Beta function

Definition

The beta function is a two-variable complex-valued function, defined on $\mathbb {C} \setminus K$ where $K$ is the set of non-positive integers. It's given by the expression:

$B(z,w)={\frac {\Gamma (z)\Gamma (w)}{\Gamma (z+w)}}$

When $z,w$ are both in the right half-plane this is also defined as:

$\int _{0}^{1}(1-t)^{z-1}t^{w-1}\,dt$

External links

• Template:Mathworld