From multiple integrals to Fredholm determinants
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We consider a multiple integral representation for the finite temperature density-density correlation functions of the one-dimensional Bose gas with delta function interaction in the limits of infinite and vanishing repulsion. In the former case a known Fredholm determinant is recovered. In the latter case a similar expression appears with permanents replacing determinants.
11 pages, section on the free Boson limit added
11 pages, section on the free Boson limit added