A series evaluation technique based on a modified Abel lemma

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

zbMATH Keywords

generalized hypergeometric functionsclosed formKummer's identityAbel lemma

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (3)

Applications of a hypergeometric identity and Ramanujan-like series ⋮ Gosper's strange series: a new, simplified proof and generalizations ⋮ Unnamed Item

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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