incomplete gamma function

incomplete gamma function

The incomplete gamma function is defined as:

Γ(α, x) = ∫_x^∞ t^α−1e^-tdt, Γ(α) = Γ(α, 0),

where α and x are complex numbers and Re(α) > 0.

The complementary incomplete gamma function is defined as:

γ(α, x) = ∫₀^x t^α−1e^-tdt = Γ(α)−Γ(α, x).