Difference between revisions of "Bohr-Mollerup theorem"
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| − | <strong>[[Bohr-Mollerup theorem|Theorem]]:</strong> (Bohr-Mollerup) The gamma function is the unique function $f$ such that $f(1)=1$, $f(x+1)=xf(x)$ for $x>0$, and $f$ is [[logarithmically convex]]. | + | <strong>[[Bohr-Mollerup theorem|Theorem]]:</strong> (Bohr-Mollerup) The [[gamma function]] is the unique function $f$ such that $f(1)=1$, $f(x+1)=xf(x)$ for $x>0$, and $f$ is [[logarithmically convex]]. |
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<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
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Revision as of 19:38, 6 June 2015
Theorem: (Bohr-Mollerup) The gamma function is the unique function $f$ such that $f(1)=1$, $f(x+1)=xf(x)$ for $x>0$, and $f$ is logarithmically convex.
Proof: █
