I know that the radius of convergence of any power series can be found by simply using the root test, ratio test etc.
I am confused as to how to find the radius of convergence for an analytic $f$ such as
$f(z)=\frac{4}{(z-1)(z+3)}$.
I can't imagine that I would have to find the power series representation of this, find the closed form, and then use one of the convergence tests. I am fairly certain that the radius of convergence would have to do with the singularities at $1$ and $-3$, however, I can't find a formula for the radius of convergence..