Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions

DOI10.1016/j.jmaa.2007.10.011zbMath1139.11023OpenAlexW2068789747MaRDI QIDQ2474942

Nayandeep Deka Baruah, Bruce C. Berndt

Publication date: 6 March 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.10.011

zbMATH Keywords

Eisenstein seriesmodular equationstheta-functions

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Holomorphic modular forms of integral weight (11F11) Elliptic functions and integrals (33E05)

Related Items

Infinite series identities derived from the very well-poised \(\Omega\)-sum, Double series expansions for \(\pi\), Series for 1/π and π with free parameters, Chudnovsky-Ramanujan type formulae for non-compact arithmetic triangle groups, A method for proving Ramanujan's series for \(1/\pi\), GAUSS SUMMATION AND RAMANUJAN-TYPE SERIES FOR 1/π, Eisenstein series and Ramanujan-type series for \(1 / \pi\), Conjectures on the evaluation of alternative modular bases and formulas approximating \(1/\pi\), Extensions of Ramanujan's two formulas for \(1/\pi\), Unnamed Item, Hypergeometric series summations and \(\pi\)-formulas, Unnamed Item, $q$-analogues of several $\pi $-formulas, Ramanujan type \(1/\pi\) approximation formulas, New hypergeometric-like series for $1/\pi^{2}$ arising from Ramanujan’s theory of elliptic functions to alternative base 3, Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae, A summation formula and Ramanujan type series, Ramanujan's Eisenstein series and new hypergeometric-like series for \(1/\pi ^{2}\), Asymptotic results of the remainder in a Ramanujan series for \(1/\pi \), RAMANUJAN SERIES UPSIDE-DOWN, Hypergeometric-like series for \(1 / \pi^2\) arising from Ramanujan's quartic theory of elliptic functions

Cites Work

• Eisenstein series and Ramanujan-type series for \(1 / \pi\)
• Cubic modular equations and new Ramanujan-type series for \(1/\pi\).
• 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
• Some Cubic Modular Identities of Ramanujan
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• A Cubic Counterpart of Jacobi's Identity and the AGM
• Some Eisenstein series identities
• On Ramanujan's quartic theory of elliptic functions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item