomials in several variables
• The Hahn and Meixner polynomials of an imaginary argument and some of their applications
• A Generalization of Gasper's Kernel for Hahn Polynomials: Application to Pollaczek Polynomials
• The lagrange polynomials in several variables
• Generating functions of Pollaczek polynomials: a revisit
• Encyclopedia of Special Functions: The Askey-Bateman Project
• A generating function and formulae defining the first-associated Meixner–Pollaczek polynomials
• Asymptotics of the associated Pollaczek polynomials
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