The β function : Beta

### 2.9.8 The β function : `Beta`

`Beta` takes as argument two reals a,b.
`Beta` returns the value of the β function at a,b ∈ ℝ, defined by :

β(x,y)= | ∫ |
1
0
| tx−1 (1−t)y−1 = |
Γ(x)*Γ(y)
Γ(x+y)

Remarkable values :

β(1,1)=1, β(n,1)= |
1
n
| , β(n,2)= |
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`