It is noticeable that g 3 / 2 is a monotonically growing function of f in f ∈ ∈ [ 0 , 1 ] , which are the only values for which the series converge. Recognizing that the second term on the right-hand side contains the expression for the average occupation number of the fundamental state ⟨ ⟨ n 0 ⟩ ⟩ , the equation of state can be rewritten as