Since their introduction by Tsallis in the late 1980s, generalized functions have been widely studied and used in different areas of knowledge. However, the non-analyticity in the complex plane of these functions has been an obstacle to expand their applicability. In this context, we present here a brief review of the generalized logarithm and exponential functions and propose a generalization for the latter that makes it analytic in the complex plane. This new generalization opens possibilities for new applications and extensions of this theory.
Keywords:
Generalized exponential function in complex plane; Generalized logarithm function; Analytic exponential function in complex plane; Solution of cubic equations