  We propose Asymptotic Expansion Conjectures of the relative
Reshetikhin-Turaev invariants, of the relative Turaev-Viro invariants and of
the discrete Fourier transforms of the quantum 6j-symbols, and prove them for
families of special cases. The significance of these expansions is that we do
not specify the way that the sequence of the colorings converges to the limit.
As a consequence, the terms in the expansion will have to depend on the index
r, but the dependence is in a way that the terms are purely geometric
invariants of the metrics on the underlying manifold and only the metrics vary
with r.
