$O(\alpha_s^2)$ corrections to polarized heavy flavour production at $Q^2\gg m^2$

We present analytic formulae for the heavy flavour coefficient functions for polarized deep inelastic lepton-hadron scattering. The expressions are valid in the kinematical regime $Q^2\gg m^2$ where $Q^2$ and $m^2$ stand for the masses squared of the virtual photon and heavy quark respectively. Using these coefficient functions we have computed the next-to-leading order $\alpha_s$ corrections to polarized charm production at HERA collider energies, where both the electron and proton beams are polarized. We also give an estimate of these corrections at fixed target experiments where the typical $Q^2$ values are much smaller than at HERA.