Order of a zero of a holomorphic function
= Order of a zero of a holomorphic function
If a nonzero holomorphic function has expansion
$$
f(z)=(z-z_0)^m g(z),
\qquad g(z_0)\ne0,
$$
then $m$ is the order or multiplicity of its zero at $z_0$.
= Order of a zero of a holomorphic function
If a nonzero holomorphic function has expansion
$$
f(z)=(z-z_0)^m g(z),
\qquad g(z_0)\ne0,
$$
then $m$ is the order or multiplicity of its zero at $z_0$.