  We calculate the $O(\alpha_s^2)$ massive operator matrix elements for the
twist--2 operators, which contribute to the heavy flavor Wilson coefficients in
unpolarized deeply inelastic scattering in the region $Q^2 \gg m^2$. The
calculation has been performed using light--cone expansion techniques. We
confirm an earlier result obtained in \cite{Buza:1995ie}. The calculation is
carried out without using the integration-by-parts method and in Mellin space
using harmonic sums, which lead to a significant compactification of the
analytic results derived previously. The results allow to determine the heavy
flavor Wilson coefficients for $F_2(x,Q^2)$ to $O(\alpha_s^2)$ and for
$F_L(x,Q^2)$ to $O(\alpha_s^3)$ for all but the power suppressed terms $\propto
(m^2/Q^2)^k, k \geq 1$.
