integral de Cauchy

The Cauchy integral formula is a fundamental result in complex analysis that expresses the value of a function at a specific point within a region in terms of an integral around the boundary of that region. Imagine drawing a closed curve around a point in a complex plane; the formula states that the value of an analytic function inside this curve can be obtained by integrating the function along the boundary, scaled appropriately. This highlights how information about the function's behavior on the boundary determines its behavior inside, underpinning many advanced results in complex analysis.