A method for proving Ramanujan's series for \(1/\pi\)

DOI10.1007/s11139-018-0113-9zbMath1440.33019arXiv1807.07394OpenAlexW2964022256MaRDI QIDQ2181590

Jesús Guillera

Publication date: 19 May 2020

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

Full work available at URL: https://arxiv.org/abs/1807.07394

zbMATH Keywords

hypergeometric seriesLegendre's relation

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Generalized hypergeometric series, ({}_pF_q) (33C20) Elliptic functions and integrals (33E05) Elliptic integrals as hypergeometric functions (33C75)

Related Items (7)

q-Analogues of some supercongruences related to Euler numbers ⋮ Harmonic sums from the Kummer theorem ⋮ Unnamed Item ⋮ Factors of certain sums involving central \(q\)-binomial coefficients ⋮ Proof of a rational Ramanujan-type series for 1/π. The fastest one in level 3 ⋮ Proof of Chudnovskys' hypergeometric series for \(1/\pi\) using Weber modular polynomials ⋮ Asymptotic results of the remainder in a Ramanujan series for \(1/\pi \)

Cites Work

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• Eisenstein series and Ramanujan-type series for \(1 / \pi\)
• On WZ-pairs which prove Ramanujan series
• Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions
• Series for 1/π using Legendre's relation
• Ramanujan-type formulae for $1/\pi$: the art of translation
• Ramanujan's Theta Functions
• RAMANUJAN'S CLASS INVARIANT λ_n AND A NEW CLASS OF SERIES FOR 1/π
• Ramanujan-type formulae for $1/\pi$: A second wind?
• Proofs of some Ramanujan series for 1/π using a program due to Zeilberger
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• HYPERGEOMETRIC MODULAR EQUATIONS
• A family of Ramanujan–Orr formulas for 1/π

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