  A strong-coupling series expansion for the Green's function and the
extremely-correlated Fermi liquid (ECFL) theory are used to calculate the
moments of the electronic spectral functions of the infinite-U Hubbard model.
Results from these two complementary methods agree very well at both, low
densities, where the ECFL solution is the most accurate, and at high to
intermediate temperatures, where the series converge. We find that a modified
first moment, which underestimates the contributions from the occupied states
and is accessible in the series through the time-dependent Green's function,
best describes the quasiparticle peak location in the strongly-correlated
regime. This is examined by the ECFL results at low temperatures, where it is
shown that the spectral function is largely skewed towards the occupied states.
