Van der Corput inequalities for Bessel functions

Árpád Baricz, Andrea Laforgia, Tibor K. Pogány

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this note, we offer some log-concavity properties of certain functions related to Bessel functions of the first kind and modified Bessel functions of the first and second kinds, by solving partially a recent conjecture on the log-convexity/log-concavity properties for modified Bessel functions of the first kind and their derivatives. Moreover, we give an application of the mentioned results by extending two inequalities of van der Corput to Bessel and modified Bessel functions of the first kind. Similar inequalities are proved also for modified Bessel functions of the second kind, as well as for log-concave probability density functions.

Original languageEnglish
Pages (from-to)78-87
Number of pages10
JournalIntegral Transforms and Special Functions
Volume26
Issue number1
DOIs
Publication statusPublished - Jan 15 2015

Keywords

  • Bessel functions of the first kind
  • log-convexity
  • modified Bessel functions of the first and second kinds
  • probability density functions
  • trigonometricand hyperbolic functions
  • van der Corput inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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