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Circulation ($\\Gamma$)

The net circulation around the airfoil cross-section. It is defined by the line integral of the velocity field: \Gamma = \oint_C \vec{v} \cdot d\vec{l}$.
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The statement of the theorem

Define the circulation Γ\Gamma around a closed contour CC enclosing the airfoil cross-section C\mathcal{C} as the line integral of the tangential component of the velocity field v⃗\vec{v}: Γ=∮Cv⃗⋅dl⃗=Im(∮Cdz⃗z−z0)\Gamma = \oint_C \vec{v} \cdot d\vec{l} = \text{Im} \left( \oint_C \frac{d\vec{z}}{z-z_0} \right) where z0z_0 is a point outside CC.