Greek Gamma in a moment generating function

Question

I'm puzzled: what does a Greek $\Gamma$ mean in statistics? For example, here http://en.wikipedia.org/wiki/Weibull_distribution in the definition of the mean.

Answer 1

Usually when you encounter a capital gamma, $\Gamma$, it refers to the gamma function. It is defined as $$\Gamma(z)=\int_{0}^{\infty}t^{z-1}e^{-t}dt$$In the special case where $z\in\mathbb{Z}_+$, $$\Gamma(z)=(z-1)!$$You can check the Wikipedia page to get some more information.