  We investigate the production of spin-3/2 hadrons in semi-inclusive deep
inelastic lepton-nucleon scatterings. The complete differential cross section
is derived through the kinematic analysis and expressed in terms of 288
structure functions, corresponding to all polarization configurations and
azimuthal modulations. For an unpolarized lepton beam, half of the 192
structure functions have nonzero leading order contributions in the parton
model, among which 42 are from rank-3 tensor polarized fragmentation functions
of the hadron. For a polarized lepton beam, one third of the 96 structure
functions contribute at the leading order and 14 of them are from rank-3 tensor
polarized fragmentation functions. In addition to the formalism, we perform a
model estimation of the spin transfer to a $S_{hLLL}$ polarized hadron and
sizable asymmetry is expected. Therefore, these newly defined observables for
the production of a spin-3/2 hadron in a deep inelastic scattering process can
be explored in future experiments to understand nucleon spin structures and
spin-dependent fragmentation functions.
