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

DOI10.7153/mia-17-07zbMath1285.26053OpenAlexW2332401764MaRDI QIDQ5409699

Yue Ping Jiang, Song-Liang Qiu, Yu-Ming Chu, Miao-Kun Wang

Publication date: 14 April 2014

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/mia-17-07

zbMATH Keywords

arithmetic meangeometric meanperimeter of an ellipseharmonic meanToader mean

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Means (26E60) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05)

Related Items (13)

Approximations for the complete elliptic integral of the second Kind ⋮ On the bounds of the perimeter of an ellipse ⋮ On the generalized power-type Toader mean ⋮ Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters ⋮ Bounds for the perimeter of an ellipse in terms of power means ⋮ On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind ⋮ Monotonicity rule for the quotient of two functions and its application ⋮ High accuracy asymptotic bounds for the complete elliptic integral of the second kind ⋮ Sharp bounds for the Toader mean in terms of arithmetic and geometric means ⋮ Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion function ⋮ Sharp generalized Seiffert mean bounds for the Toader mean of order 4 ⋮ Monotonicity and inequalities involving zero-balanced hypergeometric function ⋮ On approximating the quasi-arithmetic mean

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