The $\beta$ function : Beta

Beta takes as argument two reals a, b.
Beta returns the value of the $\beta$ function at a, b $\in$ $\mathbb {R}$, defined by :

$$\beta$$(x, y) = $$\int_{0}^{1}$$t^x-1(1 - t)^y-1 = $${\frac{{\Gamma(x)*\Gamma(y)}}{{\Gamma(x+y)}}}$$

Remarkable values :

$$\beta$$(1, 1) = 1,    $$\beta$$(n, 1) = $${\frac{{1}}{{n}}}$$,    $$\beta$$(n, 2) = $${\frac{{1}}{{n(n+1)}}}$$

Beta(x,y) is defined for x and y positive reals (to insure the convergence of the integral) and by prolongation for x and y if they are not negative integers.
Input :

Beta(5,2)

Output :

1/30

Input :

Beta(x,y)

Output :

Gamma(x)*Gamma(y)/Gamma(x+y)

Input :

Beta(5.1,2.2)

Output :

0.0242053671402