Proof of a rational Ramanujan-type series for 1/π. The fastest one in level 3

DOI10.1142/S1793042120400242zbMath1461.33009arXiv1811.01200OpenAlexW3088232867MaRDI QIDQ5857395

Jesús Guillera

Publication date: 1 April 2021

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.01200

zbMATH Keywords

hypergeometric serieselliptic modular functionsRamanujan-type series for \(1/\pi\)Russell-type modular equations

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05)

Related Items (2)

Chudnovsky-Ramanujan type formulae for non-compact arithmetic triangle groups ⋮ Proof of Chudnovskys' hypergeometric series for \(1/\pi\) using Weber modular polynomials

Cites Work

• Domb's numbers and Ramanujan-Sato type series for \(1/\pi\)
• Legendre polynomials and Ramanujan-type series for \(1/\pi\)
• A method for proving Ramanujan's series for \(1/\pi\)
• Series for 1/π using Legendre's relation
• RAMANUJAN'S CLASS INVARIANT λ_n AND A NEW CLASS OF SERIES FOR 1/π
• Rational analogues of Ramanujan's series for 1/π
• On Russell-Type Modular Equations
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
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