A note on a function involving complete elliptic integrals: monotonicity, convexity, inequalities

DOI10.1007/s10476-015-0201-7zbMath1363.33011OpenAlexW2205845904MaRDI QIDQ343289

Horst Alzer, Kendall C. Richards

Publication date: 25 November 2016

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10476-015-0201-7

zbMATH Keywords

hypergeometric functionselliptic integral

Mathematics Subject Classification ID

Elliptic integrals as hypergeometric functions (33C75)

Related Items (13)

Monotonicity, convexity and inequalities involving the generalized elliptic integrals ⋮ Inequalities for generalized Grötzsch ring function ⋮ Monotonicity, convexity, and inequalities for the generalized elliptic integrals ⋮ Sharp power-type Heronian and Lehmer means inequalities for the complete elliptic integrals ⋮ Discrete approximation of complete \(p\)-elliptic integral of the second kind and its application ⋮ Sharp approximations for complete \(p\)-elliptic integral of the second kind by weighted power means ⋮ A concavity property of the complete elliptic integral of the first kind ⋮ Monotonicity properties and bounds for the complete \(p\)-elliptic integrals ⋮ Sharp generalized Seiffert mean bounds for the Toader mean of order 4 ⋮ On a function involving generalized complete \((p, q)\)-elliptic integrals ⋮ Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind ⋮ A survey for generalized trigonometric and hyperbolic functions ⋮ Convexity and monotonicity for elliptic integrals of the first kind and applications

Cites Work

• Unnamed Item
• Bounds for complete elliptic integrals of the first kind
• Monotonicity theorems and inequalities for the complete elliptic integrals
• Inequalities and bounds for generalized complete elliptic integrals
• Elliptic integral inequalities with applications
• Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
• Inequalities for Zero-Balanced Hypergeometric Functions

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