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On Characterizations of the Gamma Function

by Yuan-Yuan Shen (Tunghai University, Taiwan)

This article originally appeared in:
Mathematics Magazine
October, 1995

Subject classification(s): Special Functions
Applicable Course(s): 4.11 Advanced Calc I, II, & Real Analysis

Two properties of the gamma function \(\Gamma (x)\) are \(\Gamma (x) > 0\) and \(\Gamma (x+1) = x \Gamma (x)\) with \(\Gamma (1) = 1\). These properties do not characterize the function, but this can be achieved with the further condition that \(\log(\Gamma x))\) is convex.

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