Monotonicity theorems and inequalities for the complete elliptic integrals\

被引：189

作者：

Alzer, H ^{[1
]}

Qiu, SL ^{[1
]}

机构：

[1] Hangzhou Inst Elect Engn, Presidents Off, Hangzhou 310037, Zhejiang, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2004年 / 172卷 / 02期

基金：

芬兰科学院;

关键词：

complete elliptic integrals; monotonicity; inequalities; mean values; Arc length of an ellipse;

D O I：

10.1016/j.cam.2004.02.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind, K and E. These results lead to sharp symmetrical bounds for K and E, which improve recently discovered inequalities. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：289 / 312

页数：24

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