“…In the thermodynamic limit (N → ∞) we show that W(β, µ) can be derived from an auxiliary function ϕ(λ) that is written only in terms of open connected sub-chains. The present approach gives a β-expansion of W(β, µ), whose coefficient of order β n can be obtained exactly for arbitrary value of n. The existence of this auxiliary function allow us to get higher order terms in the β-expansion of W(β, µ) than we were able before, in references [20,21,22]. The coefficient of order β n is analytically obtained, and it is exact.…”