# Math Help - Integral Question

1. ## Integral Question

How do you do this?

2. That's the definition of the Gamma function...

$\Gamma (a)=\int_0^{\infty} t^{a-1} e^{-t} dt$.

for a>0. The first thing you learn about this function is that

$\Gamma (a)=(a-1)\Gamma (a-1)$ and it's easy to show that

$\Gamma (1)=1$. Thus $\Gamma (2)=1$...., whence $\Gamma (n)=(n-1)!$ where n is an integer.