The Lambert-Kaniadakis Wκ function

Abstract

In the present work, we introduce the Lambert-Kaniadakis Wk function. It is a generalization of the Lambert W function that solves the equation Wk(z) expk (Wk(z))=z, where expk (z) is the κ-exponential, a generalization of the exponential function proposed by Kaniadakis. Following, the Wk function is used in the definition of the κ-disentropy. Analytical results and numerical calculations of Wk are shown, as well some applications of the κ-disentropy are discussed.