Sharp Jordan-type inequalities for Bessel functions

A. Baricz, Shanhe Wu

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper our aim is to establish some sharp Jordan and Kober type inequalities for Bessel and modified Bessel functions of the first kind by using the monotone form of l'Hospital's rule. Moreover, by using the classical Cauchy mean value theorem inductively we deduce new series expansions for the Bessel and modified Bessel functions. These results extend and improve many known results in the literature.

Original languageEnglish
Pages (from-to)107-126
Number of pages20
JournalPublicationes Mathematicae
Volume74
Issue number1-2
Publication statusPublished - 2009

Fingerprint

Modified Bessel Functions
Friedrich Wilhelm Bessel
Bessel Functions
Bessel function of the first kind
Cauchy's integral theorem
Mean value theorem
Series Expansion
Deduce
Monotone
Form

Keywords

  • Bessel functions
  • Cauchy mean value theorem
  • Circular functions
  • Hyperbolic functions
  • Jordan-type inequalities
  • Kober-type inequalities
  • Modified bessel functions
  • Modified spherical bessel functions
  • Monotone form of l'hospital's rule
  • Spherical bessel functions
  • Taylor theorem with lagrange's form of the remainder

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Sharp Jordan-type inequalities for Bessel functions. / Baricz, A.; Wu, Shanhe.

In: Publicationes Mathematicae, Vol. 74, No. 1-2, 2009, p. 107-126.

Research output: Contribution to journalArticle

Baricz, A. ; Wu, Shanhe. / Sharp Jordan-type inequalities for Bessel functions. In: Publicationes Mathematicae. 2009 ; Vol. 74, No. 1-2. pp. 107-126.
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