The partition function then takes the form of an integral.
This is what makes it different from the ordinary partition function.
The same can be said for partition functions and any ensemble.
Such is the case for the partition function in quantum field theory.
Thus a partition function can be defined for each mode.
Thus the partition function looks like the weight factor for the ensemble.
The denominator of the right side is the partition function.
This is a closed and exact expression for the partition function of the system.
Where is the closed form for the partition function.
This is the trivial term, which does not affect the partition function of the system.