The general luminosity function (M) is the differential probability distribution of galaxies of all types over absolute magnitude M. A distinction is often made between the field luminosity function and that derived for cluster galaxies ostensibly because of the well documented differences in the mixture of morphological types between these two extremes in the prevailing environment (density). With additional information it has also been possible in some situations to further subdivide luminosity functions according to morphological type T viz _T(M).

Comprehensive and critical reviews of optical luminosity functions are given by [Fe77] which draw upon the published data from [Arak70] [vdB61]; [Chr75] [Huc73] [Kia61] [Hol74] [TG76] [Sch76], while [Bin88] includes data from [Kir79] [Dav80] [San79] [Cho85] [Cho86] [Cho87] (1987); [YG84] [YG87] [PS87] and reviews both field and cluster luminosity functions. The dependence of luminosity functions on Hubble Type and environment is also reviewed in [Bin87].

More recent studies of nearby clusters including Leo, Dorado, NGC 1400, NGC 5044, Antlia, Virgo and Fornax are presented in [Fe89, FS88, FS90, FS91].

A commonly adopted (2-parameter) fitting function is the so-called ``Schechter Function'' [Sch76] described by a power-law at faint magnitudes and an exponetial cut-off at bright magnitudes, with the break between these two regimes occuring at a characteristic luminosity L

(L / L) d (L / L) = (L / L) ^- exp (-L / L) d (L / L)

An infrared luminosity function based on IRAS data for a northern hemisphere sample of galaxies has been published in [SSN86], revised in [SSM87] and updated in [SM96].

The neutral hydrogen luminosity function has also been derived [Sch96], [Brig93]

The absolute magnitudes for a select number of galaxies have been obtained from distances derived from the discovery of Cepheids from the ground and using the [FMK97] and applying the Cepheid Period-Luminosity relation [MF91]. More distance galaxies can be calibrated absolutely once a value of the Hubble constant is adopted (modulo caveats concerning large-scale flow velocities and questions of group membership in clusters and/or small groups).