  We derive an approximate analytic formula for the ground-state energy of the
charged anyon gas. Our approach is based on the harmonically confined
two-dimensional (2D) Coulomb anyon gas and a regularization procedure for
vanishing confinement. To take into account the fractional statistics and
Coulomb interaction we introduce a function, which depends on both the
statistics and density parameters (nu and r_s, respectively). We determine this
function by fitting to the ground state energies of the classical electron
crystal at very large r_s (the 2D Wigner crystal), and to the Hartree-Fock (HF)
energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas
at very small r_s. The latter is calculated by use of the Bogoliubov
approximation. Applied to the boson system (nu=0) our results are very close to
recent results from Monte Carlo (MC) calculations. For spin-polarized electron
systems (nu=1) our comparison leads to a critical judgment concerning the
density range, to which the HF approximation and MC simulations apply. In
dependence on nu, our analytic formula yields ground-state energies, which
monotonously increase from the bosonic to the fermionic side if r_s > 1. For
r_s leq 1 it shows a nonmonotonous behavior indicating a breakdown of the
assumed continuous transformation of bosons into fermions by variation of the
parameter nu .
