The properties of X-ray-selected active galactic nuclei. I - Luminosity function, cosmological evolution, and contribution to the diffuse X-ray background

X-ray luminosity functions (XLFs) and their implications for cosmological evolution are determined for 420 X-ray-selected active galactic nuclei (AGN). The local XLFs flatten considerably when L(x) is less than or equal to 5 x 10 to the 42nd ergs/s, and higher-luminosity XLF are demonstrated to fit a power-law approximation. Cosmological evolution in terms of two pure-luminosity evolutionary models is directly supported by model-independent AGN XLF, showing weak evolution when z is less than 0.4 and more pronounced evolution at higher z. The parameter C is determined for the two models, and the values support the 'slower' evolution of these AGN relative to QSOs selected optically. The deevolved XLF best-fit slope is found to be 3.05 for high luminosities and 1.35 for low luminosities, with no evidence of slope changes for other luminosities. 38 refs.