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
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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
As of this snapshot date, this entry was owned by bloftin.