Some properties of the difference between the Ramanujan constant and beta function

DOI10.1016/J.JMAA.2016.08.043zbMath1350.26024OpenAlexW2507628140MaRDI QIDQ321744

Xiao-Yan Ma, Song-Liang Qiu, Ti-Ren Huang

Publication date: 14 October 2016

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.2016.08.043

zbMATH Keywords

monotonicitybeta functionRiemann zeta functionconvexitypower seriesfunctional inequalitiesRamanujan constant

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Inequalities involving other types of functions (26D07)

Related Items (12)

Monotonicity and inequalities related to complete elliptic integrals of the second kind ⋮ A monotonicity theorem for the generalized elliptic integral of the first kind ⋮ Sharp Landen transformation inequalities for hypergeometric functions, with applications ⋮ Transformation properties of hypergeometric functions and their applications ⋮ Sharp approximations for the generalized elliptic integral of the first kind ⋮ Extensions of quadratic transformation identities for hypergeometric functions ⋮ Monotonicity properties and inequalities related to generalized Grötzsch ring functions ⋮ Monotonicity properties and inequalities for the generalized elliptic integral of the first kind ⋮ Sharp approximations for the Ramanujan constant ⋮ Precise estimates for the solution of Ramanujan's generalized modular equation ⋮ New properties for the Ramanujan \(R\)-function ⋮ Monotonicity, convexity and bounds involving the beta and Ramanujan R-functions

Cites Work

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• Generalized elliptic integrals and modular equations
• Singular values, quasiconformal maps and the Schottky upper bound
• Functional inequalities for the quotients of hypergeometric functions
• Sharp bounds for generalized elliptic integrals of the first kind
• Some monotonicity properties of generalized elliptic integrals with applications
• Asymptotic expansions and inequalities for hypergeometric function
• Some properties of the gamma and psi functions, with applications
• Infinite Products and Normalized Quotients of Hypergeometric Functions
• Inequalities for Zero-Balanced Hypergeometric Functions

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