Gamma function

The gamma function $Γ : ℂ ∖ - ℕ 0 \to ℂ$ is defined for $𝑧 \in ℂ$ with $ℜ (𝑧) > 0$ as fun

Γ (𝑎) = \int \infty 0 𝑥 𝑎 - 1 e - 𝑥 𝑑 𝑥

and otherwise by the analytic continuation.