# residue

Let $U\subset\mathbb{C}$ be a domain and let $f:U\longrightarrow\mathbb{C}$ be a function represented by a Laurent series

 $f(z):=\sum_{k=-\infty}^{\infty}c_{k}(z-a)^{k}$

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

Title residue Residue 2013-03-22 12:04:56 2013-03-22 12:04:56 djao (24) djao (24) 7 djao (24) Definition msc 30D30 CauchyResidueTheorem