Previous Up Next

6.3.13  Γ function

The Gamma function is defined by

  Γ(x)=
+∞


0
ettx−1dt,  if  x>0.

If x is a positive integer, Γ is computed by applying the recurrence Γ(x+1)=x Γ(x) with Γ(1)=1. Hence Γ(n+1)=n! which is used to generalize the factorial (see Section 11.1.1).

The Gamma command computes the Gamma function.

Examples

Gamma(5)
     
24           
Gamma(0.7)
     
1.29805533265           
Gamma(-0.3)
     
−4.32685110883           

Indeed, Γ(0.7)=−0.3·Γ(−0.3).

Gamma(-1.3)
     
3.32834700679           

Indeed, Γ(0.7)=−0.3·Γ(−0.3)=−0.3·(−1.3)·Γ(−1.3).


Previous Up Next