The **(Euler) gamma function $\Gamma(z)$** is defined by the integral
$$
\Gamma(z) = \int_0^{ \infty } e^{-t} t^{z} \frac{dt}{t}
$$
for Re$(z) > 0$. It satisfies the functional equation
$$ \Gamma(z+1) = z \Gamma(z), $$
and can thus be continued into a meromorphic function on the complex plane, whose poles are at the non-positive integers $\{0,-1,-2,\ldots\}$.

**Knowl status:**

- Review status: reviewed
- Last edited by Nicolas Mascot on 2015-07-29 00:18:41

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- 2015-07-29 00:18:41 by Nicolas Mascot (Reviewed)