Cauchy's integral formula is a fundamental result in complex analysis that expresses the value of a holomorphic function inside a disk in terms of an integral over the disk's boundary. It highlights the profound implications of analyticity, such as the fact that knowing a function on a boundary uniquely determines it inside the domain.

Cauchy's Integral Formula

Cauchy's integral formula

fundamental result in complex analysis

A holomorphic function is a complex-valued function defined on an open subset of the complex plane that is differentiable at every point in its domain. This differentiability implies that the function is infinitely differentiable and can be represented by a convergent power series within its domain, making it an essential object of study in complex analysis.

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