  We study the applicability of Pade Approximants (PA) to estimate a "sum" of
asymptotic series of the type appearing in QCD. We indicate that one should not
expect PA to converge for positive values of the coupling constant and propose
to use PA for the Borel transform of the series. If the latter has poles on the
positive semiaxis, the Borel integral does not exist, but we point out that the
Cauchy pricipal value integral can exist and that it represents one of the
possible "sums" of the original series, the one that is real on the positive
semiaxis. We mention how this method works for Bjorken sum rule, and study in
detail its application to series appearing for the running coupling constant
for the Richardson static QCD potential. We also indicate that the same method
should work if the Borel transform has branchpoints on the positive semiaxis
and support this claim by a simple numerical experiment.
