On a Sum of Modified Bessel Functions

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• 作者：árpád. Baricz (1)
  Tibor K. Pogány (2)
  
• 关键词：39B62 ; 33C10 ; 33C15 ; Modified Bessel functions ; Concentration bounds ; Functional inequalities
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：11
• 期：2
• 页码：349-360
• 全文大小：
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• 作者单位：árpád. Baricz (1)
  Tibor K. Pogány (2)
  
  1. Department of Economics, Babe?-Bolyai University, Cluj-Napoca, 400591, Romania
  2. Faculty of Maritime Studies, University of Rijeka, Rijeka, 51000, Croatia
  
• ISSN：1660-5454

文摘

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 6:222-36, 1976).