Hypergeometry of the Parbelos

DOI10.1080/00029890.2020.1669403zbMath1440.33004OpenAlexW2996387465MaRDI QIDQ5207474

Jacopo D'Aurizio, Jonathan Sondow, John Maxwell Campbell

Publication date: 2 January 2020

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00029890.2020.1669403

zbMATH Keywords

orthogonal polynomialsgeneralized hypergeometric functionarbelosparbelos

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (7)

Dirichlet series and series with Stirling numbers ⋮ Applications of a hypergeometric identity and Ramanujan-like series ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums ⋮ Moments in Pearson's four-step uniform random walk problem and other applications of very well-poised generalized hypergeometric series ⋮ On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions

Uses Software

• OEIS

Cites Work

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• Irreducible recurrences and representation theorems for \(_ 3F_ 2(1)\)
• Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant
• Ramanujan-like series for \(\frac{1}{\pi}\) involving harmonic numbers
• On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
• Solution of Sondow’s Problem: A Synthetic Proof of the Tangency Property of the Parbelos
• The Parbelos, a Parabolic Analog of the Arbelos
• Reflections on the Arbelos
• Using Fourier-Legendre expansions to derive series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\)

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