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Using the first seven known virial coefficients and forcing it to possess twobranch-point singularities, a new equation of state for the hard-sphere fluidis proposed. This equation of state predicts accurate values of the highervirial coefficients, a radius of convergence smaller than the close-packingvalue, and it is as accurate as the rescaled virial expansion and better thanthe Pad\'e [3/3] equations of state. Consequences regarding the convergenceproperties of the virial series and the use of similar equations of state forhard-core fluids in $d$ dimensions are also pointed out.

A branch-point approximant for the equation of state of hard spheres