New hypergeometric-like series for $1/\pi^{2}$ arising from Ramanujan’s theory of elliptic functions to alternative base 3

DOI10.1090/S0002-9947-2010-05180-3zbMath1213.33009OpenAlexW2069236648MaRDI QIDQ3082378

Narayan Nayak, Nayandeep Deka Baruah

Publication date: 10 March 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2010-05180-3

zbMATH Keywords

hypergeometric seriesEisenstein seriescubic theta functionscubic modular equations

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Class numbers, class groups, discriminants (11R29) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05)

Related Items (2)

A summation formula and Ramanujan type series ⋮ Hypergeometric-like series for \(1 / \pi^2\) arising from Ramanujan's quartic theory of elliptic functions

Cites Work

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• Ramanujan's Eisenstein series and new hypergeometric-like series for \(1/\pi ^{2}\)
• Cubic modular equations and new Ramanujan-type series for \(1/\pi\).
• Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions
• Ramanujan's Series for 1/π: A Survey
• RAMANUJAN'S CLASS INVARIANT λ_n AND A NEW CLASS OF SERIES FOR 1/π
• On Ramanujan's cubic transformation formula for 2 F 1(1/3, 2/3; 1; z)
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• A Cubic Counterpart of Jacobi's Identity and the AGM

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