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

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成果类型:
期刊论文
作者:
Yang, Zhen-Hang;Chu, Yu-Ming*;Zhang, Xiao-Hui
通讯作者:
Chu, Yu-Ming
作者机构:
[Chu, Yu-Ming; Yang, Zhen-Hang] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
[Yang, Zhen-Hang] State Grid Zhejiang Elect Power Res Inst, Customer Serv Ctr, Hangzhou 310009, Zhejiang, Peoples R China.
[Zhang, Xiao-Hui] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China.
通讯机构:
[Chu, Yu-Ming] H
Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
语种:
英文
关键词:
Gaussian hypergeometric function;complete elliptic integral;Stolarsky mean
期刊:
Journal of Nonlinear Sciences and Applications
ISSN:
2008-1898
年:
2017
卷:
10
期:
3
页码:
929-936
基金类别:
Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [61673169, 61374086, 11371125, 11601485, 11401191]; Tianyuan Special Funds of the Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11626101]
机构署名:
本校为第一且通讯机构
院系归属:
理学院
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 Stolar...

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