  The moments of the heavy quark-parton distribution functions in a heavy
pseudoscalar meson are calculated from QCD sum rules. Expanding these sum rules
in the inverse heavy quark mass we obtain the heavy-mass limits of the moments.
Comparison with the finite mass results reveals that while the heavy mass
expansion works reasonably well for the $b$ quark, one has to take into account
terms of higher than $(1/m_c)^2$ order for the $c$ quark. This result can
provide a quantitative assessment of $c$ and $b$ quark fragmentation models
based on the heavy-quark mass limit.
