On the exceptional zeros of cross-products of derivatives of spherical Bessel functions
type: Item
instance of: scholarly article
title: On the exceptional zeros of cross-products of derivatives of spherical Bessel functions
zbMATH Open document ID: 0588.33005
DOI: 10.1007/BF00944640
author: H. P. W. Gottlieb
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1985-01-01T00:00:00Z
review text: The author obtains an asymptotic expansion for the lowest exceptional root of the equation \[ j'\!_{\nu}(x)y'\!_{\nu}(\rho x)- j'\!_{\nu}(\rho x)y'\!_{\nu}(x) \] where \('=d/dx\) and \(j_{\nu}\) and \(y_{\nu}\) denote the spherical Bessel functions of the first and secind kind, respectively. The result is valid for \(\rho\) \(\to 1\), and it can be thought of as complementing that given by McMahon which is useful for larger zeros.
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 3944295
zbMATH Keywords: zeros of Bessel functions
zbMATH Keywords: spherical Bessel functions
reviewed by: A. Laforgia
MaRDI profile type: Publication
cites work: Q3331506
cites work: Q5508799
cites work: Tables of Zeros of Cross Product Bessel Functions J p � (ξ)Y p � (kξ) - J p � (kξ)Y p � (ξ) = 0
cites work: An Extended Table of Roots of J n � (x) Y n � (βx) - J n � (βx) Y n � (x) = 0
cites work: Q5792975
cites work: Remarks on the Zeros of Cross-Product Bessel Functions
cites work: Table of Roots for Natural Frequencies in Coaxial Type Cavities
cites work: Eigenvalues of the Laplacian with Neumann boundary conditions
cites work: Q5508370
cites work: Q5725770
cites work: Graphs and Formulas for Zeros of Cross Product Bessel Functions
cites work: Concerning the Roots of Jn′(x)Nn′(kx)−Jn′(kx)Nn′(x)=0
full work available at URL: https://doi.org/10.1007/bf00944640
OpenAlex ID: W2074964579
description: scientific article; zbMATH DE number 3944295