  We discuss a new technique to evaluate integrals of QCD Green's functions in
the Euclidean based on their Mellin-Barnes representation. We present as a
first application the evaluation of the lowest order Hadronic Vacuum
Polarization (HVP) contribution to the anomalous magnetic moment of the muon
$\frac{1}{2}(g_{\mu}-2)_{\rm\tiny HVP}\equiv a_{\mu}^{\rm HVP}$. It is shown
that with a precise determination of the slope and curvature of the HVP
function at the origin from lattice QCD (LQCD), one can already obtain a result
for $a_{\mu}^{\rm HVP}$ which may serve as a test of the determinations based
on experimental measurements of the $e^+ e^-$ annihilation cross-section into
hadrons.
