Ramanujan's Eisenstein series and new hypergeometric-like series for \(1/\pi ^{2}\)
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Publication:1041625
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
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 λn 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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