Strong asymptotics for Krawtchouk polynomials
type: Item
instance of: scholarly article
title: Strong asymptotics for Krawtchouk polynomials
zbMATH Open document ID: 0948.41018
DOI: 10.1016/S0377-0427(98)00183-6
author: Mourad E. H. Ismail
author: Plamen Simeonov
published in: Journal of Computational and Applied Mathematics
publication date: 2000-11-19T00:00:00Z
review text: The authors determine the strong asymptotics for Krawtchouk polynomials on the real line. They use their results to determine the distribution of the zeros of these polynomials \(p_n(nt;p,q)\) as \(n\to \infty)\). The polynomials \(p_n(n;p,q)\) being the Krawtchouk polynomial defined as \[ p_n(x;p,q): =\sum^n_{j=0} {x\choose j}{N-x \choose n-j}q^j(-p)^{n-j}; \] \(p,q \in(0,1)\) into \(p+q=1\) and \(N\in\mathbb{N}\), the set of positive integers into \(x\in \{0,1,\dots,N\}\).
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1326432
zbMATH Keywords: weak asymptotics
zbMATH Keywords: saddle points
zbMATH Keywords: strong asymptotics
zbMATH Keywords: Krawtchouk polynomials
reviewed by: R. P. Agarwal
MaRDI profile type: Publication
cites work: Q5736202
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full work available at URL: s0377-0427(98)00183-6
OpenAlex ID: W2088668281
description: scientific article; zbMATH DE number 1326432