Función Gamma (Incluye: propiedades)

$$$\Gamma(z) = \int _{0}^{\infty} t^{z - 1}e^{-t} dt$$

Propiedades

$$\Gamma(z + 1) = z \Gamma (z)$$

$$\Gamma \biggl( \frac {1}{2} \biggr) = \sqrt{\pi}$$

$$\Gamma(1 - z) \Gamma(z) = \frac {\pi}{\sin (\pi z)}$$

$$\Gamma(z) \Gamma \biggl( z + \frac{1}{2} \biggr) = 2^{1 - 2z} \sqrt{\pi} \Gamma(2z)$$