  We present analytic formulas for the ground state energy of the
two-dimensional (2D) anyon gas in the quantum limit of a perpendicular magnetic
field (Landau level filling factor \nu_L\le 1). These formulas, for the cases
without and with Coulomb interaction, are obtained by applying the harmonic
potential regularization for vanishing confinement to the harmonically confined
Coulomb anyon gas as in our previous paper for the case without magnetic field.
For the case without Coulomb interaction our analytic expression is exact. It
contains a contribution deriving from the anyon gauge field (characterizing the
fractional statistics by the anyon parameter \nu) and depends on \nu and \nu_L.
For the case with Coulomb interaction we introduce a function, depending on
\nu, \nu_L and the density parameter r_s, which is determined by fitting to the
interpolation formula of Fano and Ortolani in the fractional quantum Hall
regime for spin-polarized fermions in conjunction with results of Yoshioka for
the ground state energy of the 2D Coulomb boson gas in high magnetic fields.
With their dependence on \nu, our formulas apply not only to fermions (\nu=1)
but quite generally to anyons (0\le \nu\le 1).
