Uniform asymptotic expansions of the Pollaczek polynomials
type: Item
instance of: scholarly article
title: Uniform asymptotic expansions of the Pollaczek polynomials
zbMATH Open document ID: 1088.41018
author: Yuqiu Zhao
author: Jianrong Zhou
published in: Journal of Computational and Applied Mathematics
publication date: 2006-03-24T00:00:00Z
review text: The Pollaczek polynomials \(P_n(x; a,b)\) can be defined by the generating function \[ (1- we^{i\theta})^{-{1\over 2}+ ih\theta}(1- we^{-i\theta})^{{1\over 1}- ih(\theta)}, \] \(x= \cos\theta\), \(\theta\in (0,\pi)\) and \(h(\theta)= {\cos\theta+ b\over 2\sin \theta}\), \(a> \pm b\). Two uniform asymptotic expansions are obtained valid in a respective interval depending of \(n\) and a parameter \(\delta< \sqrt{a+b}\) for \(\{P_n(x; a,b)\}\). One of them contain a turning point and all possible zeros of \(P_n(\cos\theta)\) in \(\theta\in (0,{\pi\over 2})\).
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 33C47
zbMATH DE Number: 5015166
zbMATH Keywords: Pollaczek polynomials
zbMATH Keywords: uniform asymptotic expansion
zbMATH Keywords: parabolic cylinder function
zbMATH Keywords: Airy function
reviewed by: Francisco Pérez Acosta
MaRDI profile type: Publication
full work available at URL: j.cam.2005.01.049
OpenAlex ID: W2024625298
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DOI: 10.1016/J.CAM.2005.01.049
description: scientific article; zbMATH DE number 5015166