On Ramanujan's cubic transformation formula for 2 F 1(1/3, 2/3; 1; z)

DOI10.1017/S0305004198002643zbMath0949.33002OpenAlexW2073454014MaRDI QIDQ4212860

Heng Huat Chan

Publication date: 5 November 1998

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004198002643

zbMATH Keywords

hypergeometric functionstheta functionsAGM

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05)

Related Items (14)

Domb's numbers and Ramanujan-Sato type series for \(1/\pi\) ⋮ Quadratic iterations to ${\pi }$ associated with elliptic functions to the cubic and septic base ⋮ Analytic properties for the honeycomb lattice Green function at the origin ⋮ Some new Eisenstein series containing the Borweins' cubic theta functions and convolution sum \(\sum_{i+4j=n} \sigma (i)\sigma (j)\) ⋮ Explicit evaluations of cubic and quartic theta-functions ⋮ Determinant identities for theta functions ⋮ Some Eisenstein series identities ⋮ Eisenstein series identities involving the Borweins' cubic theta functions ⋮ A new approach to hypergeometric transformation formulas ⋮ Relation between Borweins' cubic theta functions and Ramanujan's Eisenstein series ⋮ Hypergeometric transformation formulas of degrees 3, 7, 11 and 23 ⋮ New hypergeometric-like series for $1/\pi^{2}$ arising from Ramanujan’s theory of elliptic functions to alternative base 3 ⋮ Analogues of the Brent-Salamin algorithm for evaluating \(\pi\) ⋮ Algebraic hypergeometric transformations of modular origin

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