  We consider a doped Mott insulator in the large dimensionality limit within
both the recently developed Extremely Correlated Fermi Liquid (ECFL) theory and
the Dynamical Mean-Field Theory (DMFT). We show that the general structure of
the ECFL sheds light on the rich frequency-dependence of the DMFT self-energy.
Using the leading Fermi-liquid form of the two key auxiliary functions
introduced in the ECFL theory, we obtain an analytical ansatz which provides a
good quantitative description of the DMFT self-energy down to hole doping level
0.2. In particular, the deviation from Fermi-liquid behavior and the
corresponding particle-hole asymmetry developing at a low energy scale are well
reproduced by this ansatz. The DMFT being exact at large dimensionality, our
study also provides a benchmark of the ECFL in this limit. We find that the
main features of the self-energy and spectral line-shape are well reproduced by
the ECFL calculations in the O(\lambda^2) `minimal scheme', for not too low
doping level >0.3. The DMFT calculations reported here are performed using a
state-of-the-art numerical renormalization-group impurity solver, which yields
accurate results down to an unprecedentedly small doping level 0.001.
