  We derive the first few terms of the asymptotic expansion of the Fredholm
equations for one-dimensional $\kappa$-component fermions with repulsive and
with attractive delta-function interaction in strong and weak coupling regimes.
We thus obtain a highly accurate result for the ground state energy of a
multicomponent Fermi gas with polarization for these regimes. This result
provides a unified description of the ground state properties of the Fermi gas
with higher spin symmetries. However, in contrast to the two-component Fermi
gas, there does not exist a mapping that can unify the two sets of Fredholm
equations as the interacting strength vanishes. Moreover, we find that the
local pair correlation functions shed light on the quantum statistic effects of
the $\kappa$-component interacting fermions. For the balanced spin case with
repulsive interaction, the ground state energy obtained confirms Yang and You's
result [Chin. Phys. Lett. {\bf 28}, 020503 (2011)] that the energy per particle
as $\kappa \to \infty$ is the same as for spinless Bosons.
