  We use the largest, most uniform, and most spectroscopically complete to
faint X-ray flux limits Chandra sample to date to construct hard 2-8 keV
rest-frame X-ray luminosity functions (HXLFs) of spectroscopically identified
active galactic nuclei (AGNs) to z~5. In addition, we use a new 2-8 keV local
sample selected by the very hard (14-195 keV) SWIFT 9-month Burst Alert
Telescope (BAT) survey to construct the local 2-8 keV HXLF. We do maximum
likelihood fits of the combined distant plus local sample (as well as of the
distant sample alone) over the redshift intervals 0<z<1.2, 0<z<3, and 0<z<5
using a variety of analytic forms, which we compare with the HXLFs. We
recommend using our luminosity dependent density evolution (LDDE) model fits of
the combined distant plus local sample over 0<z<3 for all the spectroscopically
identified sources and for the broad-line AGNs.
