Further monotonicity and convexity properties of the zeros of cylinder functions
type: Item
instance of: scholarly article
title: Further monotonicity and convexity properties of the zeros of cylinder functions
zbMATH Open document ID: 0755.33004
DOI: 10.1016/0377-0427(92)90078-C
author: C. Giordano
author: Lucia G. Rodono
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-17T00:00:00Z
review text: If \(C_{\nu k}\) be the \(k\)th positive zero of the cylinder function \(C_ \nu(x,\alpha)=\cos(\alpha)J_ \nu(x)-\sin(\alpha)Y_ \nu(x)\), \(0\leq\alpha<\pi\) then it is shown that the function \(\nu({d^ 2(C_{\nu k}) \over d\nu^ 2}+\delta)/C_{\nu k}\) increases with \(\nu\geq 0\) for suitable values of \(\delta\) and \(k-\alpha/\pi\geq 0.7070\dots\), which is shown to imply under suitable conditions that \(C_{\nu k}+{1\over 2}\delta\nu^ 2\) is a convex function of \(\nu\geq 0\). Monotonicity properties of the function \(C_{\nu k}/\nu\) are also obtained. These results improve known results.
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 96897
zbMATH Keywords: Bessel functions
zbMATH Keywords: monotonicity properties
zbMATH Keywords: cylinder function
zbMATH Keywords: convex function
reviewed by: Arun Verma
MaRDI profile type: Publication
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full work available at URL: 0377-0427(92)90078-c
OpenAlex ID: W1993704508
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description: scientific article; zbMATH DE number 96897