Received July 27, 2020, published online December 25, 2020
Ideal Bose-gas with finite particle number N is investigated. It is shown that the well-known Bose–Einstein distribution of particles over their quantum states consists of two terms — Bose–Einstein term and an additional N-dependent one. The statement that the chemical potential of the ideal Bose-gas should be negative requires tobe also corrected. It is obtained that the analytically calculated observables rather slowly approach the thermodynamic limit following the law N–1/3lnN.