A series evaluation technique based on a modified Abel lemma
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Publication:5102204
DOI10.55730/1300-0098.3177OpenAlexW4285228690WikidataQ125014842 ScholiaQ125014842MaRDI QIDQ5102204
Marco Cantarini, John Maxwell Campbell
Publication date: 6 September 2022
Published in: Turkish Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.55730/1300-0098.3177
Combinatorial identities, bijective combinatorics (05A19) Generalized hypergeometric series, ({}_pF_q) (33C20)
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Cites Work
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- Legendre functions, spherical rotations, and multiple elliptic integrals
- Evaluation of nonterminating \({}_3F_2\left(\frac{3}{4}\right)\)-series
- Abel's method on summation by parts and theta hypergeometric series
- A generalization of Kummer's identity.
- The Clausenian hypergeometric function \({}_3 F_2\) with unit argument and negative integral parameter differences
- Infinite series identities involving quadratic and cubic harmonic numbers
- Infinite series containing generalized harmonic numbers
- Infinite series identities on harmonic numbers
- On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums
- Harmonic sums from the Kummer theorem
- Lemniscate-like constants and infinite series
- Extensions of Ramanujan's two formulas for \(1/\pi\)
- Abel's lemma on summation by parts and basic hypergeometric series
- A note on Clebsch-Gordan integral, Fourier-Legendre expansions and closed form for hypergeometric series
- Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $
- Telescopic generalizations for two 3 F 2-series identities
- Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae
- Generalizations of classical summation theorems for the series2F1and3F2with applications
- Elliptic integral evaluations of Bessel moments and applications
- The modified Abel lemma on summation by parts and terminating hypergeometric series identities
- A nonterminating 7F6-series evaluation
- A WZ proof for a Ramanujan-like series involving cubed binomial coefficients
- Symbolic computations via Fourier–Legendre expansions and fractional operators
- Common extension of the Watson and Whipple sums and Ramanujan-likeπ-formulae
- Closed Forms: What They Are and Why We Care
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