  A recently developed efficient recursive approach for analytically
calculating the short-time evolution of the one-particle propagator to
extremely high orders is applied here for numerically studying the
thermodynamical and dynamical properties of a rotating ideal Bose gas of
$^{87}$Rb atoms in an anharmonic trap. At first, the one-particle energy
spectrum of the system is obtained by diagonalizing the discretized short-time
propagator. Using this, many-boson properties such as the condensation
temperature, the ground-state occupancy, density profiles, and time-of-flight
absorption pictures are calculated for varying rotation frequencies. The
obtained results improve previous semiclassical calculations, in particular for
smaller particle numbers. Furthermore, we find that typical time scales for a
free expansion are increased by an order of magnitude for the delicate regime
of both critical and overcritical rotation.
