We present a full data analysis of the pure-parallel Hubble Space Telescope (HST) imaging observations in the Brightest of Reionizing Galaxies Survey (BoRG[z9]) in Cycle 22. The medium-deep exposures with five HST/WFC3IR+UVIS filter bands from 79 independent sightlines (~370 arcmin^2) provide the least biased determination of number density for z>9 bright galaxies against cosmic variance. After a strict two-step selection for candidate galaxies, including dropout color and photometric redshift analyses, and revision of previous BoRG candidates, we identify one source at z~10 and two sources at z~9. The z~10 candidate shows evidence of line-of-sight lens magnification (mu~1.5), yet it appears surprisingly luminous (MUV ~ -22.6pm0.3 mag), making it one of the brightest candidates at z > 8 known (~ 0.3 mag brighter than the z = 8.68 galaxy EGSY8p7, spectroscopically confirmed by Zitrin and collaborators). For z ~ 9 candidates, we include previous data points at fainter magnitudes and find that the data are well fitted by a Schechter luminosity function with alpha ~ -2.1, MUV ~ -21.5 mag, and log phi ~ -4.5 Mpc^-3mag^-1, for the first time without fixing any parameters. The inferred cosmic star formation rate density is consistent with unaccelerated evolution from lower redshift.
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