Uniform asymptotic expansions for Meixner polynomials
type: Item
instance of: scholarly article
title: Uniform asymptotic expansions for Meixner polynomials
zbMATH Open document ID: 0906.41020
author: D. Massart
published in: Constructive Approximation
publication date: 1999-01-21T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1129642
zbMATH Keywords: Meixner polynomial
zbMATH Keywords: uniform asymptotic expansion
zbMATH Keywords: parabolic cylinder function
zbMATH Keywords: steepest descent method
reviewed by: Nico M. Temme
Wikidata QID: Q56475781
MaRDI profile type: Publication
full work available at URL: s003659900066
OpenAlex ID: W1994930056
DOI: 10.1007/S003659900066
description: scientific article; zbMATH DE number 1129642