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:

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

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

$\underset{0}{\overset{1}{\int }}(1-t{)}^{z-1}{t}^{w-1}dt$

External links

• Template:Mathworld