A sharp double inequality involving generalized complete elliptic integral of the first kind

被引：207

作者：

Zhao, Tie-Hong ^{[1
]}

Wang, Miao-Kun ^{[2
]}

Chu, Yu-Ming ^{[2
,3
]}

机构：

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

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

[3] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Peoples R China

来源：

AIMS MATHEMATICS | 2020年 / 5卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Gaussian hypergeometric function; generalized elliptic integral; gamma function; psi function; POWER MEAN INEQUALITY; TRANSFORMATION INEQUALITIES; HARMONIC CONVEXITIES; BOUNDS; CONCAVITY; RESPECT; FORM;

D O I：

10.3934/math.2020290

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the article, we establish a sharp double inequality involving the ratio of generalized complete elliptic integrals of the first kind, which is the improvement and generalization of some previously known results.

引用

页码：4512 / 4528

页数：17

共 50 条

[1] SHARP INEQUALITIES INVOLVING THE POWER MEAN AND COMPLETE ELLIPTIC INTEGRAL OF THE FIRST KIND
Chu, Y. M.
Qiu, S. L.
Wang, M. K.
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2013, 43 (05) : 1489 - 1496
[2] Sharp inequalities for the complete elliptic integral of the first kind
Alzer, H
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1998, 124 : 309 - 314
[3] Sharp approximations for the generalized elliptic integral of the first kind
He, Zai-Yin
Jiang, Yue-Ping
Wang, Miao-Kun
[J]. MATHEMATICA SLOVACA, 2023, 73 (02) : 425 - 438
[4] Convexity and Monotonicity Involving the Complete Elliptic Integral of the First Kind
Jing-Feng Tian
Zhen-Hang Yang
[J]. Results in Mathematics, 2023, 78
[5] Convexity and Monotonicity Involving the Complete Elliptic Integral of the First Kind
Tian, Jing-Feng
Yang, Zhen-Hang
[J]. RESULTS IN MATHEMATICS, 2023, 78 (01)
[6] A MONOTONICITY PROPERTY INVOLVING THE GENERALIZED ELLIPTIC INTEGRAL OF THE FIRST KIND
Yang, Zhen-Hang
Chu, Yu-Ming
[J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2017, 20 (03): : 729 - 735
[7] CONCAVITY AND BOUNDS INVOLVING GENERALIZED ELLIPTIC INTEGRAL OF THE FIRST KIND
Zhao, Tie-Hong
Wang, Miao-Kun
Chu, Yu-Ming
[J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2021, 15 (02): : 701 - 724
[8] Monotonicity and convexity involving generalized elliptic integral of the first kind
Zhao, Tie-Hong
Wang, Miao-Kun
Chu, Yu-Ming
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2021, 115 (02)
[9] Monotonicity and convexity involving generalized elliptic integral of the first kind
Tie-Hong Zhao
Miao-Kun Wang
Yu-Ming Chu
[J]. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021, 115
[10] Sharp Power Mean Inequalities for the Generalized Elliptic Integral of the First Kind
Miao-Kun Wang
Zai-Yin He
Yu-Ming Chu
[J]. Computational Methods and Function Theory, 2020, 20 : 111 - 124

← 1 2 3 4 5 →