# On Characterizations of the Gamma Function

by Yuan-Yuan Shen (Tunghai University, Taiwan)

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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