Residue Theorem

#Math

$\displaystyle \oint_{C}f(z),\mathrm{d}z=2\pi i\sum_{k = 1}^{n}\text{Res}{z=z{k}}f$

• $\displaystyle C$ is a positively-oriented (counter-clockwise) simple closed contour
• $\displaystyle f$ is analytic on and inside $\displaystyle C$ except at finitely many singularities $\displaystyle z_{1},\ldots z_{n}$ inside $\displaystyle C$
• $\displaystyle \text{Res}{z=z{k}}f$ are the residues of $\displaystyle f$