Monotonicity of the ratio for the complete elliptic integral and Stolarsky mean

DOI10.1186/s13660-016-1113-1zbMath1342.33041OpenAlexW2473467990WikidataQ59467016 ScholiaQ59467016MaRDI QIDQ2629140

Yu-Ming Chu, Wen Zhang, Zhen-Hang Yang

Publication date: 20 July 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-016-1113-1

zbMATH Keywords

complete elliptic integralToader-Qi meanStolarsky meanToader mean

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Means (26E60) Elliptic functions and integrals (33E05)

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Cites Work

• Accurate approximations for the complete elliptic integral of the second kind
• Bounds for the perimeter of an ellipse
• Bounds for complete elliptic integrals of the second kind with applications
• Monotonicity theorems and inequalities for the complete elliptic integrals
• Some mean values related to the arithmetic-geometric mean
• Optimal Lehmer mean bounds for the Toader mean
• Asymptotical bounds for complete elliptic integrals of the second kind
• Sharp bounds for the arithmetic-geometric mean
• Sharp bounds for Toader-Qi mean in terms of logarithmic and identric means
• The best bounds for Toader mean in terms of the centroidal and arithmetic means
• Generalizations of the Logarithmic Mean
• Extended Mean Values
• A Monotonicity Property Involving ₃F₂ and Comparisons of the Classical Approximations of Elliptical Arc Length
• An Inequality Involving the Generalized Hypergeometric Function and the Arc Length of an Ellipse
• THE LOG-CONVEXITY OF ANOTHER CLASS OF ONE-PARAMETER MEANS AND ITS APPLICATIONS
• A sharp lower bound for Toader-Qi mean with applications
• On approximating the modified Bessel function of the first kind and Toader-Qi mean
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