  In two-dimensional traps, since the theoretical study of Bose-Einstein
condensation (BEC) will encounter the problem of divergence, the actual
contribution of the divergent terms is often estimated in some indirect ways
with the accuracy to the leading order. In this paper, by using an analytical
continuation method to solve the divergence problem, we obtain the analytical
expressions of critical temperature and condensate fraction for Bose gases in a
two-dimensional anisotropic box and harmonic trap, respectively. They are
consistent with or better than previous studies. Then, we further consider the
nonvanishing chemical potential, and obtain the expressions of chemical
potential and more precise condensate fraction. These results agree with the
numerical calculation well, especially for the case of harmonic traps. The
comparison between the grand canonical and canonical ensembles shows that our
calculation in the grand canonical ensemble is reliable.
