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Cauchy Integral Formula

  • Definition: Let C be a simple closed piecewise-differentiable curve in the complex plane. Let B be the bounded component of R^2 - C. If F(z) is analytic in an open set omega that contains B and C, then for each point a of B, F(a) = +-(1/(2pi*i)) int_C [F(z)/(z-a)]dz. The sign is + if C is oriented counterclockwise, and - otherwise.

    Source: Topology (second edition) by James R. Munkres

  • Listed under: Field Of Topology, Mathematical Analysis

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