The Wallis products for Fermat curves

DOI10.1007/s10013-023-00617-3MaRDI QIDQ6632153

Giorgio Nicoletti, Alessandro Gambini, Daniele Ritelli

Publication date: 4 November 2024

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

infinite productsgeneralized trigonometric functionsWallis productEulerian functionsKeplerian maps

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Plane and space curves (14H50) Elliptic functions and integrals (33E05) Exponential and trigonometric functions (33B10) Convergence and divergence of infinite products (40A20)

Cites Work

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• Eigenvalues, embeddings and generalised trigonometric functions
• On the doubly periodic functions arising out of the curve \(x^3 + y^3 - 3\alpha xy = 1\).
• On the elliptic function solution of the equation \(x^3 + y^3= 0\).
• Estimates for Wallis' ratio and related functions
• The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion
• Keplerian trigonometry
• Amazing and Aesthetic Aspects of Analysis
• Two Notes on Notation
• A Geometric Interpretation of an Infinite Product for the Lemniscate Constant
• Viète’s Formula, Knar’s Formula, and the Geometry of the Gamma Function
• Squigonometry, Hyperellipses, and Supereggs
• An Introduction to Infinite Products
• Simple accurate balanced asymptotic approximation of Wallis' ratio using Euler-Boole alternating summation
• Squigonometry: Trigonometry in the p-Norm
• Generalized Trigonometric Functions
• Eine Verallgemeinerung der Kreis- und Hyperbelfunktionen

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