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Using the first seven known virial coefficients and forcing it to possess two branch-point singularities, a new equation of state for the hard-sphere fluid is proposed. This equation of state predicts accurate values of the higher virial coefficients, a radius of convergence smaller than the close-packing value, and it is as accurate as the rescaled virial expansion and better than the Pade [3/3] equations of state. Consequences regarding the convergence properties of the virial series and the use of similar equations of state for hard-core fluids in d dimensions are also pointed out.
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Santos et al. (2009) studied this question.
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