quotient of two entire functions Suppose we have a quotient of two entire functions , i.e. $g(z)=\frac{f(z)}{h(z)}$ where $f,h$ are entire functions in complex plane. If $f$ and $h$ have the same set of zeros, what can we tell from the order of these zeros? For example, if we have $f(z_0)=h(z_0)=0$, what can we say about order of $z_0$ as a zero of $h(z)$?
Also, in order for $g$ to be entire, we only need to examine how $g$ behaves at the neighbourhood of $g^{-1}(0)$. In this case, what conditions are needed so that $g$ is entire?

Hint: Expand the functions $f$ and $h$ in Taylor series about $z_0$.
