The imaginary zeros of a mixed Bessel function
type: Item
instance of: scholarly article
title: The imaginary zeros of a mixed Bessel function
zbMATH Open document ID: 0651.33006
DOI: 10.1007/BF00945762
author: C. B. Kouris
author: E. K. Ifantis
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1988-01-01T00:00:00Z
review text: Die gemischte Funktion mit Besselschen Funktionen 1. Art \[ M_{\nu}(z)=(\beta z^ 2+\alpha)J_{\nu}(z)+zJ'_{\nu}(z)(\nu >- 1;\alpha,\beta \in {\mathbb{C}}) \] enthält als Sonderfälle die Funktionen: \[ J'_{\nu}(z)(\alpha =\beta =0),\quad J''_{\nu}(z)(\alpha =-\nu^ 2,\beta =1)\quad und\quad H_{\nu}(z,\alpha)=\alpha J_{\nu}(z)+zJ'_{\nu}(z). \] In Verschärfung vorliegender Ergebnisse leiten die Verfasser zunächst notwendige und hinreichende Bedingungen für die Existenz rein imaginärer Nullstellen von \(M_{\nu}(z)\) her und dann unter gewissen Einschränkungen über \(\alpha\in {\mathbb{R}}\) Einschließungen für den Betrag der Nullstellen von \(H_{\nu}(z,\alpha)\) und der von \(J'_{\nu}(z)\) und \(J''_{\nu}(z)\) in Abhängigkeit von \(\nu\) her.
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 4061651
zbMATH Keywords: Bessel function
MaRDI profile type: Publication
cites work: Q5508370
cites work: Conditions for solution of a linear first-order differential equation in the Hardy-Lebesgue space and applications
cites work: An Inequality Related the Zeros of Two Ordinary Bessel Functions
cites work: A differential equation for the zeros of bessel functions
cites work: Ordering relations between the zeros of miscellaneous bessel functions
cites work: A differential equation for the positive zeros of the function \(\alpha J_{\nu}(z)+\gamma zJ'_{\nu}(z)\)
cites work: An existence theory for functional-differential equations and functional- differential systems
cites work: On zeros of bessel functions†
cites work: Rational Bounds for Ratios of Modified Bessel Functions
cites work: On the Existence of Solutions for a Class of Rotating Disc Flows and the Convergence of a Successive Approximation Scheme
full work available at URL: https://doi.org/10.1007/bf00945762
OpenAlex ID: W1977978179
description: scientific article; zbMATH DE number 4061651