LF of Hβ+[O III]λλ4960, 5008 for the different redshift ranges considered. For the fit of the LF, we limited the flux bins to the depth of (Wold et al. 2025), and discarded bins are displayed with a cross. We added previous studies of the LF using JWST/NIRCam GRISM instrument (Meyer et al. 2024; Matthee et al. 2023), a JWST/NIRCam wide field slitless spectroscopy study by (Sun et al. 2023), a JWST/NIRCam medium band survey by (Wold et al. 2025) and a former Spitzer study by De Barros et al. (2019). All the JWST surveys specifically study the [O III]λ5007Å, so we boosted their luminosity using their respective R3 ratio and [O III]λ5008/[O III]λ4960 = 2.98 (Storey & Zeippen 2000), according to our assumed line of ratios. This approximation matches the stacked median and flux measurements from these papers. The data can be found in Table C.3 and C.4 the parametrisation in Table 1.