Gamma function
From AoPSWiki
The Gamma function is a generalization of the notion of a factorial to complex numbers.
Definition
For 
, we define 
It is easy to check with integration by parts that 
. This is almost the same as the factorial identity 
, but it is off by one. Since 
, we therefore have 
for nonnegative integers 
. But with the integral, we can define the 
function for other complex numbers. We can then use the identity to extend the Gamma function to a meromorphic function on the full complex plane, with simple poles at the nonpositive integers.
This article is a stub. Help us out by expanding it.
