On the generalized modulus

DOI10.1007/s11139-015-9746-0zbMath1375.33009OpenAlexW2234460914MaRDI QIDQ1676056

Xiao-Hui Zhang

Publication date: 3 November 2017

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-015-9746-0

zbMATH Keywords

monotonicityconvexityfunctional inequalitiesgeneralized modulus

Mathematics Subject Classification ID

Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05)

Related Items (7)

Inequalities and infinite product formula for Ramanujan generalized modular equation function ⋮ Inequalities for generalized Grötzsch ring function ⋮ Generalized elliptic integrals and generalized Grötzsch function with two parameters ⋮ On the approximation of some special functions in Ramanujan's generalized modular equation with signature \(3^{\ast}\) ⋮ Monotonicity properties and inequalities related to generalized Grötzsch ring functions ⋮ Shafer-Fink type inequalities for arc lemniscate functions ⋮ Functional inequalities for the ratio of complete \(p\)-elliptic integrals

Uses Software

• DLMF

Cites Work

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• Solution to a conjecture on the Legendre \(M\)-function with an application to the generalized modulus
• On the modulus of the Grötzsch ring
• Generalized elliptic integrals and modular equations
• Functional inequalities for the quotients of hypergeometric functions
• Generalized elliptic integrals
• Generalized convexity and inequalities involving special functions
• Concavity with respect to Hölder means involving the generalized Grötzsch function
• Generalized elliptic integrals and the Legendre \(\mathcal M\)-function
• On Moduli of Rings and Quadrilaterals: Algorithms and Experiments
• Remarks on generalized elliptic integrals
• Infinite Products and Normalized Quotients of Hypergeometric Functions
• Ramanujan's Theories of Elliptic Functions to Alternative Bases

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