On a<b><i>q</i></b>-generalization of circular and hyperbolic functions

Abstract

A generalization of the circular and hyperbolic functions is proposed, based on the Tsallis statistics and on a consistent generalization of the Euler formula. Some properties of the presently proposed q-trigonometry are then investigated. The generalized functions are exact solutions of a nonlinear oscillator. Original circular and hyperbolic relations are recovered as the limiting case.