Sharp Stolarsky mean bounds for the complete elliptic integral of the second kind

DOI10.22436/jnsa.010.03.06zbMath1412.33033OpenAlexW2593417122MaRDI QIDQ4631924

Zhen-Hang Yang, Xiao-Hui Zhang, Yu-Ming Chu

Publication date: 23 April 2019

Published in: The Journal of Nonlinear Sciences and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.22436/jnsa.010.03.06

zbMATH Keywords

Gaussian hypergeometric functioncomplete elliptic integralStolarsky mean

Mathematics Subject Classification ID

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

Related Items (15)

Optimal bounds for the generalized Euler-Mascheroni constant ⋮ Monotonicity properties and bounds involving the complete elliptic integrals of the first kind ⋮ Sharp approximations for the complete elliptic integrals of the second kind by one-parameter means ⋮ Optimal convex combination bounds of geometric and Neuman means for Toader-type mean ⋮ Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters ⋮ Some new inequalities of Hermite-Hadamard type for \(s\)-convex functions with applications ⋮ Absolute monotonicity of the accuracy of Ramanujan approximations for perimeter of an ellipse ⋮ Sharp bounds for Sándor-Yang means in terms of quadratic mean ⋮ Landen inequalities for a class of hypergeometric functions with applications ⋮ 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 ⋮ Monotonicity and inequalities involving zero-balanced hypergeometric function

Uses Software

• DLMF

Cites Work

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• Bounds for complete elliptic integrals of the second kind with applications
• On comparison of Stolarsky and Gini means
• Optimal Lehmer mean bounds for the Toader mean
• Some comparison inequalities for Gini and Stolarsky means
• Generalizations of the Logarithmic Mean
• A Monotonicity Property Involving ₃F₂ and Comparisons of the Classical Approximations of Elliptical Arc Length

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