Let $f$ be a map between compact Riemann surface.
Let $e_P(f)$ be the ramification degree of $f$ at point $P$.
Let $\nu_P(f)$ be the order of $f$ at point $P$, meaning that the lowest term of the Laurent series of $f$ has order $\nu_P(f)$.
I think there is some connection between this two. For example, I feel that when $\nu_P(f)>0$, $e_P(f)=\nu_P(f)$ and when $\nu_P(f)<0$, $e_P(f)=-\nu_P(f)$, am I right?