Bohr–Mollerup theorem
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In mathematical analysis, the Bohr–Mollerup theorem is named after the Danish mathematicians Harald Bohr and Johannes Mollerup, who proved it. The theorem 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.
[edit] References
- Eric W. Weisstein, Bohr-Mollerup Theorem at MathWorld.
- Proof of Bohr-Mollerup theorem on PlanetMath
- Proof of Bohr-Mollerup theorem on PlanetMath
