The gamma function is
where .
The Gamma function satisfies
Therefore, for integer values of ,
Some values of the gamma function for small arguments are:
and the ever-useful . These values allow a quick calculation of
Where is a natural number and is any fractional value for which the Gamma function's value is known. Since , we have
Which is easy to calculate if we know .
The gamma function has a meromorphic continuation to the entire complex plane with poles at the non-positive integers. It satisfies the product formula
where is Euler's constant, and the functional equation
This entry is a derivative of the gamma function article from PlanetMath. Author of the orginial article: akrowne. History page of the original is here