CONVEXITY OF A RATIO OF THE MODIFIED BESSEL FUNCTIONS OF THE SECOND KIND WITH APPLICATIONS

被引：4

作者：

Yang, Zhen-Hang ^{[1
,2
]}

Tian, Jing-Feng ^{[3
]}

机构：

[1] North China Elect Power Univ, Engn Res Ctr Intelligent Comp Complex Energy Sys, Minist Educ, Yonghua St 619, Baoding 071003, Peoples R China

[2] Zhejiang Soc Elect Power, Hangzhou 310014, Zhejiang, Peoples R China

[3] North China Elect Power Univ, Dept Math & Phys, Yonghua St 619, Baoding 071003, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 07期

关键词：

Modified Bessel function of the second kind; convexity; complete monotonicity; functional inequality; INFINITE-DIVISIBILITY; COMPLETE MONOTONICITY; BOUNDS;

D O I：

10.1090/proc/15891

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let K-nu be the modified Bessel functions of the second kind of order nu. The ratio Q(nu) (x) - xK(nu)-1 (x) /K-nu (x) appeared in physics and probability. In this paper, we collate properties of this ratio, and prove the conjecture that (-1)(n) Q(nu)((n)) (x) > (<) 0 for x > 0 and n = 2,3 if vertical bar nu vertical bar > (<) 1/2 holds for n = 2. This yields several new consequences and improves some known results. Finally, two conjectures are proposed.

引用

页码：2997 / 3009

页数：13

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