  Kostant's partition function counts the number of ways to represent a
particular vector (weight) as a nonnegative integral sum of positive roots of a
Lie algebra. For a given weight the $q$-analog of Kostant's partition function
is a polynomial where the coefficient of $q^k$ is the number of ways the weight
can be written as a nonnegative integral sum of exactly $k$ positive roots. In
this paper we determine generating functions for the $q$-analog of Kostant's
partition function when the weight in question is the highest root of the
classical Lie algebras of types $B$, $C$ and $D$.
