The Rogers-Ramanujan continued fraction and a quintic iteration for $1/\pi$

DOI10.1090/S0002-9939-07-09031-4zbMath1141.11059OpenAlexW2034077753MaRDI QIDQ5308105

Heng Huat Chan, Shaun Cooper, Wen-Chin Liaw

Publication date: 27 September 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-07-09031-4

zbMATH Keywords

iterationcontinued fractionsRogers-Ramanujan continued fraction

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Dedekind eta function, Dedekind sums (11F20) Continued fraction calculations (number-theoretic aspects) (11Y65) Elliptic functions and integrals (33E05) Evaluation of number-theoretic constants (11Y60)

Related Items (2)

Hypergeometric series summations and \(\pi\)-formulas ⋮ A summation formula and Ramanujan type series

Cites Work

• Approximating \(\pi\) with Ramanujan's modular equations
• Ramanujan's cubic continued fraction revisited
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
• Continued fractions and modular functions
• A SIMPLE PROOF OF SOME PARTITION FORMULAE OF RAMANUJAN'S
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