A q-generalization of Laplace transforms

Abstract

The Laplace transform is generalized by using the q-exponential function ex q [1 + .1 − q/x]1=.1−q/ that emerges from Tsallis’ non-extensive statistical mechanics, and some of its properties are obtained. The usual transform is recovered as a limiting case (q ! 1). The use of the q-Laplace transform is illustrated by establishing a relation between the classical canonical q-partition function and the density of states.