Three-Parameter Logarithm and Entropy

Abstract

A three-parameter logarithmic function is derived using the notion of $q$ -analogue and ansatz technique. The derived three-parameter logarithm is shown to be a generalization of the two-parameter logarithmic function of Schwämmle and Tsallis as the latter is the limiting function of the former as the added parameter goes to 1. The inverse of the three-parameter logarithm and other important properties are also proved. A three-parameter entropic function is then defined and is shown to be analytic and hence Lesche-stable, concave, and convex in some ranges of the parameters.