On an identity of Ramanujan based on the hypergeometric series \(_2F_1(\frac{1}{3},\frac{2}{3};\frac{1}{2};x)\)

DOI10.1006/jnth.1997.2212zbMath0911.11024OpenAlexW2020310060MaRDI QIDQ1265670

Li-Chien Shen

Publication date: 5 May 1999

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2212

zbMATH Keywords

identity of Ramanujanclassical elliptic functionscoefficients of the Laurent series expansions

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05)

Related Items

Circular summation of theta functions in Ramanujan's lost notebook, SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES, Inequalities and infinite product formula for Ramanujan generalized modular equation function, Generalized elliptic integrals, Inequalities for the generalized elliptic integrals and modular functions, An addition formula for the Jacobian theta function and its applications, Ramanujan's cubic transformation and generalized modular equation, On the theory of elliptic functions based on ₂𝐹₁(\frac{1}3,\frac{2}3;\frac{1}2;𝑧), The bounds of the solutions to generalized modular equations, Precise estimates for the solution of Ramanujan's generalized modular equation, Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind

Cites Work

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• Some Cubic Modular Identities of Ramanujan
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations