RESIDUE THEOREM
Residue theorem Mathematical analysis → Complex analysis Complex analysis t e In complex analysis , the residue theorem , sometimes called Cauchy's residue theorem , is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula . From a geometrical perspective, it can be seen as a special case of the generalized Stokes' theorem . Statement [ edit ] The statement is as follows: Illustration of the setting. Let U be a simply connected open subset of the complex plane containing a finite list of points a 1 , ..., a n , U 0 = U \ { a 1 , …, a n } , and a function f defined and holomorphic on U 0 . Let γ ...