Monotonicity properties and inequalities for the generalized elliptic integral of the first kind
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Publication:1798983
DOI10.1016/j.jmaa.2018.08.061zbMath1400.33025OpenAlexW2888979815MaRDI QIDQ1798983
Ti-Ren Huang, Song-Liang Qiu, Xiao-Yan Ma
Publication date: 18 October 2018
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.2018.08.061
monotonicityconcavityGaussian hypergeometric functionsharp inequalitiescomplete elliptic integrals of the first kindgeneralized elliptic integrals of the first kindRamanujan constant (or \(R\)-function)
Inequalities for sums, series and integrals (26D15) Elliptic integrals as hypergeometric functions (33C75)
Related Items (19)
Monotonicity properties of Gaussian hypergeometric functions with respect to the parameter ⋮ Approximations for the complete elliptic integral of the second Kind ⋮ A monotonicity theorem for the generalized elliptic integral of the first kind ⋮ Sharp power mean inequalities for the generalized elliptic integral of the first kind ⋮ Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications ⋮ Sharp weighted Hölder mean bounds for the complete elliptic integral of the second kind ⋮ On the absolute monotonicity of generalized elliptic integral of the first kind ⋮ Sharp approximations for complete \(p\)-elliptic integral of the second kind by weighted power means ⋮ Monotonicity properties of generalized elliptic integrals with respect to the parameter ⋮ A note on inequalities for the ratio of zero-balanced hypergeometric functions ⋮ Monotonicity and convexity involving generalized elliptic integral of the first kind ⋮ Monotonicity theorems and inequalities for the Hübner function with applications ⋮ A concavity property of generalized complete elliptic integrals ⋮ On sharp bounds for ratios of 𝑘-balanced hypergeometric functions ⋮ Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind ⋮ On the convexity and concavity of generalized complete elliptic integral of the first kind ⋮ New properties for the Ramanujan \(R\)-function ⋮ Approximations related to the complete \(p\)-elliptic integrals ⋮ Monotonicity, convexity and bounds involving the beta and Ramanujan R-functions
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