A new one-parameter deformation of the exponential function

Recently, in Kaniadakis (Physica A 296 (2001) 405), a new one-parameter deformation for the exponential function exp({kappa})(x) = (root1 + kappa(2)x(2) + kappax)(1/K); exp({0}) (x) = exp(x), which presents a power-law asymptotic behaviour, has been proposed. The statistical distribution f = Z(-1) exp({kappa})[-beta(E - mu)], has been obtained both as stable stationary state of a proper nonlinear kinetics and as the state which maximizes a new entropic form. In the present contribution, starting from the kappa-algebra and after introducing the h-analysis, we obtain the kappa-exponential exp({kappa}) (x) as the eigenstate of the kappa-derivative and study its main mathematical properties.