  We point out that resonance saturation in QCD can be understood in the
large-Nc limit from the mathematical theory of Pade Approximants to meromorphic
functions. These approximants are rational functions which encompass any
saturation with a finite number of resonances as a particular example,
explaining several results which have appeared in the literature. We review the
main properties of Pade Approximants with the help of a toy model for the
<VV-AA> two-point correlator, paying particular attention to the relationship
among the Chiral Expansion, the Operator Product Expansion and the resonance
spectrum. In passing, we also comment on an old proposal made by Migdal in 1977
which has recently attracted much attention in the context of AdS/QCD models.
Finally, we apply the simplest Pade Approximant to the <VV-AA> correlator in
the real case of QCD. The general conclusion is that a rational approximant may
reliably describe a Green's function in the Euclidean, but the same is not true
in the Minkowski regime due to the appearance of unphysical poles and/or
residues.
