Ramanujan's Eisenstein series and new hypergeometric-like series for \(1/\pi ^{2}\)

DOI10.1016/j.jat.2008.04.002zbMath1185.33002OpenAlexW2167548779MaRDI QIDQ1041625

Nayandeep Deka Baruah, Bruce C. Berndt

Publication date: 3 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.jat.2008.04.002

zbMATH Keywords

Eisenstein seriestheta functionsmodular equationshypergeometic series

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 (8)

Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ Chudnovsky-Ramanujan type formulae for non-compact arithmetic triangle groups ⋮ \(\pi \)-formulas implied by Dougall's summation theorem for \(_{5} F _{4}\)-series ⋮ Unnamed Item ⋮ New hypergeometric-like series for $1/\pi^{2}$ arising from Ramanujan’s theory of elliptic functions to alternative base 3 ⋮ A summation formula and Ramanujan type series ⋮ Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $ ⋮ Hypergeometric-like series for \(1 / \pi^2\) arising from Ramanujan's quartic theory of elliptic functions

Cites Work

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• Eisenstein series and Ramanujan-type series for \(1 / \pi\)
• The Apéry numbers, the Almkvist-Zudilin numbers and new series for \(1/\pi\)
• Generators of some Ramanujan formulas
• Ramanujan's singular moduli
• Cubic modular equations and new Ramanujan-type series for \(1/\pi\).
• Class number three Ramanujan type series for \(1/\pi\)
• Some binomial series obtained by the WZ-method
• Domb's numbers and Ramanujan-Sato type series for \(1/\pi\)
• Hypergeometric identities for 10 extended Ramanujan-type series
• Quadratic transformations and Guillera's formulas for \(1/\pi^2\)
• Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions
• RAMANUJAN'S CLASS INVARIANT λ_n AND A NEW CLASS OF SERIES FOR 1/π
• A New Method to Obtain Series for 1/π and 1/π²
• More Ramanujan-type formulae for $ 1/\pi^2$
• Ramanujan-type formulae for $1/\pi$: A second wind?
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
• About a New Kind of Ramanujan-Type Series
• A Class of Conjectured Series Representations for 1/π
• Ramanujan's Lost Notebook
• Ramanujan-type formulae and irrationality measures of some multiples of $ {\pi}$
• On Ramanujan's quartic theory of elliptic functions
• Eisenstein series and approximations to \(\pi\)

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