Let f be a holomorphic function defined on an open set U ⊆ 𝔠 and let a ∈ U. Then f has derivatives of all orders and the nth derivative at a is given by

where C is a simple, closed, positively oriented, continuous, piecewise-smooth curve in U and a is inside C. When n = 0 this result is known as Cauchy’s integral formula. See also Taylor’s theorem.