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With the integral representation of Bose functions, the Bose-Einsteincondensation of non-interacting bosons in a three-dimensional harmonic trap wasstudied. The relation between the particle number and its phase transitiontemperature was clarified. Some next-order terms in the thermodynamicexpansions were obtained. We plotted the chemical potential, the mean energy,and the specific heat and found most of these properties obtained by using theintegral representation were almost identical with those of the seriesrepresentation of Bose functions.Comment: 7 pages, 5 figure

Bose-Einstein Condensation of Confined and Non-Interacting Bose Particles by the Integral Representation of Bose Functions