  The next-to-leading open charm production in $\gamma p$ collisions is
calculated within the Perturbative Fragmentation Functions formalism, to allow
resummation of $\as\log(\pt^2/m^2)$ terms. In the large $\pt$ region $(\pt >
m)$ the result is consistent with the fixed order NLO calculation, small
discrepancies being found for very large $\pt$ and at the edge of phase space.
The two approaches differ in the definition and the relative contribution of
the direct and resolved terms, but essentially agree on their sum. The
resummation is found to lead to a reduced sensitivity to the choice of the
renormalization/factorization scale.
