Sharp power-type Heronian and Lehmer means inequalities for the complete elliptic integrals

被引：3

作者：

Zhao, Tie-hong ^{[1
]}

Chu, Yu-ming ^{[2
]}

机构：

[1] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China

[2] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China

来源：

APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B | 2023年 / 38卷 / 03期

基金：

中国国家自然科学基金;

关键词：

power-type Heronian mean; Lehmer means; complete elliptic integrals; TRANSFORMATION INEQUALITIES; HYPERGEOMETRIC-FUNCTIONS; CONVEXITY PROPERTIES; REFINEMENTS; BOUNDS;

D O I：

10.1007/s11766-023-4223-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the article, we prove that the inequalities H-p(K(r), epsilon(r)) > pi/2, Lq(K(r, epsilon(r)) > pi/2 hold for all r is an element of (0; 1) if and only if p >= -3/4 and q >= 3/4, where H-p(a; b) and L-q (a,b) are respectively the p-th power-type Heronian mean and q -th Lehmer mean of a and b, and K (r and epsilon (r) are respectively the complete elliptic integrals of the first and second kinds.

引用

页码：467 / 474

页数：8

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