Cubic modular equations and new Ramanujan-type series for \(1/\pi\).

DOI10.2140/pjm.2000.192.219zbMath1125.11317OpenAlexW2012118008MaRDI QIDQ1568933

Wen-Chin Liaw, Heng Huat Chan

Publication date: 22 June 2000

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

Full work available at URL: https://doi.org/10.2140/pjm.2000.192.219

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Holomorphic modular forms of integral weight (11F11) Elliptic functions and integrals (33E05) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50) Evaluation of number-theoretic constants (11Y60)

Related Items (21)

Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ Ramanujan-type identities for Shimura curves ⋮ Eisenstein series and Ramanujan-type series for \(1 / \pi\) ⋮ INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS ⋮ Schwarzian conditions for linear differential operators with selected differential Galois groups ⋮ On some P-Q modular equations of degree 45 ⋮ Infinite series about harmonic numbers inspired by Ramanujan-like formulae ⋮ Infinite series of convergence rate $-1/8$ suggested by two formulae of Guillera ⋮ Extensions of Ramanujan's two formulas for \(1/\pi\) ⋮ New \(P-Q\) mixed modular equations and their applications ⋮ Schläfli modular equations for generalized Weber functions ⋮ Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions ⋮ Some new modular equations and their applications ⋮ 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 ⋮ Extensions of the classical theorems for very well-poised hypergeometric functions ⋮ New \(_{5}F_{4}\) hypergeometric transformations, three-variable Mahler measures, and formulas for \(1/ \pi \) ⋮ Ramanujan's Eisenstein series and new hypergeometric-like series for \(1/\pi ^{2}\) ⋮ Ramanujan-type \(1/\pi\)-series from bimodular forms ⋮ On certain identities for ratios of theta-functions and some new modular equations of mixed degree ⋮ Hypergeometric-like series for \(1 / \pi^2\) arising from Ramanujan's quartic theory of elliptic functions

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