exponential function trigonometric functions deformed exponential function
Issue Date:
2012
Publisher:
Bulgarian Academy of Sciences - National Committee for Mathematics
Citation:
Mathematica Balkanica New Series, Vol. 26, Fasc 1-2 (2012), 147p-158p
Abstract:
Recently, various generalizations and deformations of the elementary functions were introduced. Since a lot of natural phenomena have both discrete and continual aspects, deformations which are able to express both of them are of particular interest. In this paper, we consider the trigonometry induced by one parameter deformation of the exponential function of two variables eh(x; y) = (1 + hx)y=h (h 2 R n f0g, x 2 C n f¡1=hg, y 2 R). In this manner, we define deformed sine and cosine functions and analyze their various properties. We give series expansions of these functions, formulas which have their similar counterparts in the classical trigonometry, and interesting difference and differential properties.
