Editing Cauchy's integral formula (section)

{{short description|Provides integral formulas for all derivatives of a holomorphic function}}
{{Distinguish|Cauchy's integral theorem|Cauchy formula for repeated integration}}
{{Complex analysis sidebar}}
In mathematics, '''Cauchy's integral formula''', named after [[Augustin-Louis Cauchy]], is a central statement in [[complex analysis]]. It expresses the fact that a [[holomorphic function]] defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorphic function. Cauchy's formula shows that, in complex analysis, "differentiation is equivalent to integration": complex differentiation, like integration, behaves well under [[uniform convergence|uniform limits]] – a result that does not hold in [[real analysis]].