Common extension of the Watson and Whipple sums and Ramanujan-likeπ-formulae

DOI10.1080/10652469.2015.1030637zbMath1400.33035OpenAlexW2077711153MaRDI QIDQ5262276

Wenlong Zhang

Publication date: 13 July 2015

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2015.1030637

zbMATH Keywords

Abel's lemma on summation by partsclassical hypergeometric seriesRamanujan-like \(\pi\)-formulaeWatson and Whipple sums

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Numerical summation of series (65B10) Numerical approximation and evaluation of special functions (33F05)

Related Items (7)

Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ Hidden \(q\)-analogues of Ramanujan-like \(\pi\)-series ⋮ Infinite series formulae related to Gauss and Bailey \(_2F_1(\frac{1}{2})\)-sums ⋮ A nonterminating 7F6-series evaluation ⋮ A series evaluation technique based on a modified Abel lemma ⋮ Unnamed Item ⋮ NEW SERIES IDENTITIES FOR ${\frac{1}{\Pi}}$

Cites Work

• Unnamed Item
• A new Ramanujan-like series for \(1/\pi ^{2}\)
• Generators of some Ramanujan formulas
• Hypergeometric identities for 10 extended Ramanujan-type series
• Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $
• RAMANUJAN SERIES UPSIDE-DOWN
• Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae
• Ramanujan's Series for 1/π: A Survey
• Ramanujan-type formulae for $1/\pi$: A second wind?
• Interesting Series Involving the Central Binomial Coefficient

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