Ramanujan's cubic transformation and generalized modular equation

DOI10.1007/s11425-015-5023-3zbMath1331.33007arXiv1305.6525OpenAlexW2187824586MaRDI QIDQ904650

Yu-Ming Chu, Ying-Qing Song, Miao-Kun Wang

Publication date: 13 January 2016

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.6525

zbMATH Keywords

Gaussian hypergeometric functionmodular functioninfinite productRamanujan's cubic transformationgeneralized modular equation

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (9)

Sharp Landen transformation inequalities for hypergeometric functions, with applications ⋮ Transformation properties of hypergeometric functions and their applications ⋮ Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications ⋮ Extensions of quadratic transformation identities for hypergeometric functions ⋮ 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 \(3^{\ast}\) ⋮ Landen inequalities for Gaussian hypergeometric function ⋮ Precise estimates for the solution of Ramanujan's generalized modular equation ⋮ On the monotonicity and convexity for generalized elliptic integral of the first kind

Uses Software

• DLMF

Cites Work

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• Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions
• Landen inequalities for zero-balanced hypergeometric functions
• Generalized Hersch-Pfluger distortion function and complete elliptic integrals
• Inequalities for the generalized elliptic integrals and modular functions
• Turán type inequalities for generalized complete elliptic integrals
• Explicit Ramanujan-type approximations to pi of higher order
• Monodromy for the hypergeometric function \(_ nF_{n-1}\)
• Generalized elliptic integrals and modular equations
• On an identity of Ramanujan based on the hypergeometric series \(_2F_1(\frac{1}{3},\frac{2}{3};\frac{1}{2};x)\)
• Generalized elliptic integrals
• Partition identities and Ramanujan's modular equations
• The Behavior of the Zero-Balanced Hypergeometric Series p F p-1 Near the Boundary of its Convergence Region
• Singular values, Ramanujan modular equations, and Landen transformations
• Landen inequalities for special functions
• Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
• Asymptotic expansions and inequalities for hypergeometric function
• A Monotonicity Property Involving ₃F₂ and Comparisons of the Classical Approximations of Elliptical Arc Length
• Infinite Products and Normalized Quotients of Hypergeometric Functions
• Inequalities for Zero-Balanced Hypergeometric Functions
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• Duplication inequalities for the ratios of hypergeometric functions
• A Cubic Counterpart of Jacobi's Identity and the AGM

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