  We present a formulation which allows heavy quark (c, b, ...) mass effects to
be explicitly incorporated in both the coefficient functions and the splitting
functions in the parton evolution equations. We obtain a consistent procedure
for evolution through the threshold regions for c anti-c and b anti-b
production in deep inelastic scattering, which allows the prediction of the
charm and bottom quark densities. We use the new formulation to perform a
next-to-leading order global parton analysis of deep inelastic and related hard
scattering data. We find that the optimum fit has alpha_S(M_Z^2) = 0.118. We
give predictions for the charm components of the proton structure functions F_2
and F_L as functions of x and Q^2 and, in particular, find that F_2^c is in
good agreement with the existing measurements. We examine the Q^2 range of
validity of the photon-gluon fusion model for c anti-c electroproduction. We
emphasize the value of a precision measurement of the charm component F_2^c at
HERA.
