residueResidue2001-12-28 06:32:152006-10-12 08:15:24Definition\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
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\usepackage{xypic}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 \emph{residue} of $f$ at $a$, and denoted $\operatorname{Res}(f;a)$.