Convexity and monotonicity for elliptic integrals of the first kind and applications

DOI10.2298/AADM171015001YzbMath1499.33073arXiv1705.05703WikidataQ128063648 ScholiaQ128063648MaRDI QIDQ5028805

Jing-Feng Tian, Zhen-Hang Yang

Publication date: 10 February 2022

Published in: Applicable Analysis and Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.05703

zbMATH Keywords

inequalityhypergeometric functionconvexelliptic integralconcave

Mathematics Subject Classification ID

Convexity of real functions in one variable, generalizations (26A51) Elliptic functions and integrals (33E05)

Related Items (36)

Several absolutely monotonic functions related to the complete elliptic integral of the first kind ⋮ A family of high order approximations of Ramanujan type for perimeter of an ellipse ⋮ Approximations for the complete elliptic integral of the second Kind ⋮ A simple rational approximation to the generalized elliptic integral of the first kind ⋮ Monotonicity rules for the ratio of two Laplace transforms with applications ⋮ Absolute monotonicity involving the complete elliptic integrals of the first kind with applications ⋮ Sharp approximations for the complete elliptic integrals of the second kind by one-parameter means ⋮ A positive answer to Bhatia-Li conjecture on the monotonicity for a new mean in its parameter ⋮ Convexity of ratios of the modified Bessel functions of the first kind with applications ⋮ Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications ⋮ Sharp power-type Heronian and Lehmer means inequalities for the complete elliptic integrals ⋮ Absolute monotonicity of the accuracy of Ramanujan approximations for perimeter of an ellipse ⋮ Optimal bounds for two Seiffert-like means by arithmetic mean and harmonic mean ⋮ On the absolute monotonicity of generalized elliptic integral of the first kind ⋮ Discrete approximation of complete \(p\)-elliptic integral of the second kind and its application ⋮ A best possible upper bound for the complete elliptic integral of the first kind ⋮ Monotonicity of three kinds of functions involving the Gaussian hypergeometric function ⋮ A concavity property of the complete elliptic integral of the first kind ⋮ A sharp lower bound for the complete elliptic integrals of the first kind ⋮ Monotonicity and convexity involving generalized elliptic integral of the first kind ⋮ Bounds for the perimeter of an ellipse in terms of power means ⋮ Sharp bounds for the weighted Hölder mean of the zero-balanced generalized complete elliptic integrals ⋮ Optimal bounds for two Seiffert-like means in exponential type ⋮ Absolutely monotonic functions involving the complete elliptic integrals of the first kind with applications ⋮ New Wilker-type and Huygens-type inequalities ⋮ Sharp bounds for the Toader mean in terms of arithmetic and geometric means ⋮ Sharp generalized Seiffert mean bounds for the Toader mean of order 4 ⋮ A concavity property of generalized complete elliptic integrals ⋮ A new chain of inequalities involving the Toader-Qi, logarithmic and exponential means ⋮ Some Padé approximations and inequalities for the complete elliptic integrals of the first kind ⋮ Answers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kind ⋮ Complete monotonicity of the remainder of the asymptotic series for the ratio of two gamma functions ⋮ On the convexity and concavity of generalized complete elliptic integral of the first kind ⋮ Concavity and bounds involving generalized elliptic integral of the first kind ⋮ Convexity and monotonicity involving the complete elliptic integral of the first kind ⋮ On the monotonicity and convexity for generalized elliptic integral of the first kind

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