The $\Gamma$ function : Gamma

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

$$\Gamma$$(x) = $$\int_{0}^{{+\infty}}$$e^-tt^x-1dt, if x > 0

If x is a positive integer, $\Gamma$ is computed by applying the recurrence :

$$\Gamma$$(x + 1) = x*$$\Gamma$$(x),    $$\Gamma$$(1) = 1

Hence :

$$\Gamma$$(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)