  In Jaouadi et al. [Phys. Rev. A 83, 023616 (2011)] the authors derive an
analytical finite-size expansion for the Bose-Einstein condensation critical
temperature of an ideal Bose gas in a generic power-law trap. In the case of a
harmonic trap, this expansion adds higher order terms to the well- known first
order correction. We point out a delicate point in connection to these results,
showing that the claims of Jaouadi et al. should be treated with caution. In
particular, for a harmonic trap, the given expansion yields results that,
depending on what is considered to be the critical temperature of the finite
system, do not generally improve on the established first order correction. For
some non-harmonic traps, the results differ at first order from other results
in the literature.
