Uniform asymptotics for Meixner–Pollaczek polynomials with varying parameters

Wang, Jun; Qiu, Weiyuan; Wong, Roderick

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

Wang, Jun ¹ ; Qiu, Weiyuan ¹ ; Wong, Roderick 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, Tome 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 :

Wang, Jun ¹ ; Qiu, Weiyuan ¹ ; Wong, Roderick 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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     title = {Uniform asymptotics for {Meixner{\textendash}Pollaczek} polynomials with varying parameters},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1031--1035},
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Wang, Jun; Qiu, Weiyuan; Wong, Roderick. Uniform asymptotics for Meixner–Pollaczek polynomials with varying parameters. Comptes Rendus. Mathématique, Tome 349 (2011) no. 19-20, pp. 1031-1035. doi : 10.1016/j.crma.2011.08.020. http://www.numdam.org/articles/10.1016/j.crma.2011.08.020/

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