Following the procedure described in the gas in a box article, we can apply the Thomas–Fermi approximation which assumes that the average energy is large compared to the energy difference between levels so that the above sum may be replaced by an integral. This replacement gives the macroscopic grand potential function , which is close to :
The degeneracy dg  may be expressed for many different situations by the general formula:
where α is a constant, E is a critical energy, and Γ is the Gamma function. For example, for a massive Bose gas in a box, α=3/2 and the critical energy is given by:
where Λ is the thermal wavelength, and f is a degeneracy factor (f=1 for simple spinless bosons). For a massive Bose gas in a harmonic trap we will have α=3 and the critical energy is given by:
where V(r)=mωr/2  is the harmonic potential. It is seen that E is a function of volume only.
This integral expression for the grand potential evaluates to:
where Li(x) is the polylogarithm function.
The problem with this continuum approximation for a Bose gas is that the ground state has been effectively ignored, giving a degeneracy of zero for zero energy. This inaccuracy becomes serious when dealing with the Bose–Einstein condensate and will be dealt with in the next sections. As will be seen, even at low temperatures the above result is still useful for accurately describing the thermodynamics of just the un-condensed portion of the gas.