Redheffer type bounds for Bessel and modified Bessel functions of the first kind

A. Baricz, Khaled Mehrez

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper our aim is to show some new inequalities of the Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We also use some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalAequationes Mathematicae
DOIs
Publication statusAccepted/In press - Mar 27 2018

Fingerprint

Bessel function of the first kind
Modified Bessel Functions
Bessel functions
Friedrich Wilhelm Bessel
Monotonicity
Quotient
Tangent function
Sharp Inequality
Power series
Dirichlet
Differentiable

Keywords

  • Bessel and modified Bessel functions of the first and second kind
  • Rayleigh sum of zeros of Bessel functions of the first kind
  • Redheffer type inequalities
  • Zeros of Bessel functions

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Redheffer type bounds for Bessel and modified Bessel functions of the first kind. / Baricz, A.; Mehrez, Khaled.

In: Aequationes Mathematicae, 27.03.2018, p. 1-15.

Research output: Contribution to journalArticle

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