Bilateral Ramanujan-like series for 1/πk and their congruences

DOI10.1142/S1793042120501018zbMath1469.11030arXiv1908.05123OpenAlexW3049600853MaRDI QIDQ4970761

Jesús Guillera

Publication date: 7 October 2020

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.05123

zbMATH Keywords

supercongruencesWZ methodhypergeometric identitiesbilateral hypergeometric seriesRamanujan-like series for \(1/ \pi^k\)

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Calculation of integer sequences (11Y55)

Related Items (2)

Double series expansions for \(\pi\) ⋮ Series acceleration formulas obtained from experimentally discovered hypergeometric recursions

Uses Software

• MathOverflow

Cites Work

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• More hypergeometric identities related to Ramanujan-type series
• Hypergeometric evaluation identities and supercongruences
• Ramanujan-type supercongruences
• A \(q\)-microscope for supercongruences
• “Divergent” Ramanujan-type supercongruences
• A Matrix form of Ramanujan-type series for $1/\pi$
• Ramanujan's Series for 1/π: A Survey
• Ramanujan-type formulae for $1/\pi$: A second wind?
• WZ pairs and q-analogues of Ramanujan series for 1/π
• RAMANUJAN SERIES WITH A SHIFT
• Arithmetic hypergeometric series
• Ramanujan-like Series for 1/π²and String Theory

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