  Polarons, that is, charge carriers correlated with lattice deformations, are
ubiquitous quasiparticles in semiconductors, and play an important role in
electrical conductivity. To date most theoretical studies of so-called large
polarons, in which the lattice can be considered as a continuum, have focused
on the original Fr\"ohlich model: a simple (non-degenerate) parabolic isotropic
electronic band coupled to one dispersionless longitudinal optical phonon
branch. The Fr\"ohlich model allows one to understand characteristics such as
polaron formation energy, radius, effective mass and mobility. Real cubic
materials, instead, have electronic band extrema that are often degenerate or
anisotropic and present several phonon modes. In the present work, we address
such issues. We keep the continuum hypothesis inherent to the large polaron
Fr\"ohlich model, but waive the isotropic and non-degeneracy hypotheses, and
also include multiple phonon branches. For polaron effective masses, working at
the lowest order of perturbation theory, we provide analytical results for the
case of anisotropic electronic energy dispersion, with two distinct effective
masses (uniaxial) and numerical simulations for the degenerate 3-band case,
typical of III-V and II-VI semiconductor valence bands. We also deal with the
strong-coupling limit, using a variational treatment: we propose trial
wavefunctions for the above-mentioned cases, providing polaron radii and
energies. Then, we evaluate the polaron formation energies, effective masses
and localisation lengths using parameters representative of a dozen II-VI,
III-V and oxide semiconductors, for both electron and hole polarons...In the
non-degenerate case, we compare the perturbative approach with the Feynman path
integral approach in characterisizing polarons in the weak coupling limit...
