The Bohr-Mollerup Theorem
Click on the image for a detailed proof
In the late 1720s, Euler posed a problem to find a continuous function defined for x>0 that equals n! when x=n, where n is an integer. While Euler succeeded in finding such a Function, now known as the Gamma Function, it is simple to see that it is not the only solution to this problem.
However, the frequent appearance of the Gamma function suggested that it may have a unique status.
Bohr and Mollerup established the necessary conditions in 1922.
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