PL relations of radial modes of AGB and RGB stars observed with Kepler (blue pluses) and OGLE (black symbols). The proxy of the luminosity is derived from the estimate . Each sequence, corresponding to a fixed radial order, is fitted with the model provided by Eq. (10) (gray solid lines). The thick red line, provided by ν_max ≃ 1/P, indicates the location of ratio n_max = ν_max/Δν − ε_obs. The blue dashed line corresponds to the tip of the RGB. The horizontal green dot-dashed lines shows the region where the oscillation regime changes.