 This enables the definition of a proper probability density according to
whose integral over all energies is unity on the strength of the definition of formula_17, which is referred to as the partition function, or generating function.The latter name is due to the fact that the derivatives of its logarithm generates the central moments, namely,
and so on, where the first term is the mean energy and the second one is the dispersion in energy.The fact that formula_12 increases no faster than a power of the energy ensures that these moments will be finite.