Discrete approximation of complete p-elliptic integral of the second kind and its application

被引：0
|
作者：
Zhao, Tiehong [1 ]
Wang, Miaokun [2 ]
机构：
[1] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China
[2] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2024年 / 118卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Complete p-elliptic integrals; Discrete approximation; Generalized Toader mean; SHARP APPROXIMATIONS; BOUNDS;
D O I：
10.1007/s13398-023-01537-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
By virtue of the generalized trigonometric function sinp(theta) and the generalized pi p, Legendre's complete elliptic integrals are generalized to the complete p-elliptic integral by Takeuchi. In this article, it was shown, for p = 3, 4, that complete p-elliptic integrals of the second kind can be obtained efficiently by the decreasing and increasing recursive sequences. As an application, we find the optimal weighted Lehmer mean bounds for a new generalized Toader mean, and equivalently get an upper bound for complete 3-elliptic integral of the second kind.
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页数：18
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