Residue (complex analysis)
COEFFICIENT OF THE TERM OF ORDER −1 IN THE LAURENT EXPANSION OF A FUNCTION HOLOMORPHIC OUTSIDE A POINT, WHOSE VALUE CAN BE EXTRACTED BY A CONTOUR INTEGRAL
Residue of an analytic function; Residue at a pole; Complex residue; Residue (mathematics)
In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function f\colon \mathbb{C} \setminus \{a_k\}_k \rightarrow \mathbb{C} that is holomorphic except at the discrete points {ak}k, even if some of them are essential singularities.