# Bounds of the perimeter of an ellipse using arithmetic, geometric and harmonic means

@article{Wang2014BoundsOT, title={Bounds of the perimeter of an ellipse using arithmetic, geometric and harmonic means}, author={Miao-Kun Wang and Yuming Chu and Yue-Ping Jiang and Song-Liang Qiu}, journal={Mathematical Inequalities \& Applications}, year={2014}, pages={101-111} }

In this paper, we present several bounds for the perimeter of an ellipse in terms of arithmetic, geometric, and harmonic means, which improve some known results. Mathematics subject classification (2010): 41A10, 33E05, 33C05, 26E60.

## 8 Citations

Bounds for the perimeter of an ellipse in terms of power means

- MathematicsJournal of Mathematical Inequalities
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In the article, we provide several precise bounds for the perimeter of an ellipse in terms of the power means, and present new bounds for the complete elliptic integral of the second kind. The given…

Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters

- MathematicsJournal of inequalities and applications
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The best possible parameters λ=λ( p)$\lambda=\lambda (p)$ and μ=μ(p) $\mu=\mu(p), such that the double inequality holds for any p∈[1,∞) p in [1, \infty) and all a,b>0$a, b>0 with a≠b$a\neq b.

High accuracy asymptotic bounds for the complete elliptic integral of the second kind

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- 2019

On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind

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A Bibliography of Publications about the Arithmetic–Geometric Mean Iteration

- Physics

(a, b)← ( a+3b 4 , √ ab+b 2 ) [BB89]. 1 [BM88]. 2 [BM88, Gau02, KM10, KM12]. 3 [LR07]. $49.95 [Ber88]. B [SL98]. D4 [Sol95]. e [Has13b, Has14, YY01]. E6 [Sol95]. E8 [Sol95]. λ [SMY14]. C [CT13a]. μ…

On approximating the quasi-arithmetic mean

- Chemistry, MathematicsJournal of Inequalities and Applications
- 2019

AbstractIn this article, we prove that the double inequalities
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Monotonicity rule for the quotient of two functions and its application

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- 2017

A monotonicity rule for the function P(x) is provided, and new bounds for the complete elliptic integral E(r) are presented, such that the sequence {an/bn}n=n0∞$ is increasing (decreasing) with an0/bn0≥(≤)1.

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