Singular values, Ramanujan modular equations, and Landen transformations

DOI10.4064/SM-121-3-221-230zbMath0872.30010OpenAlexW1023429201MaRDI QIDQ3124219

Matti Vuorinen

Publication date: 15 October 1997

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/216353

zbMATH Keywords

complete elliptic integralLanden transformationmodulus of Grötzsch domainplane quasiconformal maps

Mathematics Subject Classification ID

Quasiconformal mappings in the complex plane (30C62) Elliptic integrals as hypergeometric functions (33C75)

Related Items (21)

Monotonicity and inequalities related to complete elliptic integrals of the second kind ⋮ Inequalities and infinite product formula for Ramanujan generalized modular equation function ⋮ Bounds for quasiconformal distortion functions ⋮ Sharp approximations for the complete elliptic integrals of the second kind by one-parameter means ⋮ Sharp inequalities involving the power mean and complete elliptic integral of the first kind ⋮ Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications ⋮ An optimal power mean inequality for the complete elliptic integrals ⋮ Sharp inequalities for the complete elliptic integrals of the first and second kinds ⋮ Ramanujan's cubic transformation and generalized modular equation ⋮ On Alzer and Qiu's conjecture for complete elliptic integral and inverse hyperbolic tangent function ⋮ Concavity of the complete elliptic integrals of the second kind with respect to Hölder means ⋮ Convexity of the complete elliptic integrals of the first kind with respect to Hölder means ⋮ Landen inequalities for a class of hypergeometric functions with applications ⋮ Inequalities for the Gaussian hypergeometric function ⋮ On the approximation of some special functions in Ramanujan's generalized modular equation with signature \(3^{\ast}\) ⋮ Modular equations and distortion functions ⋮ Monotonicity properties and inequalities related to generalized Grötzsch ring functions ⋮ Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion function ⋮ Precise estimates for the solution of Ramanujan's generalized modular equation ⋮ Sharp bounds for generalized elliptic integrals of the first kind ⋮ Accurate approximations for the complete elliptic integral of the second kind

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