Eisenstein series and approximations to \(\pi\)
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Publication:5954253
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)
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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