  Using the complete orthonormal sets of radial parts of nonrelativitistic
exponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor spherical
harmonics of rank s the new formulae for the 2(2s+1)-component relativistic
spinors useful in the quantum mechanical description of the arbitrary
half-integral spin particles by the generalized Dirac equation introduced by
the author are established in position, momentum and four-dimensional spaces,
where 1/ 2, 3 / 2, 5 / 2, ... s = . These spinors are complete without the
inclusion of the continuum. The 2(2s+1)component spinors obtained are reduced
to the independent sets of two-component spinors defined as a product of
complete orthonormal sets of radial parts of orbitals and twocomponent spinor
type tensor spherical harmonics. We notice that the new idea presented in this
work is the unified treatment of half-integral spin and scalar particles in
position, momentum and four-dimensional spaces. Relations presented in this
study can be useful in the linear combination of atomic orbitals approximation
for the solution of different problems arising in the relativistic quantum
mechanics when the orthonormal basis sets of relativistic exponential type
spinor wave functions and Slater type spinor orbitals in position, momentum and
four -dimensional spaces are employed.
