Rewrite $\Gamma(-z)$ in terms of $\Gamma(z)$

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Is it possible to rewrite $\Gamma(-z)$ in terms of $\Gamma(z)$ where $\Gamma(z) = \int^\infty_0 t^{z-1}e^{-t}dt$?

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There is the Euler's reflection formula:, which, together with the functional equation for Gamma ($\Gamma(t+1) = t \Gamma(t)$) gives you want you want.