INEQUALITIES FOR THE RATIO OF COMPLETE ELLIPTIC INTEGRALS

被引：26

作者：

Alzer, Horst ^{[1
]}

Richards, Kendall ^{[2
]}

机构：

[1] Morsbacher Str 10, D-51545 Waldbrol, Germany

[2] Southwestern Univ, Dept Math & Comp Sci, Georgetown, TX USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 04期

关键词：

Complete elliptic integrals; functional inequalities; means; FUNCTIONAL INEQUALITIES; 1ST KIND;

D O I：

10.1090/proc/13337

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present various inequalities for the complete elliptic integral of the first kind, K(r) = integral(pi/2)(0) 1/root 1-r(2)sin(2)(t) dt (0 < r < 1) Among others, we prove that the inequalities 1/1 + 1/4 r < K(r)/K(root r) and K(root 1 -r(2)) /K(root 1 -r) < 2/1 + root r are valid for all r is an element of (0, 1). These estimates refine results published by Anderson, Vamanamurthy, and Vuorinen in 1990.

引用

页码：1661 / 1670

页数：10

共 16 条

[11] Bounds for complete elliptic integrals of the second kind with applications
Chu, Yu-Ming
Wang, Miao-Kun
Qiu, Song-Liang
Jiang, Yue-Ping
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (07) : 1177 - 1184
[12] Erdelyi A., 1953, HIGHER TRANSCENDENTA
[13] Sharp estimates for complete elliptic integrals
Qiu, SL
Vamanamurthy, MK
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1996, 27 (03) : 823 - 834
[14] A POWER MEAN INEQUALITY INVOLVING THE COMPLETE ELLIPTIC INTEGRALS
Wang, Gendi
Zhang, Xiaohui
Chu, Yuming
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2014, 44 (05) : 1661 - 1667
[15] Asymptotical bounds for complete elliptic integrals of the second kind
Wang, Miao-Kun
Chu, Yu-Ming
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 402 (01) : 119 - 126
[16] Convexity of the complete elliptic integrals of the first kind with respect to Holder means
Wang, Miao-Kun
Chu, Yu-Ming
Qiu, Song-Liang
Jiang, Yue-Ping
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 388 (02) : 1141 - 1146

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