  We present the complete twist-4 results for the semi-inclusive annihilation
process $e^+ +e^- \to h+ \bar q+X$ at the tree level of perturbative quantum
chromodynamics. The calculations are carried out by using the formalism
obtained by applying the collinear expansion to this process where the multiple
gluon scattering is taken into account and gauge links are obtained
systematically and automatically. We present the results for structure
functions in terms of gauge invariant fragmentation functions up to twist-4 and
the corresponding results for the azimuthal asymmetries and polarizations of
hadrons produced. The results obtained show in particular that similar to that
for semi-inclusive deeply inelastic scattering, for structure functions
associated with sine or cosine of odd number of azimuthal angle(s), there are
only twist-3 contributions, while for those of even number of azimuthal
angle(s), there are leading twist and twist-4 contributions. For all those
structure functions that have leading twist contributions, there are twist-4
addenda to them. Hence twist-4 contributions may even have large influences on
extracting leading twist fragmentation functions from the data. We also suggest
a method for a rough estimation of twist-4 contributions based on the leading
twist fragmentation functions.
