  Expansions through the 24th order at high-temperature and up to 11th order at
low-temperature are derived for the main observables of the Blume-Capel model
on bipartite lattices (sq, sc and bcc) in 2d and 3d with various values of the
spin and in presence of a magnetic field. All expansion coefficients are
computed exactly as functions of the crystal and magnetic fields. Several
critical properties of the model are analyzed in the two most studied cases of
spin S=1 and S=3/2.
