Zeros and poles
= Zeros and poles
{wiki}
<Zeros and poles> describe the positive and negative local orders of a meromorphic function. Locally $f(z)=(z-a)^m g(z)$ with $g$ holomorphic and nonzero at $a$: $m>0$ is a zero, $m<0$ is a pole, and $m=0$ is a regular nonzero value. A <simple pole> has $m=-1$, and the <order of vanishing> records $m$.