  Here we provide the most comprehensive determinations of the rest-frame $UV$
LF available to date with HST at z~2, 3, 4, 5, 6, 7, 8, and 9. Essentially all
of the non-cluster extragalactic legacy fields are utilized, including the
Hubble Ultra Deep Field (HUDF), the Hubble Frontier Field parallel fields, and
all five CANDELS fields, for a total survey area of 1136 arcmin^2. Our
determinations include galaxies at z~2-3 leveraging the deep HDUV, UVUDF, and
ERS WFC3/UVIS observations available over a ~150 arcmin^2 area in the GOODS
North and GOODS South regions. All together, our collective samples include
>24,000 sources, >2.3x larger than previous selections with HST. 5766, 6332,
7240, 3449, 1066, 601, 246, and 33 sources are identified at z~2, 3, 4, 5, 6,
7, 8, and 9, respectively. Combining our results with an earlier z~10 LF
determination by Oesch+2018a, we quantify the evolution of the $UV$ LF. Our
results indicate that there is (1) a smooth flattening of the faint-end slope
alpha from alpha~-2.4 at z~10 to -1.5 at z~2, (2) minimal evolution in the
characteristic luminosity M* at z>~2.5, and (3) a monotonic increase in the
normalization log_10 phi* from z~10 to z~2, which can be well described by a
simple second-order polynomial, consistent with an "accelerated" evolution
scenario. We find that each of these trends (from z~10 to z~2.5 at least) can
be readily explained on the basis of the evolution of the halo mass function
and a simple constant star formation efficiency model.
