  Perturbative expansions in physical applications are generically divergent,
and their physical content can be studied using Borel analysis. Given just a
finite number of terms of such an expansion, this input data can be analyzed in
different ways, leading to vastly different precision for the extrapolation of
the expansion parameter away from its original asymptotic regime. Here we
describe how conformal maps and uniformizing maps can be used, in conjunction
with Pad'e approximants, to increase the precision of the information that can
be extracted from a finite amount of perturbative input data. We also summarize
results from the physical interpretation of Pad'e approximations in terms of
electrostatic potential theory.
