The equation of state for a collection of ideal bosons in both the low-density and high-density regions is found using the method of cluster expansion with a new generating function. The importance of the radius of convergence in the cluster expansion and its connection to the Bose–Einstein condensation phenomenon are studied. The radius of convergence of the partition function is calculated and the values of critical density, fugacity and other thermodynamic properties at condensation are obtained using Mayer’s convergence method.