  A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional
trap can be described with the lowest Landau-level set of states. In this case,
the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 +
y^2, multiplied by an analytic function P(z) of the single complex variable z=
x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar
description is used for a rapidly rotating anisotropic two-dimensional trap
with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate
wave function psi(x,y) has the form of a complex anisotropic Gaussian with a
phase proportional to xy, multiplied by an analytic function P(zeta), where
zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter
that depends on the trap anisotropy and the rotation frequency. The zeros of
P(zeta) again fix the locations of the vortices. Within the set of lowest
Landau-level states at zero temperature, an anisotropic parabolic density
profile provides an absolute minimum for the energy, with the vortex density
decreasing slowly and anisotropically away from the trap center.
