Finite-size effects on the Bose–Einstein condensation critical temperature in a harmonic trap

•We obtain finite-size effects on the Bose–Einstein condensation critical temperature.•The setting is the general anisotropic harmonic trap.•We extend the known analytical first order result to higher orders.•The new results are very accurate throughout a wide regime.•These results are particularly important for low particle numbers.

We obtain second and higher order corrections to the shift of the Bose–Einstein critical temperature due to finite-size effects. The confinement is that of a harmonic trap with general anisotropy. Numerical work shows the high accuracy of our expressions. We draw attention to a subtlety involved in the consideration of experimental values of the critical temperature in connection with analytical expressions for the finite-size corrections.