Sharp bounds for the complete elliptic integral of the first kind in term of the inverse tangent hyperbolic function

DOI10.1007/s10986-024-09644-0MaRDI QIDQ6622512

Zhen-Hang Yang, Jing-Feng Tian

Publication date: 22 October 2024

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

inequalityarithmetic-geometric meancomplete elliptic integral of the first kindinverse tangent hyperbolic function

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Means (26E60) Elliptic functions and integrals (33E05)

Cites Work

• Monotonicity theorems and inequalities for the complete elliptic integrals
• Inequalities for compound mean iterations with logarithmic asymptotes
• Inequalities for means
• Sharp inequalities for the generalized elliptic integrals of the first kind
• On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
• On certain inequalities for means
• Convexity and monotonicity involving the complete elliptic integral of the first kind
• Several absolutely monotonic functions related to the complete elliptic integral of the first kind
• Monotonicity, convexity and inequalities involving the generalized elliptic integrals
• Absolute monotonicity involving the complete elliptic integrals of the first kind with applications
• A sharp lower bound for the complete elliptic integrals of the first kind
• Sharp bounds for the arithmetic-geometric mean
• Sharp bounds for generalized elliptic integrals of the first kind
• Some monotonicity properties of generalized elliptic integrals with applications
• Functional Inequalities for Complete Elliptic Integrals and Their Ratios
• Asymptotic Expansion of the First Elliptic Integral
• Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
• Some Inequalities for the Growth of Elliptic Integrals
• Sharp inequalities for the complete elliptic integral of the first kind
• Landen inequalities for hypergeometric functions
• Monotonicity properties and bounds involving the complete elliptic integrals of the first kind
• A monotonicity property involving the generalized elliptic integral of the first kind
• The best bounds in Wallis’ inequality
• Sharp Estimates for Complete Elliptic Integrals
• Convexity and monotonicity for elliptic integrals of the first kind and applications
• Absolutely monotonic functions involving the complete elliptic integrals of the first kind with applications
• Monotonicity and inequalities involving zero-balanced hypergeometric function
• The Logarithmic Mean
• THE LOG-CONVEXITY OF ANOTHER CLASS OF ONE-PARAMETER MEANS AND ITS APPLICATIONS
• A new upper bound for the complete elliptic integral of the first kind
• A best possible upper bound for the complete elliptic integral of the first kind

This page was built for publication: Sharp bounds for the complete elliptic integral of the first kind in term of the inverse tangent hyperbolic function