Trigonometric Functions in the p-norm
DOI:
https://doi.org/10.33043/Q5HyzDCBA8Abstract
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 π values.
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Copyright (c) 2026 Sunil Chebolu, Andrew Hatfield, Riley Klette, Christopher Moore, Elizabeth Warden
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