  We recently derived an explicit expression for the gluon distribution
function G(x, Q^2) = xg(x, Q^2) in terms of the proton structure function
F_2^{\gamma p} (x, Q^2) in leading-order (LO) QCD by solving the the LO DGLAP
equation for the Q^2 evolution of F_2^{\gamma p} (x, Q^2) analytically, using a
differential-equation method. We re-derive and extend the results here using a
Laplace-transform technique, and show that the singlet quark structure function
F_S(x,Q^2) can be determined directly in terms of G from the DGLAP gluon
evolution equation. To illustrate the method and check the consistency of
existing LO quark and gluon distributions, we used the published values of the
LO quark distributions from the CTEQ5L and MRST2001LO analyses to form
F_2^{\gamma p} (x, Q^2), and then solved analytically for G(x,Q^2). We find
that the analytic and fitted gluon distributions from MRST2001LO agree well
with each other for all x and Q^2, while those from CTEQ5L differ significantly
from each other for large x values, x>~0.03 - 0.05 at all Q^2. We conclude that
the published CTEQ5L distributions are incompatible in this region. Using a
non-singlet evolution equation, we obtain a sensitive test of quark
distributions which holds in both LO and NLO perturbative QCD. We find in
either case that the CTEQ5 quark distributions satisfy the tests numerically
for small x, but fail the tests for x>~0.03 - 0.05 - their use could
potentially lead to significant shifts in predictions of quantities sensitive
to large x. We encountered no problems with the MRST2001LO distributions or
later CTEQ distributions. We suggest caution in the use of the CTEQ5
distributions.
