Let $f$ be an entire function, with $f(0)=f'(0)=0$. Is $g(z)=\frac {f(z)}{z^2}$ for $z \neq 0$, $g(0)=0$ holomorphic?
So, I think not. It seems like $z=0$ is a pole of order 1, because if it seems like if it were $g(z)=\frac {f(z)}{z}$ for $z \neq 0$ and $g(0)=0$ then $g$ was holomorphic. How can I show it isn't holomorphic / or it is?
Thanks in advance!