Let $f(z)$ be a complex-valued meromorphic function.
If we say that $k$ is "the order of zero or pole" of $f(z)$ the the point $z=z_0$. What does this exactly mean?
As far as I understand it, if the function has no zeros or poles at $z_0$, we should say that $k=0$, and if it has a zero or order $r$, that $k=r$. Is this correct?
And if $f$ has a pole of order $s$, should it be $k=s$ or $k=-r$?0
Thanks in advance for any information