Calculation of thermodynamic properties of finite Bose-Einstein systems

We derive an exact recursion formula for the calculation of thermodynamic functions of finite systems obeying Bose-Einstein statistics. The formula is applicable for canonical systems where the particles can be treated as noninteracting in some approximation, e.g., like Bose-Einstein condensates in magnetic traps. The numerical effort of our computation scheme grows only linearly with the number of particles. As an example, we calculate the relative ground-state fluctuations and specific heats for ideal Bose gases with a finite number of particles enclosed in containers of different shapes.