Gamma function
Revision as of 21:43, 21 June 2009 by 5849206328x (talk | contribs)
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.