  A Bessel excursion is a Bessel process that begins at the origin and first
returns there at some given time $T$. We study the distribution of the area
under such an excursion, which recently found application in the context of
laser cooling. The area $A$ scales with the time as $A \sim T^{3/2}$,
independent of the dimension, $d$, but the functional form of the distribution
does depend on $d$. We demonstrate that for $d=1$, the distribution reduces as
expected to the distribution for the area under a Brownian excursion, known as
the Airy distribution, deriving a new expression for the Airy distribution in
the process. We show that the distribution is symmetric in $d-2$, with
nonanalytic behavior at $d=2$. We calculate the first and second moments of the
distribution, as well as a particular fractional moment. We also analyze the
analytic continuation from $d<2$ to $d>2$. In the limit where $d\to 4$ from
below, this analytically continued distribution is described by a one-sided
L\'evy $\alpha$-stable distribution with index $2/3$ and a scale factor
proportional to $[(4-d)T]^{3/2}$.
