Grand canonical weight

Set

context $ \Xi(\beta,\mu) $ … grand canonical partition function
definiendum $w: \mathbb N \to {\mathbb R\times\mathbb R} \to \mathbb R$
definiendum $w_N(\beta,\mu):=\frac{1}{\Xi(\beta,\mu)}\ z(\beta,\mu)^N\cdot Z_N(\beta)$


Requirements

Grand canonical partition function, Fugacity