  We discuss how the operator product expansion (OPE) can be used to derive
asymptotic expressions for certain integrals. This yields operator matrix
elements (OME's) which determine the matching conditions for $\bar{\rm MS}$
parton densities across heavy flavour thresholds. Then we construct four and
five-flavour densities from a three-flavour set via the AP equation using LO
and NLO splitting functions.
