The 2.4 $\mu$m Galaxy Luminosity Function as Measured Using WISE. III.
  Measurement Results
  The WISE satellite surveyed the entire sky multiple times in four infrared
wavelengths (3.4, 4.6, 12, and $22\,\mu$m; Wright et al. 2010). The
unprecedented combination of coverage area and depth gives us the opportunity
to measure the luminosity function of galaxies, one of the fundamental
quantities in the study of them, at $2.4\ \mu$m to an unparalleled level of
formal statistical accuracy in the near infrared. The big advantage of
measuring luminosity functions at wavelengths in the window $\approx 2$ to
$3.5\,\mu$m is that it correlates more closely to the total stellar mass in
galaxies than others. In this paper we report on the parameters for the
$2.4\,\mu$m luminosity function of galaxies obtained from applying the
spectroluminosity functional based methods defined in Lake et al. (2017b) to
the data sets described in Lake et al. (2017a) using the mean and covariance of
$2.4\,\mu$m normalized SEDs from Lake & Wright (2016). In terms of single
Schechter function parameters evaluated at the present epoch, the combined
result is: $\phi_\star = 5.8 \pm [0.3_{\mathrm{stat}},\, 0.3_{\mathrm{sys}}]
\times 10^{-3} \operatorname{Mpc}^{-3}$, $L_\star = 6.4 \pm
[0.1_{\mathrm{stat}},\, 0.3_{\mathrm{sys}}] \times 10^{10}\,
L_{2.4\,\mu\mathrm{m}\,\odot}$ ($M_\star = -21.67 \pm [0.02_{\mathrm{stat}},\,
0.05_{\mathrm{sys}}]\operatorname{AB\ mag}$), and $\alpha = -1.050 \pm
[0.004_{\mathrm{stat}},\, 0.03_{\mathrm{sys}}]$, corresponding to a galaxy
number density of $0.08\operatorname{Mpc}^{-3}$ brighter than $10^6\,
L_{2.4\,\mu\mathrm{m}\,\odot}$ ($10^{-3} \operatorname{Mpc}^{-3}$ brighter than
$L_\star$) and a $2.4\,\mu$m luminosity density equivalent to
$3.8\times10^{8}\,L_{2.4\,\mu\mathrm{m}\,\odot}\operatorname{Mpc}^{-3}$.
$\ldots$
