More hypergeometric identities related to Ramanujan-type series

DOI10.1007/s11139-012-9442-2zbMath1278.33003arXiv1104.1994OpenAlexW2087927673MaRDI QIDQ385611

Jesús Guillera

Publication date: 2 December 2013

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

Full work available at URL: https://arxiv.org/abs/1104.1994

zbMATH Keywords

hypergeometric identitiesRamanujan seriesWZ-method

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Evaluation of number-theoretic constants (11Y60) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (8)

A hypergeometric version of the modularity of rigid Calabi-Yau manifolds ⋮ Series containing squared central binomial coefficients and alternating harmonic numbers ⋮ Unnamed Item ⋮ Supercongruences related to 3F2(1) involving harmonic numbers ⋮ Ramanujan-like series for \(\frac{1}{\pi}\) involving harmonic numbers ⋮ New series involving harmonic numbers and squared central binomial coefficients ⋮ Bilateral Ramanujan-like series for 1/πk and their congruences ⋮ A WZ proof for a Ramanujan-like series involving cubed binomial coefficients

Cites Work

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• A new Ramanujan-like series for \(1/\pi ^{2}\)
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• Mosaic Supercongruences of Ramanujan Type
• A Matrix form of Ramanujan-type series for $1/\pi$
• Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae
• Ramanujan's Series for 1/π: A Survey
• Rational Functions Certify Combinatorial Identities
• About a New Kind of Ramanujan-Type Series
• Arithmetic hypergeometric series
• Ramanujan-like Series for 1/π²and String Theory

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