A new Ramanujan-like series for \(1/\pi ^{2}\)
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Publication:409036
DOI10.1007/s11139-010-9259-9zbMath1238.33003arXiv1003.1915OpenAlexW1975215860MaRDI QIDQ409036
Publication date: 12 April 2012
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1003.1915
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 (13)
Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ Formulas for generalized two-qubit separability probabilities ⋮ Special Hypergeometric Motives and Their L-Functions: Asai Recognition ⋮ More hypergeometric identities related to Ramanujan-type series ⋮ ON GUILLERA’S -SERIES FOR ⋮ Unnamed Item ⋮ $q$-analogues of several $\pi $-formulas ⋮ Series expansions for \(1/\pi^m\) and \(\pi^m\) ⋮ A summation formula and Ramanujan type series ⋮ New families of double hypergeometric series for constants involving ${1}/{\pi ^2}$ ⋮ q-Analogues of Guillera’s two series for π±2 with convergence rate 27 64 ⋮ Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $ ⋮ Common extension of the Watson and Whipple sums and Ramanujan-likeπ-formulae
Cites Work
- Generators of some Ramanujan formulas
- Hypergeometric series acceleration via the WZ method
- Some binomial series obtained by the WZ-method
- Hypergeometric identities for 10 extended Ramanujan-type series
- A Matrix form of Ramanujan-type series for $1/\pi$
- On Sp_4 modularity of Picard--Fuchs differential equations for Calabi--Yau threefolds (with an appendix by Vicentiu Pasol)
- Ramanujan's Series for 1/π: A Survey
- Rational Functions Certify Combinatorial Identities
- About a New Kind of Ramanujan-Type Series
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