7.3.13  Gamma function

The Gamma function is defined by

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 12.1.1).

The Gamma command computes the Gamma function.

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

Examples

Indeed, Γ(0.7)=−0.3·Γ(−0.3).

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

If a=n/d∈ℚ∖ℤ where d>0, then the exact value Γ(a) is computed from Γ(m/d), where 0<2m<d and either m−n or m+n is divisible by d. (If d=2, then the value Γ(a) does not involve another Gamma value.) In particular, this leads to simplification of certain products of Gamma values.