The Rq,Q function and the q-Diode

Abstract

Two generalizations of the Lambert W function were recently discussed in the literature, the Lambert–Tsallis​ Wq and the Lambert–Kaniadakis Wk functions. Both of them have been used in interesting problems in physics and engineering. In this direction, the present work introduces a third generalization, the new function Rq,Q(z), solution of the equation Rq,Q(z) X Q exp (Rq,Q(z)) = z. It is shown this new function can be used to construct new disentropy as well it is used to model the q-diode, a hypothetical electronic device whose electrical current depends q-exponentially on the voltage between its terminals. Analytical and numerical results for the new disentropy and q-diode are provided.