The Γ function : Gamma

### 5.9.13 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)