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arXiv · 2109.14036

Trigonometric functions in the $p$-norm

Sunil Chebolu·Andrew Hatfield·Riley Klette·Christopher Moore·Elizabeth Warden
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Abstract

Trigonometry is the study of circular functions, which are functions defined on the unit circle $x^2+y^2 =1$, where distances are measured using the Euclidean norm. When distances are measured using the $L_p$-norm, we get generalized trigonometric functions. These are parametrizations of the unit $p$-circle $|x|^p+|y|^p =1$. Investigating these new functions leads to interesting connections involving double angle formulas, norms induced by inner products, Stirling numbers, Bell polynomials, Lagrange inversion, gamma functions, and generalized $\pi$ values.

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Sunil Chebolu, Andrew Hatfield, Riley Klette, Christopher Moore, Elizabeth Warden. 2021-09-28. Trigonometric functions in the $p$-norm. https://arxiv.org/abs/2109.14036

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