After revisiting the properties of generalized trigonometric functions, i.e., the trigonometric function linked to the planar (Fermat) curve $x^p+y^p=1$, using the tool of Keplerian trigonometry, introduced in (Gambini et al.: Monatsh. Math. 195, 55–72, 2021), we present the extension to this class of functions of the Wallis product, discovering connections with the representations of ordinary trigonometric functions by means of infinite products.
The Wallis Products for Fermat Curves / Gambini, Alessandro; Nicoletti, Giorgio; Ritelli, Daniele. - In: VIETNAM JOURNAL OF MATHEMATICS. - ISSN 2305-221X. - (2023), pp. 1-16. [10.1007/s10013-023-00617-3]
The Wallis Products for Fermat Curves
Gambini, Alessandro;
2023
Abstract
After revisiting the properties of generalized trigonometric functions, i.e., the trigonometric function linked to the planar (Fermat) curve $x^p+y^p=1$, using the tool of Keplerian trigonometry, introduced in (Gambini et al.: Monatsh. Math. 195, 55–72, 2021), we present the extension to this class of functions of the Wallis product, discovering connections with the representations of ordinary trigonometric functions by means of infinite products.| File | Dimensione | Formato | |
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