  The hadronic vacuum polarization contribution to the anomalous magnetic
moment of a lepton is considered as a function of the lepton mass. We show how
the analyticity properties of this function allow for its full reconstruction
when it is only known in a restricted mass region. Assuming that LQCD could
evaluate it in an optimal mass region we show, within the framework of a
phenomenological model, how to reconstruct the function elsewhere, in
particular at the muon mass value.
