  A representation of the amplitude $\gamma^*(q^2)\to\gamma\pi\pi$ is proposed
which combines large $N_c$ chiral resonance Lagrangian modelling with general
unitarity and analyticity properties. The amplitude is constrained from
$\gamma\gamma$ scattering results and $e^+ e^- \to\gamma\pi^0\pi^0$
measurements by the CMD-2 and SND collaborations. As an application, the
contribution of the $\pi\pi+\gamma$ states in the HVP contribution to the muon
$g-2$ are reconsidered, taking into account the effect of the strong $S$-wave
$\pi\pi$ rescattering in a model independent way.
