Van der Corput inequalities for Bessel functions

被引：1

作者：

Baricz, Arpad ^{[1
,2
]}

Laforgia, Andrea ^{[3
]}

Pogany, Tibor K. ^{[2
,4
]}

机构：

[1] Univ Babes Bolyai, Dept Econ, Cluj Napoca 400591, Romania

[2] Obuda Univ, John von Neumann Fac Informat, Inst Appl Math, H-1034 Budapest, Hungary

[3] Roma Tre Univ, Dept Math, I-00146 Rome, Italy

[4] Univ Rijeka, Fac Maritime Studies, Rijeka 51000, Croatia

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2015年 / 26卷 / 01期

关键词：

Bessel functions of the first kind; log-convexity; trigonometricand hyperbolic functions; modified Bessel functions of the first and second kinds; van der Corput inequality; probability density functions; 39B72; 26A51; 26D07; 33C10; 1ST KIND; RATIOS;

D O I：

10.1080/10652469.2014.975419

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：78 / 87

页数：10

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