Monotonicity of the zeros of the third derivative of Bessel functions
type: Item
instance of: scholarly article
title: Monotonicity of the zeros of the third derivative of Bessel functions
zbMATH Open document ID: 0833.33003
author: Lee Lorch
author: Peter Szego
published in: Methods and Applications of Analysis
publication date: 1996-03-17T00:00:00Z
review text: The aim of the authors is to show that the zeros of the third derivative of the Bessel function \(J_\nu (\lambda)\) are increasing functions of the order \(\nu\). To this end they consider the boundary-value problem satisfied by \(y(x) = J_\nu (\lambda x)\), namely: \[ (xy')' = (\nu^2/x) y - \lambda^2 xy, \quad x \in (0,1) \qquad y(0) = 0, \quad y'''(1) = 0, \] which permits them to show that \(d\lambda/d \nu > 0\) when \(\nu > 0\), \(\lambda \geq \sqrt 3\) and \(\lambda \neq j'''_{11}\). Here \(j'''_{11}\) stands for the first zero of \(j'''_{11}(\lambda)\). Notice that all the results obtained in the paper concern the case where \(\nu\) is real (and positive).
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 798947
reviewed by: Mithat Idemen
MaRDI profile type: Publication
DOI: 10.4310/MAA.1995.V2.N1.A7
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description: scientific article; zbMATH DE number 798947