Asymptotic expansions of truncated hypergeometric series for \(1 / \pi\)

DOI10.1016/j.jmaa.2024.128672MaRDI QIDQ6614368

Chaoping Chen, Lorenz Milla

Publication date: 7 October 2024

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

asymptotic expansionhypergeometric seriesStirling seriesRamanujanChudnovsky algorithmconstant \(\pi\)

Mathematics Subject Classification ID

Discontinuous groups and automorphic forms (11Fxx) Computational number theory (11Yxx) Hypergeometric functions (33Cxx)

Cites Work

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• Modular equations and approximations to \(\pi\).
• An efficient determination of the coefficients in the Chudnovskys' series for \(1/ \pi \)
• Asymptotic expansions for the truncation error in Ramanujan-type series
• Asymptotic results of the remainder in a Ramanujan series for \(1/\pi \)
• An Elementary Proof of Binet's Formula for the Gamma Function
• Eisenstein series and approximations to \(\pi\)

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