On lemniscate functions

DOI10.1080/10652469.2012.684054zbMath1273.26020OpenAlexW1990984399MaRDI QIDQ4915312

Edward Neuman

Publication date: 10 April 2013

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

Full work available at URL: https://doi.org/10.1080/10652469.2012.684054

zbMATH Keywords

inequalitieselliptic integralsJacobian elliptic functionslemniscate functionslemniscatic meanarc lemniscate functions

Mathematics Subject Classification ID

Other functions defined by series and integrals (33E20) Elliptic functions and integrals (33E05) Inequalities involving other types of functions (26D07)

Related Items (16)

Sharp bounds for Gauss lemniscate functions and lemniscatic means ⋮ A method to prove inequalities and its applications ⋮ Padé approximant related to inequalities for Gauss lemniscate functions ⋮ Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions ⋮ On approximating the arc lemniscate functions ⋮ Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions ⋮ Sharp exponential type inequalities for the arc lemniscate sine function with applications ⋮ Analytical and asymptotic representations for two sequence related to Gauss’ lemniscate functions ⋮ WILKER AND HUYGENS-TYPE INEQUALITIES INVOLVING GUDERMANNIAN AND THE INVERSE GUDERMANNIAN FUNCTIONS ⋮ Sharp power mean bounds for the lemniscate type means ⋮ Inequalities on generalized trigonometric and hyperbolic functions ⋮ Shafer-Fink type inequalities for arc lemniscate functions ⋮ Lemniscate-like constants and infinite series ⋮ Several Optimal Bounds for Some Means Derived from the Lemniscatic Mean ⋮ Wilker- and Huygens-type inequalities for Jacobian elliptic and theta functions ⋮ Sharp Shafer-Fink type inequalities for Gauss lemniscate functions

Uses Software

• DLMF

Cites Work

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• Inequalities for Jacobian elliptic functions and Gauss lemniscate functions
• On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities
• A New Simple Proof of Wilker's Inequality
• One- and two-sided inequalities for Jacobian elliptic functions and related results
• A weighted and exponential generalization of Wilker's inequality and its applications
• On Wilker-type inequalities
• Algorithms Involving Arithmetic and Geometric Means

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