  We study a problem of Jeong and Taniguchi asking to find all rational maps
which are Ahlfors functions. We prove that the rational Ahlfors functions of
degree two are characterized by having positive residues at their poles. We
then show that this characterization does not generalize to higher degrees,
with the help of a numerical method for the computation of analytic capacity.
We also provide examples of rational Ahlfors functions in all degrees.
