The Γ function : Gamma

### 2.9.7 The Γ function : `Gamma`

`Gamma` takes as argument a number a.
`Gamma` returns the value of the Γ function in a, defined by :

Γ(x)= | ∫ |
+∞
0
| e−ttx−1dt, if x>0

If x is a positive integer, Γ is computed by applying the recurrence :

Γ(x+1)=x*Γ(x), Γ(1)=1

Hence :

Γ(n+1)=n!

Input :

`Gamma(5)`

Output :

`24`

Input :

`Gamma(0.7)`

Output :

`1.29805533265`

Input :

`Gamma(-0.3)`

Output :

`-4.32685110883`

Indeed : `Gamma(0.7)=-0.3*Gamma(-0.3)`
Input :

`Gamma(-1.3)`

Output :

`3.32834700679`

Indeed `Gamma(0.7)=-0.3*Gamma(-0.3)=(-0.3)*(-1.3)*Gamma(-1.3)`