  A systematic expansion of the induced inclusive gluon radiation associated
with jet production in a dense QCD plasma is derived using a reaction operator
formalism. Analytic expressions for the transverse momentum and light-cone
momentum distributions are derived to all orders in powers of the gluon opacity
of the medium, $N\sigma_g/A=L/\lambda_g$. The reaction operator approach also
leads to a simple algebraic proof of the ``color triviality'' of single
inclusive distributions and to a solvable set of recursion relations. The
analytic solution generalizes previous continuum solutions (BDMPS) for
applications to mesoscopic QCD plasmas. The solution is furthermore not
restricted to uncorrelated geometries and allows for evolving screening scales
as well as the inclusion of finite kinematic constraints. The later is
particularly important because below LHC energies the kinematic constraints
significantly decrease the non-abelian energy loss. Our solution for the
inclusive distribution also generalizes the finite order exclusive (tagged)
distribution case studied previously (GLV1). The form of the analytic solution
is well suited for numerical implementation in Monte Carlo event generators to
enable more accurate calculations of jet quenching in ultra-relativistic
nuclear collisions. Numerical results illustrating the constributions of the
first three orders in opacity are compared to the ``self-quenching'' hard
radiation intensity. A surprising result is that the induced gluon radiation
intensity is dominated by the (quadratic in $L$) first order opacity
contribution for realistic geometries and jet energies in nuclear collisions.
