Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions

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We evaluate the virial coefficients Bk for BK for k ≤ hard spheres in dimensions D Virial coefficients with k even are found to be negative when D≥ This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D. Further analysis provides evidence that negative virial coefficients will be seen for some k > 10 for D = 4, and there is a distinct possibility that negative virial coefficients will also eventually occur for D = 3.

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