 Residues can be computed quite easily and, once known, allow the determination of general contour integrals via the residue theorem.The residue of a meromorphic function formula_2 at an isolated singularity formula_3, often denoted formula_4 or formula_5, is the unique value formula_6 such that formula_7 has an analytic antiderivative in a punctured disk formula_8.Alternatively, residues can be calculated by finding Laurent series expansions, and one can define the residue as the coefficient "a"−1 of a Laurent series.