The K-Band Galaxy Luminosity Function^{* **}

We measured the K-band luminosity function using a complete sample of 4192 morphologically typed 2MASS galaxies with μ = 20 mag arcsec^-2 isophotal magnitudes 7 < K₂₀ < 11.25 mag spread over 2.12 sr. Early-type (T ≤ -0.5) and late-type (T > -0.5) galaxies have similarly shaped luminosity functions, α_e = -0.92 ± 0.10 and α_l = -0.87 ± 0.09. The early-type galaxies are brighter, M_K*e = -23.53 ± 0.06 mag compared to M_K*l = -22.98 ± 0.06 mag, but less numerous, n_*e = (0.45 ± 0.06) × 10^-2 h³ Mpc^-3 compared to n_*l = (1.01 ± 0.13) × 10^-2 h³ Mpc^-3 for H₀ = 100 h km s^-1 Mpc^-1, such that the late-type galaxies slightly dominate the K-band luminosity density, j_late/j_early = 1.17 ± 0.12. Including a factor of 1.20 ± 0.04 correction for the conversion of the isophotal survey magnitudes to total magnitudes, the local K-band luminosity density is j = (7.14 ± 0.75) × 10⁸ h L_☉ Mpc^-3, which implies a stellar mass density relative to critical of Ω_*h = (1.9 ± 0.2) × 10^-3 for a Kennicutt initial mass function (IMF) and Ω_*h = (3.4 ± 0.4) × 10^-3 for a Salpeter IMF. Our morphological classifications are internally consistent, are consistent with previous classifications, and lead to luminosity functions unaffected by the estimated uncertainties in the classifications. These luminosity functions accurately predict the K-band number counts and redshift distributions for K ≲ 18 mag, beyond which the results depend on galaxy evolution and merger histories.