Taylor coefficient ($a_n=f^{(n)}(z_0)/n!$)

The coefficient of $(z-z_0{)}^n$ in the Taylor series of a function at $z_0$. The displayed formula defines it whenever the indicated derivative exists. For a holomorphic function on a disk, the Cauchy integral formula also gives $a_n=(2\pi i{)}^{-1}\oint f(z)(z-z_0{)}^{-n-1}dz$ along a circle enclosing the center within that disk.