Bohr–Mollerup theorem

The Bohr–Mollerup theorem is a result in mathematical analysis that characterizes the gamma function among other functions. Specifically, it provides a characterization of the gamma function using properties of a specific class of functions. The theorem states that if a function \( f : (0, \infty) \to \mathbb{R} \) satisfies the following conditions: 1. \( f(x) \) is continuous on \( (0, \infty) \).