  The MUonE proposal at the CERN SPS consists in extracting the value of the
hadronic vacuum polarization self-energy function (HVP) from its contribution
to the differential cross-section of elastic muon-electron scattering. The HVP
contribution to the muon anomalous magnetic moment can then be obtained from a
weighted integral of the measured HVP self-energy function. This, however,
requires a knowledge of the HVP function in its full integration domain. This
paper discusses a procedure to reconstruct the HVP function in the regions not
directly accessible to measurement. The method is based on the so-called
transfer theorems, due to Flajolet and Odlyzko, which we explain and adapt to
HVP.
