Editing Gamma function (section)

== Practical implementations ==
Unlike many other functions, such as a [[Normal Distribution]], no obvious fast, accurate implementation that is easy to implement for the Gamma Function <math>\Gamma(z)</math> is easily found.  Therefore, it is worth investigating potential solutions.  For the case that speed is more important than accuracy, published tables for <math>\Gamma(z)</math> are easily found in an Internet search, such as the Online Wiley Library.  Such tables may be used with [[linear interpolation]].  Greater accuracy is obtainable with the use of [[Cubic Hermite spline|cubic interpolation]] at the cost of more computational overhead.  Since <math>\Gamma(z)</math> tables are usually published for argument values between 1 and 2, the property <math>\Gamma(z+1) = z\ \Gamma(z)</math> may be used to quickly and easily translate all real values <math>z <1 </math> and <math>z>2</math> into the range <math>1\leq z \leq 2</math>, such that only tabulated values of <math>z</math> between 1 and 2 need be used.<ref>{{cite journal|first1=Helmut|last1=Werner|first2=Robert|last2=Collinge|title=Chebyshev approximations to the Gamma Function|journal=Math. Comput.|year=1961|pages=195–197|volume=15|number=74|doi=10.1090/S0025-5718-61-99220-1 |jstor=2004230}}</ref>

If interpolation tables are not desirable, then the [[Gamma function#Approximations|Lanczos approximation]] mentioned above works well for 1 to 2 digits of accuracy for small, commonly used values of z.  If the Lanczos approximation is not sufficiently accurate, the [[Stirling's approximation#Stirling's formula for the gamma function|Stirling's formula for the Gamma Function]] may be used.