Residue (complex analysis)

In mathematics, more specifically complex analysis, the residue of a function at a point of its domain 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:\mathbb {C} \smallsetminus \{a_{k}\}_{k}\rightarrow \mathbb {C} } ⁠ that is holomorphic except at the discrete points ⁠ { a k } k {\displaystyle \{a_{k}\}_{k}} ⁠, which may include essential singularities.) Residues are typically readily computed and, once known, allow the determination of general contour integrals via the residue theorem.

Source: Wikipedia — Residue (complex analysis) (CC BY-SA 4.0)