Residue (complex analysis)

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 ${\displaystyle f\colon \mathbb {C} \setminus \{a_{k}\}_{k}\rightarrow \mathbb {C} }$ that is holomorphic except at the discrete points {a_k}_k, even if some of them are essential singularities.) Residues can be computed quite easily and, once known, allow the determination of general contour integrals via the residue theorem.