Inequalities for the generalized elliptic integrals and modular functions

DOI10.1016/j.jmaa.2006.09.070zbMath1122.33007OpenAlexW2095090348MaRDI QIDQ878496

Yu-Ming Chu, Xiao-Hui Zhang, Gen-Di Wang

Publication date: 26 April 2007

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.2006.09.070

zbMATH Keywords

Gaussian hypergeometric functions

Mathematics Subject Classification ID

Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05) Elliptic integrals as hypergeometric functions (33C75)

Related Items (26)

Monotonicity and inequalities related to complete elliptic integrals of the second kind ⋮ On generalized complete elliptic integrals and modular functions ⋮ Inequalities and infinite product formula for Ramanujan generalized modular equation function ⋮ A monotonicity theorem for the generalized elliptic integral of the first kind ⋮ Topics in Special Functions III ⋮ 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 ⋮ An inequality for generalized complete elliptic integral ⋮ Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications ⋮ Ramanujan's cubic transformation and generalized modular equation ⋮ A note on Jordan type inequalities for hyperbolic functions ⋮ Generalized Hersch-Pfluger distortion function and complete elliptic integrals ⋮ Inequalities for the generalized elliptic integrals with respect to Hölder means ⋮ 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 ⋮ Monotonicity theorems and inequalities for the Hübner function with applications ⋮ Inequalities and bounds for generalized complete elliptic integrals ⋮ Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion function ⋮ Monotonicity properties and inequalities for the generalized elliptic integral of the first kind ⋮ On a function involving generalized complete \((p, q)\)-elliptic integrals ⋮ Monotonicity and inequalities involving zero-balanced hypergeometric function ⋮ Precise estimates for the solution of Ramanujan's generalized modular equation ⋮ Functional inequalities for generalized complete elliptic integrals with two parameters ⋮ A survey for generalized trigonometric and hyperbolic functions ⋮ On approximating the error function

Cites Work

• A certain quotient of eta-functions found in Ramanujan's lost notebook.
• Some inequalities for the Hersch-Pfluger distortion function
• Generalized elliptic integrals and modular equations
• On an identity of Ramanujan based on the hypergeometric series \(_2F_1(\frac{1}{3},\frac{2}{3};\frac{1}{2};x)\)
• Class number three Ramanujan type series for \(1/\pi\)
• RAMANUJAN'S CLASS INVARIANT λ_n AND A NEW CLASS OF SERIES FOR 1/π
• Ramanujan and hypergeometric and basic hypergeometric series
• Inequalities for Zero-Balanced Hypergeometric Functions
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• A Cubic Counterpart of Jacobi's Identity and the AGM
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