residue

Let $U\subset ℂ$ be a domain and let $f:U⟶ℂ$ be a function represented by a Laurent series

$$f(z):=\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}{c}_k{(z-a)}^k$$

centered about $a$. The coefficient $c_{-1}$ of the above Laurent series is called the residue of $f$ at $a$, and denoted $\mathrm{Res}(f;a)$.