where g i is the degeneracy of state i and Φ Φ ( ε ε i ) = { e β β ( ε ε i − − μ μ ) , for particles obeying Maxwell-Boltzmann statistics e β β ( ε ε i − − μ μ ) − − 1 , for particles obeying Bose-Einstein statistics e β β ( ε ε i − − μ μ ) + 1 , for particles obeying Fermi-Dirac statistics with β = 1/ k B T, the Boltzmann constant k B, temperature T, and chemical potential μ. (See Maxwell–Boltzmann statistics, Bose–Einstein statistics, and Fermi–Dirac statistics.)