The average particle number for that single-particle substate is given by ⟨ ⟨ N ⟩ ⟩ = k B T 1 Z ( ∂ ∂ Z ∂ ∂ μ μ ) V , T = 1 exp ⁡ ⁡ ( ( ε ε − − μ μ ) / k B T ) − − 1 This result applies for each single-particle level and thus forms the Bose–Einstein distribution for the entire state of the system.