Gamma Function

Contents

Definition

Weierstrass's Definition

Γ(z) = e^{-γ z} / z Π_{n = 1 ⋯ ∞}(1 + (z / n))^-1 e^{z / n}, γ ~ 0.577216 is the Euler–Mascheroni constant. Γ(z) Γ(1 - z) = π / sin(π z), Γ(ε - n) = (-1)^{n - 1} Γ(-ε) Γ(1 + ε) / Γ(n + 1 + ε). Γ(z) Γ(z + (1 / 2)) = 2^{1 - 2 z} (π)^{1 / 2} Γ(2 z).

References