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Comptes Rendus Mathématique
Volume 349, n° 19-20
pages 1031-1035 (novembre 2011)
Doi : 10.1016/j.crma.2011.08.020
Received : 1 August 2011 ;  accepted : 25 August 2011
Uniform asymptotics for Meixner–Pollaczek polynomials with varying parameters
Analyse asymptotique uniforme des polynômes de Meixner–Pollaczek avec des paramètres variables
 

Jun Wang a, 1 , Weiyuan Qiu a , Roderick Wong b
a School of Mathematical Sciences, Fudan University, Shanghai 200433, China 
b Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong 

Abstract

In this Note, we study the uniform asymptotics of the Meixner–Pollaczek polynomials   with varying parameter   as  , where   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.

The full text of this article is available in PDF format.
Résumé

Dans cette Note, nous effectuons une analyse asymptotique uniforme des polynômes de Meixner–Pollaczek   avec un paramètre   lorsque  , où   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.

The full text of this article is available in PDF format.
1  This author was supported by NNSF of China Nos. 10871047, 11001057.


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