Wilker- and Huygens-type inequalities for Jacobian elliptic and theta functions

DOI10.1080/10652469.2013.838761zbMath1283.26007OpenAlexW1988804636MaRDI QIDQ2874122

Edward Neuman

Publication date: 28 January 2014

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

Full work available at URL: https://doi.org/10.1080/10652469.2013.838761

zbMATH Keywords

Jacobian elliptic functionsbivariate meansWilker- and Huygens-type inequalitiescompletely symmetric elliptic integral of the first kindcircular and hyperbolic functionsclassical theta functions

Mathematics Subject Classification ID

Elliptic functions and integrals (33E05) Inequalities involving other types of functions (26D07)

Related Items (15)

A method to prove inequalities and its applications ⋮ The inverse hyperbolic tangent function and Jacobian sine function ⋮ Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions ⋮ A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions ⋮ WILKER AND HUYGENS-TYPE INEQUALITIES INVOLVING GUDERMANNIAN AND THE INVERSE GUDERMANNIAN FUNCTIONS ⋮ New inequalities for hyperbolic functions based on reparameterization ⋮ New Wilker-type and Huygens-type inequalities ⋮ Some properties of the generalized Jacobian elliptic functions II ⋮ Generalized Gudermannian function ⋮ Generalized Wilker-type inequalities with two parameters ⋮ Sharp inequalities of Mitrinovic-Adamovic type ⋮ An unity of Mitrinovic-Adamovic and Cusa-Huygens inequalities and the analogue for hyperbolic functions ⋮ Some properties of the generalized Jacobian elliptic functions III ⋮ Some properties of the generalized Jacobian elliptic functions ⋮ Refinements of Huygens-Wilker-Lazarovic inequalities via the hyperbolic cosine polynomials

Uses Software

• DLMF

Cites Work

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• Permutation symmetry for theta functions
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• A further refinement of Wilker's inequality
• L'Hospital Rules for Monotonicity and the Wilker-Anglesio Inequality
• One- and two-sided inequalities for Jacobian elliptic functions and related results
• On lemniscate functions
• A weighted and exponential generalization of Wilker's inequality and its applications
• On Wilker-type inequalities
• Analytic Inequalities

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