### 5.9.8 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 ensure 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