Bohr-Mollerup theorem

Let f:++ be a functionMathworldPlanetmath with the following properties:

  1. 1.

    logf(x) is a convex function (i.e. f is logarithmically convex);

  2. 2.

    f(x+1)=xf(x) for all x>0;

  3. 3.


Then f(x)=Γ(x) for all x>0.
That is, the only function satisfying those properties is the gamma functionDlmfDlmfMathworldPlanetmath (restricted to the positive reals.)

Title Bohr-Mollerup theoremMathworldPlanetmath
Canonical name BohrMollerupTheorem
Date of creation 2013-03-22 13:15:10
Last modified on 2013-03-22 13:15:10
Owner Koro (127)
Last modified by Koro (127)
Numerical id 5
Author Koro (127)
Entry type Theorem
Classification msc 33B15
Synonym characterization of the gamma function
Related topic GammaFunction
Related topic LogarithmicallyConvexFunction