Some Pade approximations and inequalities for the complete elliptic integrals of the first kind

被引：0
|
作者：
Mahmoud, Mansour [1 ]
Anis, Mona [2 ]
机构：
[1] King Abdulaziz Univ, Fac Sci, Math Dept, POB 80203, Jeddah 21589, Saudi Arabia
[2] Mansoura Univ, Fac Sci, Math Dept, Mansoura 35516, Egypt
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2021年 / 2021卷 / 01期
关键词：
Complete elliptic integrals; Hypergeometric function; Inequality; Pade approximant; Best possible constant; Error; MONOTONICITY; CONVEXITY;
D O I：
10.1186/s13660-021-02568-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present Pade approximations of some functions involving complete elliptic integrals of the first kind K(x), and motivated by these approximations we also present the following double inequality: 1 - X-2/1 - X-2 + X-4/62 < 2e(2/pi K(x)-1)/(1 + 1/root 1 - X-2 < 1 - 96/100X(2)/1 - 96/100X(2) + X-4/64, X is an element of (0, 1). Our results have superiority over some new recent results.
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页数：13
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