Total IR LF out to z ∼ 2.3. The red stars are derived from our de-blended catalogue in COSMOS (filled red stars: our LF above the completeness limit; empty red stars: our LF below the completeness limit). Error bars on the red stars only represent Poisson errors. The black squares are from Magnelli et al. (2013) based on observations of the GOODS-S ultradeep field. The green squares are also from Magnelli et al. (2013), but based on observations of the GOODS-N/S deep fields. The dashed line in each panel is the best-fit double power-law from Magnelli et al. (2013). The vertical dotted line indicates the location of the transition luminosity, i.e. L_knee in Eq. (2) and (3), as derived in Magnelli et al. (2013).