Asymptotic expansion of the Krawtchouk polynomials and their zeros
type: Item
instance of: scholarly article
title: Asymptotic expansion of the Krawtchouk polynomials and their zeros
zbMATH Open document ID: 1053.33005
DOI: 10.1007/BF03321065
author: Weiyuan Qiu
author: Roderick Wong
published in: Computational Methods and Function Theory
publication date: 2004-09-28T00:00:00Z
review text: The generating function \( (1-pw)^{ N-x}(1+qw)^x=\sum_{n=0}^\infty K_n^N(x;p,q) w^n \) and Cauchy's formula are used for obtaining an asymptotic expansion for large \(n\) for the Krawtchouk polynomials \(K_n^N(x;p,q)\). The expansion holds for fixed or bounded \(x\) and is uniformly for \(\mu=N/n \in [1,\infty)\). The main approximants are confluent hypergeometric functions. Asymptotic approximations are also derived for the zeros of \(K_n^N(x;p,q)\) for various cases depending on the values of \(p\), \(q\), and \(\mu\).
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 2104124
zbMATH Keywords: Krawtchouk polynomials
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: confluent hypergeometric functions
zbMATH Keywords: zeros
reviewed by: Nico M. Temme
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03321065
OpenAlex ID: W2061320371
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description: scientific article; zbMATH DE number 2104124