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.
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页数：13
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