Abstract
Certain statistical ensembles,e.g. open chemical systems with randomly varying number of particles, are characterized by partition functions of the type\(\mathop \sum \limits_n \exp [ - a_1 n - a_2 n^2 - ... - a_s n^s ]\),n being a natural number anda j ’s generalized temperatures. The state of the system is well defined if one knows the dependence ofa j ’s on ensemble averages 〈n j 〉. For making the equations 〈n j 〉=〈n j 〉 (a 1, ...,a s) at least more accessible for numerical calculations a transformation of the partition function to a series of Fourier integrals is proposed. In the special case of\(\mathop \sum \limits_n \exp [ - an - bn^2 ]\) the integrals can be calculated analytically transforming the statistical sum into a series of error functions.
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