A family of logarithmically concave functions defined by an integral over the modified Bessel function of order \(1\)
type: Item
instance of: scholarly article
title: A family of logarithmically concave functions defined by an integral over the modified Bessel function of order \(1\)
zbMATH Open document ID: 0847.33003
author: Andreas Findling
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-03-24T00:00:00Z
review text: This paper deals with questions regarding logarithmic concavity of the function \[ c(\tau, z):= \int^\beta_0 zI_1 (\cos (s) z)ds \] (\(\beta= \text{arcsin} (\tau))\), where \(I_1\) stands for the modified Bessel function of order one. It is shown that for fixed \(\tau\in (0,1)\) the function \(c(\tau, z)\) is strictly logarithmic-concave on \(\mathbb{R}^*= \mathbb{R} \setminus \{0\}\) (see Theorem 7). Also the logarithmic-concavity (on \(\mathbb{R}^*\)) of \(zI_1 (z)\) is established.
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 859210
zbMATH Keywords: inequalities
zbMATH Keywords: logarithmic concavity
zbMATH Keywords: modified Bessel function
reviewed by: Edward Neuman
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1305
OpenAlex ID: W2046799653
DOI: 10.1006/JMAA.1995.1305
description: scientific article; zbMATH DE number 859210