  We compute the three-loop QCD corrections to the massive
quark-anti-quark-photon form factors $F_1$ and $F_2$ in the large-$N_c$ limit.
The analytic results are expressed in terms of Goncharov polylogarithms. This
allows for a straightforward numerical evaluation. We also derive series
expansions, including power suppressed terms, for three kinematic regions
corresponding to small and large invariant masses of the photon momentum, and
small velocities of the heavy quarks.
