  At low Q^2, charm production in deep-inelastic scattering is adequately
described by assuming generation in electroweak boson-light parton scattering
(dominantly boson-gluon fusion) which naturally incorporates the correct
threshold behaviour. At high Q^2 this description is inadequate, since it does
not sum logs in Q^2/m_c^2, and is replaced by the treatment of the charm quark
as a light parton. We show how the problem of going from one description to the
other can be solved in a satisfactory manner to all orders. The key ingredient
is the constraint of matching the evolution of the physical structure function
F_2 order by order in alpha_s(Q^2) in addition to the matching of the value of
F_2 itself. This leads to new expressions for the coefficient functions
associated with the charm parton which are unique in incorporating both the
correct threshold and asymptotic behaviours at each order in perturbation
theory. The use of these improved coefficients lead to an improvement in global
fits and an excellent description of the observed F_2,charm.
