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Zbl 0906.41020
Jin, X.-S.; Wong, R.
Uniform asymptotic expansions for Meixner polynomials. (English)
[J] Constructive Approximation 14, No.1, 113-150 (1998). ISSN 0176-4276; ISSN 1432-0940/e

Meixner polynomials $m_n(x;\beta,c)$ are considered for large values of $n$. Two uniform expansions of $m_n(n\alpha;\beta,c)$ are given, in terms of parabolic cylinder functions, one holding uniformly for $\alpha\in [\varepsilon,1+a]$ and the other one for $\alpha\in [1-b,M]$, where $\varepsilon, a$ and $b$ are small positive numbers and $M<\infty$. The results are obtained by steepest descent methods and include five asymptotic formulas given earlier by W. M. Y. Goh.
[N.M.Temme (Amsterdam)]

MSC 2000:: *41A60 Asymptotic problems in approximation
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: Meixner polynomial; uniform asymptotic expansion; parabolic cylinder function; steepest descent method

Cited in: Zbl 0906.41012

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