X-ray luminosity functions of HMXB detected during eRASS1. Green and blue points mark the expected number of sources per dex. A Poisson distribution of measured numbers is assumed. The blue and green lines mark the best-fit power-law correlation for the luminosity functions of confidence classes 1−5 and 1 and 2, respectively. The red line marks the universal power-law correlation found by Grimm et al. (2003). Left: HMXB XLF in the detection band of the eRASS1 catalogue scaling catalogue count rates assuming an absorbed power-law model with N_H = 6×10²⁰ cm⁻² and Γ = 1. Right: extrapolation to 2−12 keV range.