Inequalities for Jacobian elliptic functions and Gauss lemniscate functions

DOI10.1016/J.AMC.2012.01.041zbMath1241.33018OpenAlexW2048147897MaRDI QIDQ419523

Edward Neuman

Publication date: 18 May 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2012.01.041

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Elliptic functions and integrals (33E05)

Related Items (16)

A method to prove inequalities and its applications ⋮ Padé approximant related to inequalities for Gauss lemniscate functions ⋮ The inverse hyperbolic tangent function and Jacobian sine function ⋮ Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions ⋮ Sharp bounds for Toader-type means in terms of two-parameter means ⋮ Inequalities involving generalized Jacobian elliptic functions ⋮ On lemniscate functions ⋮ Some properties of the generalized Jacobian elliptic functions II ⋮ Shafer-Fink type inequalities for arc lemniscate functions ⋮ Lemniscate-like constants and infinite series ⋮ Some properties of the generalized Jacobian elliptic functions III ⋮ A note on the Jacobian elliptic sine function ⋮ Some properties of the generalized Jacobian elliptic functions ⋮ Product formulas and inequalities involving θ functions ⋮ 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

• On Jordan type inequalities for hyperbolic functions
• On one-parameter family of bivariate means
• Symmetry in c, d, n of Jacobian elliptic functions
• Inequalities and bounds for elliptic integrals
• On Wilker and Huygens type inequalities
• Product formulas and bounds for Jacobian elliptic functions with applications
• On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities
• One- and two-sided inequalities for Jacobian elliptic functions and related results
• Algorithms Involving Arithmetic and Geometric Means
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