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Zbl 0991.41020
Dunster, T.M.
Uniform asymptotic expansions for Charlier polynomials. (English)
[J] J. Approximation Theory 112, No.1, 93-133 (2001). ISSN 0021-9045

The author investigates the asymptotic behavior of the Charlier polynomials $C_n^{(a)}$ as $n \to \infty $. The polynomials $C_n^{(a)}$ are not regarded as functions of $x$ with $a$ as a parameter, but rather with the roles reversed via a second-order linear differential equation in which $a$ is the (real or complex valued) independent variable and $x$ is a parameter.
[Matthew He (Ft.Lauderdale)]

MSC 2000:: *41A60 Asymptotic problems in approximation
33C45 Orthogonal polynomials and functions of hypergeometric type
34E20 Asymptotic singular perturbations, methods (ODE)

Keywords: asymptotic expansion; Charlier polynomials

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