Inequalities involving Bessel and modified Bessel functions
type: Item
instance of: scholarly article
title: Inequalities involving Bessel and modified Bessel functions
zbMATH Open document ID: 0709.33003
DOI: 10.1016/0022-247X(90)90394-U
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The authors define a self-adjoint and compact operator whose eigenvalues are given by \(\pm 2/j_{\nu k}\), where \(j_{\nu k}\) is the kth positive zero of the Bessel function \(J_{\nu}(x)\) of the first kind. Using operator techniques the authors derive some lower and upper bounds for \(J_{\nu +1}(x)/J_{\nu}(x)\) and \(I_{\nu +1}(x)/I_{\nu}(x)\), where \(I_{\nu}(x)\) is a modified Bessel function of the first kind. The comparison between new and old inequalities shows the sharpness of the new bounds.
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 4165320
zbMATH Keywords: selfadjoint operator
zbMATH Keywords: eigenvalues
zbMATH Keywords: Bessel function
author: E. K. Ifantis
author: Panayiotis D. Siafarikas
reviewed by: A. Laforgia
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4165320