  The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) has
been proved one of the best models to probe the exotic structures in deformed
nuclei. In DRHBc, the potentials and densities are expressed in terms of the
multipole expansion with Legendre polynomials, the dependence on which has only
been touched for light nuclei so far. In this paper, taking a light nucleus
$^{20}$Ne and a heavy nucleus $^{242}$U as examples, we investigated the
dependence on the multipole expansion of the potentials and densities in DRHBc.
It is shown that the total energy converges well with the expansion truncation
both in the absence of and presence of the pairing correlation, either in the
ground state or at a constrained quadrupole deformation. It is found that to
reach a same accuracy of the total energy, even to a same relative accuracy by
percent, a larger truncation is required by a heavy nucleus than a light one.
The dependence of the total energy on the truncation increases with
deformation. By decompositions of the neutron density distribution, it is shown
that a higher-order component has a smaller contribution. With the increase of
deformation, the high-order components get larger, while at the same
deformation, the high-order components of a heavy nucleus play a more important
role than that of a light one.
