in mathematics, cauchy's integral formula is a central statement in complex analysis. the statement is named after augustin-louis cauchy. it expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk. the statement also 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 limits – a result denied in real analysis.