Accurate approximations for the complete elliptic integral of the second kind

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:438

Article

Yang, Zhen-Hang¹  Chu, Yu-Ming¹  Zhang, Wen² 

[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

关键词: Gaussian hypergeometric function;    Complete elliptic integral;    Stolarsky mean;   

DOI  :  10.1016/j.jmaa.2016.02.035

来源: Elsevier

【 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.

【 授权许可】

Free