Taylor coefficient
= Taylor coefficient
{c}
{title2=$a_n=f^{(n)}(z_0)/n!$}
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.