  We study the composite fermion construction at and below the single vortex
($L=N$) state of weakly interacting rotating Bose gases, presenting a new
method for handling the large number of derivatives typically occurring via the
Slater determinant. Remarkably, the CF wave function at $L=N$ becomes {\em
exact} in the large $N$ limit, even though this construction is not, {\em a
priori}, expected to work in the low angular momentum regime. This implies an
interesting mathematical identity which may be useful in other contexts.
