Let $f $ be meromorphic in $\mathbb C $ with three simple poles (in $\mathbb C $), that have residues $a_1$, $a_2$ and $a_3$. If $f $ is holomorphic at infinity, what is the form of $f$? Assuming that the zero at infinity is of order $2$, what is the relation between $a_1$, $a_2$ and $a_3$?
I don't understand well what does this exercise ask: I know that under these conditions, $f $ must be a rational function with a zero of order $1$ in $\mathbb C $, namely $$\frac {z-a} {(z-b)(z-c)(z-d)}$$ for some complex numbers. This should be an answer to the first answer, but what is the relation between the residues? Thank you