Infinite series identities derived from the very well-poised \(\Omega\)-sum
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Publication:829650
DOI10.1007/s11139-020-00259-wzbMath1466.33004OpenAlexW3042874788MaRDI QIDQ829650
Publication date: 6 May 2021
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-020-00259-w
Apéry seriesbisection seriesDougall's formula for well-poised seriesformula of BBP-typeinfinite series of Ramanujan-type
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INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS ⋮ Infinite series about harmonic numbers inspired by Ramanujan-like formulae ⋮ Summation formulas on harmonic numbers and five central binomial coefficients ⋮ Infinite series of convergence rate $-1/8$ suggested by two formulae of Guillera
Cites Work
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- A new Ramanujan-like series for \(1/\pi ^{2}\)
- \(\pi \)-formulas implied by Dougall's summation theorem for \(_{5} F _{4}\)-series
- Eisenstein series and Ramanujan-type series for \(1 / \pi\)
- New formulae of BBP-type with different moduli
- On the series \(\sum ^{\infty}_{k=1}\binom{2k}{k}^{-1}k^{-n}\) and related sums
- Generators of some Ramanujan formulas
- New \(_{5}F_{4}\) hypergeometric transformations, three-variable Mahler measures, and formulas for \(1/ \pi \)
- The hyperelliptic integrals and \(\pi \)
- Ramanujan's Eisenstein series and new hypergeometric-like series for \(1/\pi ^{2}\)
- A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
- The quest for pi
- Hypergeometric series acceleration via the WZ method
- Cubic modular equations and new Ramanujan-type series for \(1/\pi\).
- Dougall's \(_5F_4\) sum and the WZ algorithm
- \(q\)-series reciprocities and further \(\pi\)-formulae
- Class number three Ramanujan type series for \(1/\pi\)
- Some binomial series obtained by the WZ-method
- Domb's numbers and Ramanujan-Sato type series for \(1/\pi\)
- Faster and faster convergent series for \(\zeta(3)\)
- Hypergeometric identities for 10 extended Ramanujan-type series
- Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions
- Evaluations of binomial series
- Central Binomial Sums, Multiple Clausen Values, and Zeta Values
- Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $
- Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae
- On the rapid computation of various polylogarithmic constants
- RAMANUJAN'S CLASS INVARIANT λn AND A NEW CLASS OF SERIES FOR 1/π
- A New Method to Obtain Series for 1/π and 1/π2
- Experimental Determination of Apéry-like Identities for ς(2n + 2)
- More Ramanujan-type formulae for $ 1/\pi^2$
- Ramanujan-type formulae for $1/\pi$: A second wind?
- More Formulas for π
- Interesting Series Involving the Central Binomial Coefficient
- Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
- Hypergeometric series and the Riemann zeta function
- A Simple Formula for π
- Empirically Determined Apéry-Like Formulae for ζ(4n+3)
- Borwein and Bradley's Apérv-Like Formulae for ζ(4n + 3)
- About a New Kind of Ramanujan-Type Series
- Simultaneous Generation of Koecher and Almkvist-Granville's Apéry-Like Formulae
- Common extension of the Watson and Whipple sums and Ramanujan-likeπ-formulae
- A Class of Conjectured Series Representations for 1/π
- INFINITE SERIES WITH HARMONIC NUMBERS AND CENTRAL BINOMIAL COEFFICIENTS
- Ramanujan's Lost Notebook
- Symmetric functions and the Riemann zeta series
- On Ramanujan's quartic theory of elliptic functions
- Eisenstein series and approximations to \(\pi\)