Editing Residue (complex analysis) (section)

{{Short description|Attribute of a mathematical function}}
{{Complex analysis sidebar}}
In [[mathematics]], more specifically [[complex analysis]], the '''residue''' is a [[complex number]] proportional to the [[Contour integration|contour integral]] of a [[meromorphic function]] along a path enclosing one of its [[mathematical singularity|singularities]]. (More generally, residues can be calculated for any function <math> f\colon \mathbb{C} \setminus \{a_k\}_k \rightarrow \mathbb{C}</math> that is [[Holomorphic function|holomorphic]] except at the discrete points {''a''<sub>''k''</sub>}<sub>''k''</sub>, even if some of them are [[essential singularity|essential singularities]].) Residues can be computed quite easily and, once known, allow the determination of general contour integrals via the [[residue theorem]].