Applications of a hypergeometric identity and Ramanujan-like series

DOI10.1007/s40840-023-01627-7OpenAlexW4389564999MaRDI QIDQ6186330

Omran Kouba

Publication date: 9 January 2024

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-023-01627-7

zbMATH Keywords

generalized hypergeometric seriesCatalan numbersharmonic numberscentral binomial coefficient

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Generalized hypergeometric series, ({}_pF_q) (33C20)

Cites Work

• Ramanujan-like series for \(\frac{1}{\pi}\) involving harmonic numbers
• On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums
• Harmonic sums from the Kummer theorem
• Series with harmonic-like numbers and squared binomial coefficients
• On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
• A series evaluation technique based on a modified Abel lemma
• Hypergeometry of the Parbelos
• Using Fourier-Legendre expansions to derive series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\)
• Binomial identities obtained from the Gegenbauer series expansion
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