A deformed exponential function of two variables - Motivation and applications

Abstract

In the recent development in various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In last two decades, the Tsallis version has found a lot of applications. In this paper, we consider a deformation which has two purposes. First, we introduce it as more general mathematical tool where the Tsallis exponential function is the special case. Then, we prove that it has a lot of interesting properties from mathematical point of view and possibilities in the applications. We emphasize the differential and difference properties of our deformation which are important for the formation and explanation of continuous and discrete models of numerous phenomena. © 2011 American Institute of Physics.