Sharp weighted Holder mean bounds for the complete elliptic integral of the second kind

被引：2

作者：

Wang, Miao-Kun ^{[1
]}

He, Zai-Yin ^{[2
]}

Zhao, Tie-Hong ^{[3
,5
]}

Bao, Qi ^{[4
]}

机构：

[1] Huzhou Univ, Dept Math, Huzhou, Peoples R China

[2] Hunan Univ, Sch Math, Changsha, Peoples R China

[3] Hangzhou Normal Univ, Sch Math, Hangzhou, Peoples R China

[4] East China Normal Univ, Sch Math Sci, Shanghai, Peoples R China

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

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2023年 / 34卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Complete elliptic integrals; weighted Holder mean; monotonicity; inequality; FUNCTIONAL INEQUALITIES; MONOTONICITY; TANGENT; SINE; APPROXIMATIONS; THEOREMS; FORMULA;

D O I：

10.1080/10652469.2022.2155819

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the complete integral of the second kind E(r) approximated by the weighted Holder mean. In general, there are two ways to be considered. One is to find the best exponential parameters with a given weight, and the other is to find the optimal weights with a given exponential order. The second method will be used in this paper where we find the sharp weighted Holder mean bounds for E(r) in a sense of weight. As a result, we also provide a new method to find the optimal Holder mean bounds for E(r).

引用

页码：537 / 551

页数：15

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