  We derive a second-order linear differential equation for the leading order
gluon distribution function G(x,Q^2) = xg(x,Q^2) which determines G(x,Q^2)
directly from the proton structure function F_2^p(x,Q^2). This equation is
derived from the leading order DGLAP evolution equation for F_2^p(x,Q^2), and
does not require knowledge of either the individual quark distributions or the
gluon evolution equation. Given an analytic expression that successfully
reproduces the known experimental data for F_2^p(x,Q^2) in a domain
x_min<=x<=x_max, Q_min^2<=Q^2<=Q_max^2 of the Bjorken variable x and the
virtuality Q^2 in deep inelastic scattering, G(x,Q^2) is uniquely determined in
the same domain. We give the general solution and illustrate the method using
the recently proposed Froissart bound type parametrization of F_2^p(x,Q^2) of
E. L. Berger, M. M. Block and C-I. Tan, PRL 98, 242001, (2007). Existing
leading-order gluon distributions based on power-law description of individual
parton distributions agree roughly with the new distributions for x>~10^-3 as
they should, but are much larger for x<~10^-3.
