  We propose a method to compute the hadronic vacuum polarization function on
the lattice at continuous values of photon momenta bridging between the
spacelike and timelike regions. We provide two independent demonstrations to
show that this method leads to the desired hadronic vacuum polarization
function in Minkowski spacetime. We show with the example of the leading-order
QCD correction to the muon anomalous magnetic moment that this approach can
provide a valuable alternative method for calculations of physical quantities
where the hadronic vacuum polarization function enters.
