26.1 Beta

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