  With the integral representation of Bose functions, the Bose-Einstein
condensation of non-interacting bosons in a three-dimensional harmonic trap was
studied. The relation between the particle number and its phase transition
temperature was clarified. Some next-order terms in the thermodynamic
expansions were obtained. We plotted the chemical potential, the mean energy,
and the specific heat and found most of these properties obtained by using the
integral representation were almost identical with those of the series
representation of Bose functions.
