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.
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页码：2997 / 3009
页数：13
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