Abstract: The huge partition function is a difficult problem in teaching equilibrium statistical physics. In the

present textbooks，the logarithm of huge partition function is introduced firstly，and then the correctness of this formula

producing thermodynamics functions is affirmed. However，this is not order in the logic. Based on the average

energy，the average particle number and the generalized force of the T-μ-Vsystem，this paper derives the quantum

huge partition function by using collecting full differential method and unfined integral method，respectively. The

physical mean of what variables regarded to two independent parameters is discussed.

Key words: quantum statistics, huge partition function, collecting full differential method, idefinite integration