Beta Function

The beta function, \(\mathrm{B}\), is defined by the integral
\[ \mathrm{B}(a, b) = \int_0^1 t^{a-1} (1-t)^{b-1} \, \mathrm{d}t \]
and is related to the gamma function by
\[ \mathrm{B}(a, b) = \frac{\Gamma(a) \times \Gamma(b)}{\Gamma(a+b)} \]