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]].
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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]].
 
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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: