New Sharp Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean

被引：7

作者：

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

Tian, Jing-Feng ^{[3
]}

Zhu, Ya-Ru ^{[3
]}

机构：

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

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

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

来源：

MATHEMATICS | 2020年 / 8卷 / 06期

关键词：

modified Bessel function of the first kind; hyperbolic function; mean; inequality; INEQUALITIES; MONOTONICITY; RATIOS; TERMS;

D O I：

10.3390/math8060901

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let I-v (x) be he modified Bessel function of the first kind of order v. We prove the double inequality root sinht/t cosh(1/q) (qt) < I-0 (t) root sinh t/t cosh(1/p) (pt) hold for t > 0 if and only if p >= 2/3 and q <= ( ln 2) / ln pi. The corresponding inequalities for means improve already known results.

引用

页数：13

共 36 条

[1]

Abramowitz M., 1972, HDB MATH FUNCTIONS F

[2] INEQUALITIES FOR AVERAGE VALUES [J].