q-deformed Gamma function, q-deformed probability distributions and q-deformed statistical physics based on Tsallis's q-exponential function

Abstract

In this paper we consider a new q-number from the expansion of the q-exponential function appearing in Tsallis's non-extensive entropy theory. Using this q-number we define the q-Gamma function and use this to discuss some q-deformed distributions and q-deformed statistical physics.