  The thermal photon emissivity of the quark-gluon plasma is determined by the
in-medium spectral function of the electromagnetic current at lightlike
kinematics, $\sigma(\omega)$. In this work, we present the first lattice QCD
results on moments of $\sigma(\omega)/\omega$, defined by the weight function
$1/(\omega^2+ (2\pi T n)^2)$, $n\in\mathbb{Z}$ and computed without
encountering an inverse problem. We employ two dynamical flavours of
O($a$)-improved Wilson fermions at a temperature $T\approx 250\;$MeV and
perform the continuum limit. We compare our results for the first two moments
to those obtained dispersively by integrating over the spectral function
computed at weak coupling by Arnold, Moore and Yaffe.
