  In quantum many-body system, dimensionality plays a critical role on type of
the quantum phase transition. In order to study the quantum system during
dimensional crossover, we studied the Bose-Hubbard model on cubic lattice with
anisotropic hopping by using the high order symbolic strong coupling expansion
method. The analytic series expanded boundaries between the Mott-insulator and
superfluid phase up to eighth order are calculated. The critical exponents are
extracted by Pad\'{e} re-summation method, which clearly shows the dimensional
crossover behavior. Meanwhile, the critical points at commensurate filling can
also be obtained, and they match well with the prediction of renormalization
group theory. The scaling of the gap energy and whole phase diagram are given
at last, and they can be taken as the benchmark for experiment and numerical
simulations in the future study.
