Uniform asymptotics for Meixner–Pollaczek polynomials with varying parameters

Jun Wang; Weiyuan Qiu; Roderick Wong

doi:10.1016/j.crma.2011.08.020

Mathematical Analysis

Uniform asymptotics for Meixner–Pollaczek polynomials with varying parameters
[Analyse asymptotique uniforme des polynômes de Meixner–Pollaczek avec des paramètres variables]

Présenté par : Philippe G. Ciarlet

Jun Wang ¹ ; Weiyuan Qiu ¹ ; Roderick Wong ²

¹ School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong

Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1031-1035.

Résumé
Abstract

Dans cette Note, nous effectuons une analyse asymptotique uniforme des polynômes de Meixner–Pollaczek $P_{n}^{(λ_{n})} (z; ϕ)$ avec un paramètre $λ_{n} = (n + \frac{1}{2}) A$ lorsque $n \to \infty$ , où $A > 0$ est une constante. Des développements asymptotiques en termes de fonctions paraboliques cylindriques et de fonctions élémentaires sont obtenus de manière uniforme en z dans deux régions qui recouvrent tout le plan complexe.

In this Note, we study the uniform asymptotics of the Meixner–Pollaczek polynomials $P_{n}^{(λ_{n})} (z; ϕ)$ with varying parameter $λ_{n} = (n + \frac{1}{2}) A$ as $n \to \infty$ , where $A > 0$ is a constant. Uniform asymptotic expansions in terms of parabolic cylinder functions and elementary functions are obtained for z in two overlapping regions which together cover the whole complex plane.

Reçu le : 2011-08-01
Accepté le : 2011-08-25
Publié le : 2011-09-16

DOI : 10.1016/j.crma.2011.08.020

Affiliations des auteurs :

Jun Wang ¹ ; Weiyuan Qiu ¹ ; Roderick Wong ²

¹ School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong

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     author = {Jun Wang and Weiyuan Qiu and Roderick Wong},
     title = {Uniform asymptotics for {Meixner{\textendash}Pollaczek} polynomials with varying parameters},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1031--1035},
     publisher = {Elsevier},
     volume = {349},
     number = {19-20},
     year = {2011},
     doi = {10.1016/j.crma.2011.08.020},
     language = {en},
}

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Jun Wang; Weiyuan Qiu; Roderick Wong. Uniform asymptotics for Meixner–Pollaczek polynomials with varying parameters. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1031-1035. doi : 10.1016/j.crma.2011.08.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.020/

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