linguistic:translation, information:extraction
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: C ∖ { a k } k → C {\displaystyle f\colon \mathbb {C} \smallsetminus \{a_{k}\}_{k}\rightarrow \mathbb {C} } that is holomorphic except at the discrete points { a }, 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.