Γ function

### 6.3.13 Γ function

The Gamma function is 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) 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.

- Gamma takes a, a number.
- Gamma(a) returns the value Γ(a).

#### 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).