Uniform upper and lower bounds on the zeros of Bessel functions of the first kind
type: Item
instance of: scholarly article
title: Uniform upper and lower bounds on the zeros of Bessel functions of the first kind
zbMATH Open document ID: 0845.33002
author: Stephen Breen
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-09-09T00:00:00Z
review text: The author derives upper and lower bounds for the positive zeros \(j_{\nu,k}\), \(k = 1,2, \dots\), of the Bessel function \(J_\nu (x)\) in terms of the zeros \(a_k\), \(k = 1, 2, \dots\), of the Airy function \(Ai (x)\). These bounds hold, except for one lower bound, for all real \(\nu \geq 1/2\) and are close to asymptotic approximations which instead are valid only when \(k\) or \(\nu\) are very large.
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 861802
zbMATH Keywords: Bessel function
zbMATH Keywords: Airy function
reviewed by: Luigi Gatteschi
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1395
OpenAlex ID: W2070282054
DOI: 10.1006/JMAA.1995.1395
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description: scientific article; zbMATH DE number 861802