Eisenstein series and approximations to \(\pi\)

zbMath0998.33003MaRDI QIDQ5954253

Heng Huat Chan, Bruce C. Berndt

Publication date: 17 February 2002

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Eisenstein seriesapproximations to \(\pi\)singular moduli

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)

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Domb's numbers and Ramanujan-Sato type series for \(1/\pi\) ⋮ Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ Ramanujan-type identities for Shimura curves ⋮ Chudnovsky-Ramanujan type formulae for non-compact arithmetic triangle groups ⋮ Eisenstein series and Ramanujan-type series for \(1 / \pi\) ⋮ Ramanujan–Sato series for $1/\pi $ ⋮ Legendre polynomials and Ramanujan-type series for \(1/\pi\) ⋮ Conjectures on the evaluation of alternative modular bases and formulas approximating \(1/\pi\) ⋮ Ramanujan type \(1/\pi\) approximation formulas ⋮ An efficient determination of the coefficients in the Chudnovskys' series for \(1/ \pi \) ⋮ Ramanujan's Eisenstein series and new hypergeometric-like series for \(1/\pi ^{2}\) ⋮ Asymptotic expansions for the truncation error in Ramanujan-type series ⋮ Ramanujan-type \(1/\pi\)-series from bimodular forms

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