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Suppose U {\displaystyle U} is a domain in C {\displaystyle \mathbb {C} } and f : U → C {\displaystyle f:U\to \mathbb {C} } is a holomorphic function. Suppose γ {\displaystyle \gamma } is the circle of radius r {\displaystyle r} centered at a point z 0 ∈ U {\displaystyle z_{0}\in U} , such that γ {\displaystyle \gamma } lies completely inside U {\displaystyle U} . Then, for any point z ∈ U {\displaystyle z\in U} , we have:
f ( n ) ( z ) = n ! 2 π i ∮ γ f ( ξ ) ( ξ − z ) n + 1 d ξ {\displaystyle f^{(n)}(z)={\frac {n!}{2\pi i}}\oint _{\gamma }{\frac {f(\xi )}{(\xi -z)^{n+1}}}\,d\xi }
