On quasi-gamma functions

Abstract

We define the quasi-gamma functions as the functions f :]0, infinity[->]0, infinity[ such that f(1) = 1, f(x + 1) = x f(x) for every x > 0, and f is quasi-convex. The main example of quasi-gamma function is the gamma function defined by Euler. We study some properties of the quasi-gamma functions and of the class Q of these functions.