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
![{\displaystyle {\begin{matrix}\Gamma (n+f)&=&(n+f-1)\Gamma (n+f-1)\\&=&(n+f-1)(n+f-2)\Gamma (n+f-2)\\&\vdots &\\&=&(n+f-1)(n+f-2)\cdots (f)\Gamma (f)\end{matrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26de95d0ed9cefdb9c278c6934769cb4952a1faf)
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