A concavity property of the complete elliptic integral of the first kind

DOI10.1080/10652469.2020.1738423zbMath1447.26013OpenAlexW3011267284MaRDI QIDQ5121004

Kendall C. Richards, Horst Alzer

Publication date: 16 September 2020

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2020.1738423

zbMATH Keywords

concavityinequalitieshypergeometric functioncomplete elliptic integral of the first kind

Mathematics Subject Classification ID

Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05) Inequalities involving other types of functions (26D07)

Related Items (7)

Several absolutely monotonic functions related to the complete elliptic integral of the first kind ⋮ Optimal bounds for Seiffert-like elliptic integral mean by harmonic, geometric, and arithmetic means ⋮ Extended elliptic-type integrals with associated properties and Turán-type inequalities ⋮ On the absolute monotonicity of generalized elliptic integral of the first kind ⋮ A concavity property of generalized complete elliptic integrals ⋮ On the convexity and concavity of generalized complete elliptic integral of the first kind ⋮ Convexity and monotonicity involving the complete elliptic integral of the first kind

Uses Software

• DLMF

Cites Work

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• A note on a function involving complete elliptic integrals: monotonicity, convexity, inequalities
• A power mean inequality involving the complete elliptic integrals
• On the modulus of the Grötzsch ring
• Bounds for complete elliptic integrals of the first kind
• Monotonicity theorems and inequalities for the complete elliptic integrals
• On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
• Monotonicity of the ratio for the complete elliptic integral and Stolarsky mean
• Inequalities for the ratio of complete elliptic integrals
• Functional Inequalities for Complete Elliptic Integrals and Their Ratios
• Monotonicity properties and bounds involving the complete elliptic integrals of the first kind
• Convexity and monotonicity for elliptic integrals of the first kind and applications
• Analytic Inequalities

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