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

被引：12
|
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.
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页数：9
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