Trigonometric Functions in the p-norm

Mathematics Exchange 2026 Open access

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Authors: Sunil K. Chebolu, Andrew Hatfield, Riley Klette, Christopher Samuel Moore, Elizabeth Warden
DOI: 10.33043/q5hyzdcba8
Cited by: 0
References: 8

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 π values.

Fields of Study & Subjects

Geophysics and Gravity Measurements Mathematical functions and polynomials Iterative Methods for Nonlinear Equations

Publication details

Journal / source
Mathematics Exchange
Publisher
Ball State University Libraries
Volume
16
Issue
1
Pages
2–22
Publication date
3 March 2026
Language
EN