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We consider the nth-order spacing distribution, P^n (s), in the statistical theory of energy levels of complex systems. Each P^n is written as a sum of multiple integrals over correlation functions. This procedure is used to establish the identity of the spacing distributions for all members of a class of Hamiltonian unitary ensembles. A power-series expansion of P^n (s), valid for all n, is developed.
Fox et al. (Mon,) studied this question.