  The line shape of resonances in the overlapping regime is studied by using
the eigenvalues and eigenfunctions of the effective Hamiltonian of an open
quantum system. A generalized expression $\tilde q_k(E)$ for the Fano parameter
of the resonance state $k$ is derived that contains the interaction of the
state $k$ with neighboured states $l\ne k$ via the continuum. It is energy
dependent since the coupling coefficients between the state $k$ and the
continuum show a resonance-like behaviour at the energies of the neighboured
states $l\ne k$. Under certain conditions, the energy dependent $\tilde q_k(E)$
are equivalent to the generalized complex energy independent Fano parameters
that are introduced by Kobayashi et al. in analyzing experimental data.
Long-lived states appear mostly isolated from one another in the cross section,
also when they are overlapped by short-lived resonance states. The $\tilde
q_k(E)$ of narrow resonances allow therefore to study the complicated interplay
between different time scales in the regime of overlapping resonance states by
controlling them as a function of an external parameter.
