On a Sum of Modified Bessel Functions

Árpád Baricz, Tibor K. Pogány

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Abstract

In this paper we consider a sum of modified Bessel functions of the first kind of which particular case is used in the study of Kanter's sharp modified Bessel function bound for concentrations of some sums of independent symmetric random vectors. We present some monotonicity and convexity properties for that sum of modified Bessel functions of the first kind, as well as some Turán type inequalities, lower and upper bounds. Moreover, we point out an error in Kanter's paper (J Multivariate Anal 6:222-236, 1976).

Original languageEnglish
Pages (from-to)349-360
Number of pages12
JournalMediterranean Journal of Mathematics
Volume11
Issue number2
DOIs
Publication statusPublished - Jan 1 2014

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Keywords

  • Concentration bounds
  • Functional inequalities
  • Modified Bessel functions

ASJC Scopus subject areas

  • Mathematics(all)

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