residue

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

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About residue

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. Residues are typically readily computed and, once known, allow the determination of general contour integrals via the residue theorem.

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