Cauchy integral formula

The Cauchy integral formula is a fundamental result in complex analysis, a branch of mathematics that studies functions of complex numbers. It states that if you have a holomorphic function (one that is complex differentiable) within a certain region, you can compute the value of this function at any point inside that region by integrating it around the boundary. Essentially, it shows how values of a function are connected over a circular path, emphasizing the importance of surrounding context. This formula is vital for solving problems in physics, engineering, and other fields that utilize complex analysis.