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- #1

So the poles are at the negative integers and 0. I suspect there must be a formula than since this is an infinite set.

$\Gamma(z) = \dfrac{e^{-\gamma z}}{z}\prod\limits_{n=1}^{\infty}\left(1+\dfrac{z}{n}\right)^{-1}e^{z/n}$

Should I start by logarithmically differentiating?