Solution to a conjecture on the Legendre \(M\)-function with an application to the generalized modulus

DOI10.1016/J.JMAA.2015.06.033zbMath1332.33031OpenAlexW791448652WikidataQ123253669 ScholiaQ123253669MaRDI QIDQ491880

Xiao-Hui Zhang

Publication date: 19 August 2015

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.06.033

zbMATH Keywords

hypergeometric functiongeneralized modulusLegendre \(M\)-function

Mathematics Subject Classification ID

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 ⋮ On the generalized modulus ⋮ Generalized elliptic integrals and generalized Grötzsch function with two parameters ⋮ Shafer-Fink type inequalities for arc lemniscate functions ⋮ Monotonicity and inequalities involving zero-balanced hypergeometric function ⋮ Functional inequalities for the ratio of complete \(p\)-elliptic integrals

Cites Work

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• Generalized elliptic integrals and modular equations
• Generalized elliptic integrals
• Generalized elliptic integrals and the Legendre \(\mathcal M\)-function
• Remarks on generalized elliptic integrals
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• SOME INEQUALITIES FOR THE GENERALIZED GRÖTZSCH FUNCTION
• On hypergeometric functions and generalizations of Legendre's relation

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