  The correction to the muon anomalous magnetic moment from the pion-pole
contribution to the hadronic light-by-light scattering is considered using a
description of the pi0 - gamma* - gamma* transition form factor based on the
large-Nc and short-distance properties of QCD. The resulting two-loop integrals
are treated by first performing the angular integration analytically, using the
method of Gegenbauer polynomials, followed by a numerical evaluation of the
remaining two-dimensional integration over the moduli of the Euclidean loop
momenta. The value obtained, a_{mu}(LbyL;pi0) = +5.8 (1.0) x 10^{-10},
disagrees with other recent calculations. In the case of the vector meson
dominance form factor, the result obtained by following the same procedure
reads a_{mu}(LbyL;pi0)_{VMD} = +5.6 x 10^{-10}, and differs only by its overall
sign from the value obtained by previous authors. Inclusion of the eta and
eta-prime poles gives a total value a_{mu}(LbyL;PS) = +8.3 (1.2) x 10^{-10} for
the three pseudoscalar states. This result substantially reduces the difference
between the experimental value of a_{mu} and its theoretical counterpart in the
standard model.
