Thermodynamics of quantum gases for the entire range of temperature
  We have analytically explored thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials of the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become plausible specially in the intermediate regime between the classical and quantum limits. 
Shyamal Biswas and Debnarayan Jana
cond-mat.quant-gas cond-mat.stat-mech