Bohr-Mollerup theorem
= Bohr-Mollerup theorem
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On $(0,\infty)$, the <Gamma function> is the unique positive <function> $f$ satisfying $f(1)=1$, $f(x+1)=xf(x)$, and the condition that $\log f$ is a <convex function>. This last condition concerns the <natural logarithm> of $f$, rather than $f$ itself, and removes the interpolation freedom left by the <Gamma function recurrence>.https://dlmf.nist.gov/5.5#iv[NIST DLMF, Section 5.5(iv): Bohr-Mollerup theorem]{ref}