Accurate approximations for the complete elliptic integral of the second kind

被引：26
|
作者：
Yang, Zhen-Hang [1 ]
Chu, Yu-Ming [1 ]
Zhang, Wen [2 ]
机构：
[1] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China
[2] Yeshiva Univ, Albert Einstein Coll Med, New York, NY 10033 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 438卷 / 02期
关键词：
Gaussian hypergeometric function; Complete elliptic integral; Stolarsky mean; 1ST KIND; INEQUALITIES; BOUNDS;
D O I：
10.1016/j.jmaa.2016.02.035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove that the double inequality lambda S-11/4,S-7/4(1,r') < epsilon(r) < mu S-11/4,S-7/4(1,r') holds for all r is an element of (0,1) if and only if lambda <= mu/2 = 1.570796... and mu >= 11/7 = 1.571428..., where r' = (1 - r(2))(1/2), epsilon(r) = integral(pi/2)(0) root 1-r(2)sin(2)(t)dt is the complete elliptic integral of the second kind, and S-p,S-q (a,b) = [q(a(p) - b(p))/(p(aq - bq))](1/(p-q)) is the Stolarsky mean of a and b. (C) 2016 Elsevier Inc. All rights reserved.
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页码：875 / 888
页数：14
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