  Let $F$ be a $p$-adic field, and $G_n$ one of the groups $GL(n,F)$,
$GSO(2n-1,F)$, $GSp(2n,F)$, or $GSO(2(n-1),F)$. Using the mirabolic subgroup or
analogues of it, and related "derivative" functors, we give an asymptotic
expansion of functions in the Whittaker model of generic representations of
$G_n$, with respect to a minimal set of characters of subgroups of the maximal
torus. Denoting by $Z_n$ the center of $G_n$, and by $N_n$ the unipotent
radical of its standard Borel subgroup, we characterize generic representations
occurring in $L^2(Z_nN_n\backslash G_n)$ in terms of these characters. This is
related to a conjecture of Lapid and Mao for general split groups, asserting
that the generic representations occurring in $L^2(Z_nN_n\backslash G_n)$ are
the generic discrete series; we prove it for the group $G_n$.
