# Cauchy s integral formula problems

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Sep 15, 2009 · Arbolis, that's the next section after the introduction of Cauchy's Integral Formula. It's called "Differentiability of Cauchy-Type Integrals". It's in any text on Complex Analysis. My favorite is "Basic Complex Analysis" by Marsden and Hoffman. Cauchy's Integral Formula is a fundamental result in complex analysis.It states that if is a subset of the complex plane containing a simple counterclockwise loop and the region bounded by , and is a complex-differentiable function on , then for any in the interior of the region bounded by , Cauchy's integral formula may be used to obtain an expression for the derivative of f (z).Differentiating Eq. (11.30) with respect to z 0, and interchanging the differentiation and the z integration, 3 33 CAUCHY INTEGRAL FORMULA October 27, 2006 REMARK This is a continuous analogue of something we did for homework, for polynomials. PROOF Let C be a contour which wraps around the circle of radius R around z Complex Analysis II: Cauchy Integral Theorems and Formulas The main goals here are major results relating “differentiability” and “integrability”. In a very real sense, it will be these results, along with the Cauchy-Riemann equations, that will make complex analysis so useful in many advanced applications.