Editing Beta function (section)

==Software implementation==
Even if unavailable directly, the complete and incomplete beta function values can be calculated using functions commonly included in [[spreadsheet]] or [[computer algebra system]]s. 

In [[Microsoft Excel]], for example, the complete beta function can be computed with the <code>[[Gamma_function#Log-gamma function|GammaLn]]</code> function (or <code>special.gammaln</code> in [[Python (programming language)|Python's]] [[SciPy]] package):
:<code>Value = Exp(GammaLn(a) + GammaLn(b) − GammaLn(a + b))</code>

This result follows from the properties [[#Properties|listed above]].

The incomplete beta function cannot be directly computed using such relations and other methods must be used. In [https://www.gnu.org/software/gsl/doc/html/specfunc.html#incomplete-beta-function GNU Octave], it is computed using a [[continued fraction]] expansion.

The incomplete beta function has existing implementation in common languages. For instance, <code>betainc</code> (incomplete beta function) in [[MATLAB]] and [[GNU Octave]], <code>pbeta</code> (probability of beta distribution) in [[R (programming language)|R]] and <code>betainc</code> in [[SymPy]]. In [[SciPy]], <code>special.betainc</code> computes the [[Beta distribution#Cumulative distribution function|regularized incomplete beta function]]—which is, in fact, the cumulative beta distribution. To get the actual incomplete beta function, one can multiply the result of <code>special.betainc</code> by the result returned by the corresponding <code>beta</code> function. In [[Mathematica]], <code>Beta[x, a, b]</code> and <code>BetaRegularized[x, a, b]</code> give <math> \Beta(x;\,a,b) </math> and <math> I_x(a,b) </math>, respectively.