Math — Cauchy's Theorem & Residues

\oint_C f(z)\,dz = 0 \;\text{(analytic)}

\oint_C f(z)\,dz = 2\pi i \sum \operatorname{Res}

\operatorname{Res}_{z=a} f = \lim_{z\to a}(z-a)f(z)

f(a) = \frac{1}{2\pi i}\oint_C \frac{f(z)}{z-a}\,dz