A Rational Approximation for the Complete Elliptic Integral of the First Kind

被引：13

作者：

Yang, Zhen-Hang ^{[1
,2
]}

Tian, Jingfeng ^{[3
]}

Zhu, Ya-Ru ^{[3
]}

机构：

[1] North China Elect Power Univ, Minist Educ, Engn Res Ctr Intelligent Comp Complex Energy Syst, Yonghua St 619, Baoding 071003, Peoples R China

[2] Zhejiang Soc Elect Power, Hangzhou 310014, Peoples R China

[3] North China Elect Power Univ, Dept Math & Phys, Yonghua St 619, Baoding 071003, Peoples R China

来源：

MATHEMATICS | 2020年 / 8卷 / 04期

关键词：

complete integrals of the first kind; arithmetic-geometric mean; rational approximation; ASYMPTOTIC-EXPANSION; INEQUALITIES; MONOTONICITY;

D O I：

10.3390/math8040635

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let IC (r) be the complete elliptic integral of the first kind. We present an accurate rational 51'i)2+126r/ +61 lower approximation for IC (r). More precisely, we establish the inequality 4 IC (r) > 61(1'1)2+1101'1+21 for r E (0,1), where r' = A/1 r2. The lower bound is sharp.

引用

页数：9

共 27 条

[21] Sharp approximations for the complete elliptic integrals of the second kind by one-parameter means
Yang, Zhen-Hang
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 467 (01) : 446 - 461
[22] ON APPROXIMATING THE ERROR FUNCTION
Yang, Zhen-Hang
Qian, Wei-Mao
Chu, Yu-Ming
Zhang, Wen
[J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2018, 21 (02): : 469 - 479
[23] On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
Yang, Zhen-Hang
Qian, Wei-Mao
Chu, Yu-Ming
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[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 462 (02) : 1714 - 1726
[24] A MONOTONICITY PROPERTY INVOLVING THE GENERALIZED ELLIPTIC INTEGRAL OF THE FIRST KIND
Yang, Zhen-Hang
Chu, Yu-Ming
[J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2017, 20 (03): : 729 - 735
[25] On rational bounds for the gamma function
Yang, Zhen-Hang
Qian, Wei-Mao
Chu, Yu-Ming
Zhang, Wen
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
[26] A Double Inequality for the Trigamma Function and Its Applications
Yang, Zhen-Hang
Chu, Yu-Ming
Tao, Xiao-Jing
[J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
[27] Sharp bounds for the arithmetic-geometric mean
Yang, Zhen-Hang
Song, Ying-Qing
Chu, Yu-Ming
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,

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