Absolute monotonicity of the accuracy of Ramanujan approximations for perimeter of an ellipse

被引：1
|
作者：
Tian, Jing-Feng [1 ,2 ]
Yang, Zhen-Hang [3 ]
机构：
[1] North China Elect Power Univ, Dept Math & Phys, Yonghua St 619, Baoding 071003, Peoples R China
[2] North China Elect Power Univ, Hebei Key Lab Phys & Energy Technol, Yonghua St 619, Baoding 071003, Peoples R China
[3] State Grid Zhejiang Elect Power Co Res Inst, Dept Sci & Technol, Hangzhou 310014, Zhejiang, Peoples R China
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2023年 / 117卷 / 03期
关键词：
Perimeter of an ellipse; Ramanujan approximation; Recurrence method; Absolute monotonicity; Inequality; INTEGRALS; BOUNDS; KIND;
D O I：
10.1007/s13398-023-01465-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove that the absolute errors of 11 mean value approximations for the perimeter of an ellipse are all absolutely monotonic with respect to the eccentricity of this ellipse. More interestingly, we find that the relative errors of two Ramanujan approximations have the same property.
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页数：16
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