  We show how to compute the optical functions when Rydberg Excitons appear,
including the effect of the coherence between the electron-hole pair and the
electromagnetic field. We use the Real Density Matrix Approach (RDMA), which,
combined with Green's function method, enables one to derive analytical
expressions for the optical functions. Choosing the susceptibility, we
performed numerical calculations appropriate to a Cu$_2$0 crystal. The effect
of the coherence is displayed in the line shape. We also examine in details and
explain the dependence of the oscillator strength and the resonance placement
on the state number. We report a good agreement with recently published
experimental data.
