Bohr-Mollerup theorem: Meaning (information, definition, explanation, facts)

In mathematical analysis, the Bohr-Mollerup theorem, named after the Danish mathematicians Harald Bohr and Johannes Mollerup, who proved it, characterizes the gamma function, defined for x > 0 by

as the only function f on the interval x > 0 that simultaneously has the three properties

• f(1) = 1, and
• and
• logf is a convex function.

That log f is convex is often expressed by saying that f is log-convex, i.e., a log-convex function is one whose logarithm is convex.