On the power of the zeros of Bessel functions
type: Item
instance of: scholarly article
title: On the power of the zeros of Bessel functions
zbMATH Open document ID: 0661.33005
DOI: 10.1007/BF02844903
author: Á. Elbert
author: A. Laforgia
publication date: 1987-01-01T00:00:00Z
review text: For \(\nu\geq 0\) let \(c_{\nu k}\) be the k-th positive zero of the cylinder function \[ C_{\nu}(t)=J_{\nu}(t)\cos \alpha - Y_{\nu}(t)\sin \alpha,\quad 0\leq \alpha <\pi, \] where \(J_{\nu}(t)\) and \(Y_{\nu}(t)\) denote the Bessel functions of the first and the second kind, respectively. We prove that \(c_{\nu k}^{1+H(x)}\) is convex as a function of \(\nu\), if \(c_{\nu k}\geq x>0\) and \(\nu\geq 0\), where H(x) is specified in Theorem 1.1.
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 4079896
zbMATH Keywords: cylinder function
zbMATH Keywords: Bessel functions
MaRDI profile type: Publication
cites work: Q3874513
cites work: On the Square of the Zeros of Bessel Functions
cites work: On the Convexity of the Zeros of Bessel Functions
cites work: FURTHER RESULTS ON THE ZEROS OF BESSEL FUNCTIONS
cites work: Some consequences of a lower bound for the second derivative of the zeros of Bessel functions
cites work: Monotonicity and concavity properties of zeros of Bessel functions
cites work: Q5846799
full work available at URL: https://doi.org/10.1007/bf02844903
OpenAlex ID: W1985206631
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4079896