quantum mechanics - What is meant by finite harmonic oscillator?

What does it mean to take finite harmonic oscillator, In research article "http://iopscience.iop.org/article/10.1088/1367-2630/17/11/113015 ",

we were finding effective number of cobosons in ground state $\langle N_0\rangle$ of multilevel system (harmonic trap) .There they used approximation that $\langle N_0 \rangle = \langle N_0 \rangle _{f} - (T/T_0)^3 N S$.Where $\langle N_0 \rangle_f$ is number of cobosons in ground state for finite harmonic oscillator.

I donnot understand how did they approximate it.