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