Mathematical Analysis
Uniform asymptotics for Meixner–Pollaczek polynomials with varying parameters
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1031-1035.

In this Note, we study the uniform asymptotics of the Meixner–Pollaczek polynomials Pn(λn)(z;ϕ) with varying parameter λn=(n+12)A as n, 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.

Dans cette Note, nous effectuons une analyse asymptotique uniforme des polynômes de Meixner–Pollaczek Pn(λn)(z;ϕ) avec un paramètre λn=(n+12)A lorsque n, 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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.08.020
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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Wang, Jun; Qiu, Weiyuan; Wong, Roderick. 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. http://www.numdam.org/articles/10.1016/j.crma.2011.08.020/

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