On a conjecture regarding the extrema of Bessel functions and its generalization
type: Item
instance of: scholarly article
title: On a conjecture regarding the extrema of Bessel functions and its generalization
zbMATH Open document ID: 1018.33005
DOI: 10.1016/S0022-247X(03)00015-5
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: For zeros \(j_k\) and \(j_{k+1}\) of any Bessel function with real order and the zeros \(j_k'\) of its derivative, the estimate \(j_k'> \sqrt{j_k j_{k+1}}\) is proved, together with an upper bound for \(j_k'\). The method, using traditional Sturm type arguments based on the normal form of the Bessel equation is quite general, and is lucidly explained.
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 1915604
zbMATH Keywords: Bessel functions
zbMATH Keywords: zeros
zbMATH Keywords: Sturm methods
Wikidata QID: Q123245917
author: Javier Segura
reviewed by: Jochen Denzler
MaRDI profile type: Publication
cites work: Some recent results on the zeros of Bessel functions and orthogonal polynomials
cites work: Q3215519
cites work: Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros
cites work: The Zeros of Special Functions from a Fixed Point Method
cites work: Computing the Zeros and Turning Points of Solutions of Second Order Homogeneous Linear ODEs
cites work: Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
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description: scientific article; zbMATH DE number 1915604