# Integral Question

• Mar 13th 2009, 08:06 PM
VkL
Integral Question
• Mar 13th 2009, 08:08 PM
o_O
• Mar 13th 2009, 10:40 PM
matheagle
That's the definition of the Gamma function...

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

$\Gamma (a)=(a-1)\Gamma (a-1)$ and it's easy to show that
$\Gamma (1)=1$. Thus $\Gamma (2)=1$...., whence $\Gamma (n)=(n-1)!$ where n is an integer.