  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
linear 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
numbers of particles enclosed in containers of different shapes.
