Express the residue of a function at an isolated singularity as a contour integral in
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This Is Residue Theorem
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In complex analysis, a discipline within mathematics, 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.
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In the removable singularity case the residue is 0.) This says that the limit exists and equals the residue. Conversely, if the limit exists then either the pole is simple, or � is analytic at �0. In both cases the limit equals the residue.
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Hope that helps you a lot
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