On the zeros of quotients of Bessel functions
type: Item
instance of: scholarly article
title: On the zeros of quotients of Bessel functions
zbMATH Open document ID: 0961.33002
DOI: 10.1142/S0252959900000315
published in: Chinese Annals of Mathematics. Series B
publication date: 2001-05-24T00:00:00Z
review text: The modified Bessel functions of the first kind are usually denoted by \(I_\nu(z)=e^{-i\pi\nu/2}J_\nu(z e^{i\pi/2})\). The authors prove that for \(m\geq 2\) the equation \[ {{I_m(x)}\over{I_{m-1}(x)}}- {{m+1}\over{2m}} {{I_1(x)}\over{I_0(x)}}= 0, \quad x\in{\mathbb R}_+, \] has a unique solution \(x_m\). Further on if \(2\leq k<m\), then \(x_k<x_m\) holds true. The main tool to prove this theorem is to show that the function \(I_1(x)/I_0(x)\) is concave on \({\mathbb R}_+\).
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 1530099
zbMATH Keywords: Bessel functions
zbMATH Keywords: zeros
zbMATH Keywords: quotient
Wikidata QID: Q116009564
author: A. Friedman
author: Bei Hu
author: Juan J. Velázquez
reviewed by: Wolfgang zu Castell
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1530099