Sharp Stolarsky mean bounds for the complete elliptic integral of the second kind

被引：17
|
作者：
Yang, Zhen-Hang [1 ,2 ]
Chu, Yu-Ming [1 ]
Zhang, Xiao-Hui [3 ]
机构：
[1] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China
[2] State Grid Zhejiang Elect Power Res Inst, Customer Serv Ctr, Hangzhou 310009, Zhejiang, Peoples R China
[3] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China
来源：
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2017年 / 10卷 / 03期
关键词：
Gaussian hypergeometric function; complete elliptic integral; Stolarsky mean; MONOTONICITY;
D O I：
10.22436/jnsa.010.03.06
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the article, we prove that the double inequality 25/16 < epsilon(r)/S-5/2,S-2 (1, r ') < pi/2, holds for all r is an element of(0, 1) with the best possible constants 25/16 and pi/2, 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,(q) (a, b) - [q(a(p) - b(p))/(p(a(q) - b(q)))](1/(p - q)), is the Stolarsky mean of a and b. (C) 2017 All rights reserved.
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页码：929 / 936
页数：8
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