Beta function

### 7.3.16 Beta function

The β function is defined by

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

This is defined for x and y positive reals (to ensure the convergence of the integral) and by extension for x and y if they are not negative integers. Notably, β(1,1)=1, β(n,1)=1/n and β(n,2)=1/n(n+1).

The Beta command computes the β function.

- Beta takes two arguments: a and b, real numbers.
- Beta(a,b) returns the value of the β(a,b).

#### Examples

Beta(5,2)

1
30

Beta(x,y)

Γ | ⎛ ⎝ | x | ⎞ ⎠ | Γ | ⎛ ⎝ | y | ⎞ ⎠
Γ | ⎛ ⎝ | x+y | ⎞ ⎠

Beta(5.1,2.2)

0.0242053671402 |  |  |  |  |  |  |  |  |  |