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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

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