6.8.13 The Γ function: Gamma
The Gamma function is defined by
If x is a positive integer, Γ is computed by applying the
recurrence:
Hence:
and the Gamma function is used to generalize the factorial (see
Section 6.6.1).
The Gamma command computes the Gamma function.
-
Gamma takes one argument:
a, a number.
- Gamma(a) returns the value Γ(a).
Examples.
-
Input:
Gamma(5)
Output:
- Input:
Gamma(0.7)
Output:
- Input:
Gamma(-0.3)
Output:
Indeed: Gamma(0.7)=-0.3*Gamma(-0.3)
- Input:
Gamma(-1.3)
Output:
Indeed Gamma(0.7)=-0.3*Gamma(-0.3)=(-0.3)*(-1.3)*Gamma(-1.3)