  Closed form analytic expressions are derived for the density profile of a
harmonically trapped noninteracting Fermi gas in $d$ dimensions. Shell
structure effects are included to leading order in 1/N, where $N$ is the number
of particles. These corrections to the local density approximation scale as
$\delta n/n\sim N^{-\alpha}$, where $\alpha=(1+1/d)/2$.
