Cauchy's integral formula is a theorem in complex analysis which relates a holomorphic function defined on a disk to its values on the edge of the disk, and gives a formula for f(a) for every a within the disk, or outside if the function is holomorphic everywhere.

f^{(n)}(a)=\dfrac{n!}{2\pi i}\oint_\gamma\frac{f(z)}{(z-a)^{n+1}}dz

If n=0 , this simplifies to

f(a)=\dfrac{1}{2\pi i}\oint_\gamma\frac{f(z)}{z-a}dz

See also