We know that the average occupation number cannot be negative for all systems and chemical potential must be negative in Ideal Bose Gas. This fact leads us to arrive a conclusion for fugacity which is related by chemical potential, as I quoted below: The restriction of the fugacity to the interval 0<=z<=1 is very important in the following. For a large volume, the sum over all one-particle states can be rewritten in terms of integral. (Greiner, Neise, Stocker, "Thermodynamics and Statistical Mechanics") So my question is, how can negative chemical potential helps us to convert the sum to the integral for a large volume? As what can I think fugacity in an İdeal Bose Gas?