Analogues of the Brent-Salamin algorithm for evaluating \(\pi\)

DOI10.1007/S11139-014-9560-0zbMath1369.11108OpenAlexW2064638369MaRDI QIDQ746388

Heng Huat Chan

Publication date: 16 October 2015

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-014-9560-0

zbMATH Keywords

hypergeometric seriestheta serieselliptic integralsmodular equationsBrent-Salamin algorithm

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Elliptic functions and integrals (33E05) Evaluation of number-theoretic constants (11Y60)

Cites Work

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• Fast Multiple-Precision Evaluation of Elementary Functions
• Computation of π Using Arithmetic-Geometric Mean
• On Ramanujan's cubic transformation formula for 2 F 1(1/3, 2/3; 1; z)
• Some Cubic Modular Identities of Ramanujan
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• A Cubic Counterpart of Jacobi's Identity and the AGM
• A simple proof of η(— 1/τ)= η(τ)√τ/i
• On Ramanujan's quartic theory of elliptic functions

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