  [ABRIDGED] We present the first statistical analysis of the complete
ESO-Sculptor redshift survey (ESS). The flux-calibrated sample of 617 galaxy
spectra with R_c<20.5 is separated into 3 spectral classes (early,
intermediate, and late). We report in detail on the spectral classification,
the polynomial K-corrections, and all sources of corresponding random and
systematic errors. The derived luminosity functions (LF) in the Johnson-Cousins
B and Rc bands are in agreement with the results from the comparable CNOC2
survey (Lin et al. 1999), whereas the ESS provides the first estimates of LFs
per spectral type in the Johnson V band. A renewed interpretation of the galaxy
LFs from a redshift survey are obtained by fitting the ESS LFs with composite
functions based on the local LFs per morphological type (Sandage, Binggeli &
Tammann 1985; Jerjen & Tammann 1997). As good or better fits than with pure
Schechter functions are obtained using: for the early-type LF, a two-wing
Gaussian; for the intermediate-type LF, the sum of a Gaussian modeling the
Spiral galaxies and a steep Schechter function (alpha=-1.5) representing the
dwarf elliptical galaxies; for the late-type LF, a similar composite function
with a flat or weaker slope (-0.8<alpha<-0.3) for the Schechter component which
represents the dwarf Irregular galaxies. This analysis illustrates how LFs per
spectral type may be affected by morphological type mixing, and emphasizes the
need for a quantitative morphological classification at z>0.1 which separates
the giant and dwarf galaxy populations.
