Hypergeometric-like series for \(1 / \pi^2\) arising from Ramanujan's quartic theory of elliptic functions

DOI10.1016/j.jat.2016.01.008zbMath1335.33006OpenAlexW2256181920MaRDI QIDQ259097

Bing He

Publication date: 10 March 2016

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2016.01.008

zbMATH Keywords

hypergeometric functionsEisenstein seriesmodular equationsRamanujan's theta functions

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) (q)-gamma functions, (q)-beta functions and integrals (33D05) Classical hypergeometric functions, ({}_2F_1) (33C05)

Cites Work

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• Eisenstein series and Ramanujan-type series for \(1 / \pi\)
• Ramanujan's Eisenstein series and new hypergeometric-like series for \(1/\pi ^{2}\)
• Cubic modular equations and new Ramanujan-type series for \(1/\pi\).
• Some binomial series obtained by the WZ-method
• Domb's numbers and Ramanujan-Sato type series for \(1/\pi\)
• Quadratic transformations and Guillera's formulas for \(1/\pi^2\)
• Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions
• New hypergeometric-like series for $1/\pi^{2}$ arising from Ramanujan’s theory of elliptic functions to alternative base 3
• RAMANUJAN'S CLASS INVARIANT λ_n AND A NEW CLASS OF SERIES FOR 1/π
• A New Method to Obtain Series for 1/π and 1/π²
• About a New Kind of Ramanujan-Type Series
• On Ramanujan's quartic theory of elliptic functions

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