This is an old version, view current version.

27.1 Beta

The beta function, $\text{B}(a, b)$, computes the normalizing constant for the beta distribution, and is defined for $a > 0$ and $b > 0$ by $$\text{B}(a,b) \ = \ \int_0^1 u^{a - 1} (1 - u)^{b - 1} \, du \ = \ \frac{\Gamma(a) \, \Gamma(b)}{\Gamma(a+b)} \, ,$$ where $\Gamma(x)$ is the Gamma function.