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High accuracy asymptotic 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, Wen
通讯作者:
Chu, Yu-Ming
作者机构:
[Yang, Zhen-Hang] Hunan City Univ, Coll 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.
[Chu, Yu-Ming] Huzhou Univ, Dept Math, Hzhou 313000, Peoples R China.
[Zhang, Wen] Icahn Sch Med Mt Sinai, Friedman Brain Inst, New York, NY 10029 USA.
通讯机构:
[Chu, Yu-Ming] H
Huzhou Univ, Dept Math, Hzhou 313000, Peoples R China.
语种:
英文
关键词:
Complete elliptic integral;Gaussian hypergeometric function;Asymptotic bound;High accuracy
期刊:
Applied Mathematics and Computation
ISSN:
0096-3003
年:
2019
卷:
348
页码:
552-564
基金类别:
The research was supported by the National Natural Science Foundation of China (Grants nos. 11701176, 11626101, 11601485) and the Natural Science Foundation of the Zhejiang Provincial Department of Education, China (Grant no. Y201635325).
机构署名:
本校为第一机构
院系归属:
理学院
摘要:
In the article, we prove that the double inequality pi/2J(r') - 51 pi-160/160 r(16) < epsilon(r) < pi/2(r') - 5 pi/3x2(31 )r(16) holds for all r is an element of (0, 1), where epsilon(r) = integral( pi/2)(0)root 1-r(2)sin(2)(t)dt is the complete elliptic integral of the second kind, r' = (1 - r(2))(1/2) and J(r) = 51r(2) + 20r root r + 50r + 20 root r + 51/16(5r + 2 root r...

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