Padé approximant related to inequalities for Gauss lemniscate functions

DOI10.1186/s13660-016-1262-2zbMath1351.26033OpenAlexW2559847910WikidataQ59466087 ScholiaQ59466087MaRDI QIDQ2374193

Chao-Ping Chen, Juan Liu

Publication date: 14 December 2016

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

Full work available at URL: https://doi.org/10.1186/s13660-016-1262-2

zbMATH Keywords

approximationinequalitylemniscate functions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inequalities involving other types of functions (26D07)

Related Items (8)

A method to prove inequalities and its applications ⋮ New bounds and asymptotic expansions for the volume of the unit ball in \(\mathbb{R}^n\) based on Padé approximation ⋮ Padé approximant related to inequalities involving the constant \(e\) and a generalized Carleman-type inequality ⋮ A constructive method for approximating trigonometric functions and their integrals ⋮ Sharp bounds for the lemniscatic mean by the one-parameter geometric and quadratic means ⋮ Lemniscate-like constants and infinite series ⋮ Monotonicity and inequalities related to the generalized inverse lemniscate functions ⋮ Padé approximant related to the Wallis formula

Cites Work

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• Refinements of Jordan-Stečkin and Becker-Stark inequalities
• New representations of Padé, Padé-type, and partial Padé approximants
• Refinements of certain hyperbolic inequalities via the Padé approximation method
• Estimates for the arctangent function related to Shafer's inequality
• On a quadratic estimate of Shafer
• Wilker and Huygens type inequalities for the Lemniscate functions
• Wilker and Huygens type inequalities for the Lemniscate functions, II
• On lemniscate functions
• Algorithms Involving Arithmetic and Geometric Means
• On Quadratic Approximation

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