A complex analysis newbie here.
Since Mobius transformations are able to cover the Riemann sphere and are automorphisms of the Riemann sphere to itself, is one able to represent any meromorphic complex function on the Riemann sphere via Mobius transformations?
Similarly, given a function on the plane, can I find a "stereographically projected" version of that function that's equivalent to some Mobius transformation on the Riemann sphere? If so, is there a computationally feasible way to find the $a,b,c,d$ in $ \frac{az + b}{cz + d}$?