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Uniform asymptotic expansions for Meixner polynomials. (English) Zbl 0906.41020
Meixner polynomials m n (x;β,c) are considered for large values of n. Two uniform expansions of m n (nα;β,c) are given, in terms of parabolic cylinder functions, one holding uniformly for α[ε,1+a] and the other one for α[1-b,M], where ε,a and b are small positive numbers and M<. The results are obtained by steepest descent methods and include five asymptotic formulas given earlier by W. M. Y. Goh.

MSC:
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
33C45Orthogonal polynomials and functions of hypergeometric type