2011 | OriginalPaper | Chapter
Cauchy’s Residue Theorem
Authors : Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
Published in: An Introduction to Complex Analysis
Publisher: Springer US
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In this lecture, we shall use Laurent’s expansion to establish Cauchy’s Residue Theorem, which has far-reaching applications. In particular, it generalizes Cauchy’s integral formula for derivatives (18.5), so that integrals that have a finite number of isolated singularities inside a contour can be integrated rather easily.