Discrete monotonicity of means and its applications

DOI10.1090/proc/13897zbMath1387.33028OpenAlexW2782754602MaRDI QIDQ4604686

Ryo Nishimura

Publication date: 5 March 2018

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13897

zbMATH Keywords

inequalitiescomplete elliptic integralsinfinite product

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05)

Related Items (1)

The t-modification of homogeneous symmetric means concerning complete elliptic integrals

Cites Work

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• Monotonicity theorems and inequalities for the complete elliptic integrals
• New properties of the lemniscate function and its transformation
• Mapping properties, growth, and uniqueness of Vieta (infinite cosine) products
• Inequalities for means
• New inequalities and infinite product formulas for trigonometric and the lemniscate functions
• Inequalities for the ratio of complete elliptic integrals
• Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
• Algorithms Involving Arithmetic and Geometric Means
• The Logarithmic Mean

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