  We derive semi--analytic expressions for the analytic continuation of the
Mellin transforms of the heavy flavor QCD coefficient functions for neutral
current deep inelastic scattering in leading and next-to-leading order to
complex values of the Mellin variable $N$. These representations are used in
Mellin--space QCD evolution programs to provide fast evaluations of the heavy
flavor contributions to the structure functions $F_2(x,Q^2), F_L(x,Q^2)$ and
$g_1(x,Q^2)$.
