2021/09/28 by Chebolu, Sunil, Hatfield, Andrew, Klette, Riley +2
#26A99 #33E99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2109.14036
Trigonometry is the study of circular functions, which are functions defined on the unit circle x2+y2 =1, where distances are measured using the Euclidean norm. When distances are measured using the Lp-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.