The Wallis Products for Fermat Curves
The Wallis Products for Fermat Curves
Abstract After revisiting the properties of generalized trigonometric functions, i.e., the trigonometric function linked to the planar (Fermat) curve $$x^p+y^p=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>x</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>y</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , using the tool of Keplerian trigonometry, introduced in (Gambini et al.: Monatsh. Math. …