On Alzer and Qiu's conjecture for complete elliptic integral and inverse hyperbolic tangent function
From MaRDI portal
Publication:642727
DOI10.1155/2011/697547zbMath1226.33010OpenAlexW1983560735WikidataQ58654404 ScholiaQ58654404MaRDI QIDQ642727
Yu-Ming Chu, Ye-Fang Qiu, Miao-Kun Wang
Publication date: 27 October 2011
Published in: Abstract and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1155/2011/697547
Related Items
Topics in Special Functions III ⋮ Optimal convex combination bounds of geometric and Neuman means for Toader-type mean ⋮ Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters ⋮ Monotonicity, convexity, and inequalities for the generalized elliptic integrals ⋮ On approximating the Toader mean by other bivariate means ⋮ Notes on the complete elliptic integral of the first kind ⋮ Sharp inequalities for the complete elliptic integrals of the first and second kinds ⋮ Sharp bounds for Sándor-Yang means in terms of quadratic mean ⋮ A necessary and sufficient condition for the convexity of the generalized elliptic integral of the first kind with respect to Hölder mean ⋮ Landen inequalities for a class of hypergeometric functions with applications ⋮ On the approximation of some special functions in Ramanujan's generalized modular equation with signature \(3^{\ast}\) ⋮ On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind ⋮ Sharp bounds for the lemniscatic mean by the one-parameter geometric and quadratic means ⋮ Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion function ⋮ Approximation for the complete elliptic integral of the first kind ⋮ Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means ⋮ Monotonicity and inequalities involving zero-balanced hypergeometric function ⋮ On approximating the quasi-arithmetic mean ⋮ Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean ⋮ Precise estimates for the solution of Ramanujan's generalized modular equation
Cites Work
- Bounds for complete elliptic integrals of the first kind
- Monotonicity theorems and inequalities for the complete elliptic integrals
- Turán type inequalities for generalized complete elliptic integrals
- Distortion functions for plane quasiconformal mappings
- Some inequalities for the Hersch-Pfluger distortion function
- Generalized elliptic integrals and modular equations
- Inequalities for means
- Elliptic integral inequalities with applications
- Functional Inequalities for Complete Elliptic Integrals and Their Ratios
- Singular values, Ramanujan modular equations, and Landen transformations
- Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
- A Monotonicity Property Involving 3F2 and Comparisons of the Classical Approximations of Elliptical Arc Length
- An Inequality Involving the Generalized Hypergeometric Function and the Arc Length of an Ellipse
- Characteristic Subgroups of Lattice-Ordered Groups
- Inequalities for the perimeter of an ellipse
- Unnamed Item
- Unnamed Item
- Unnamed Item
