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

J. Stat. Phys. 122: 15-57 (2006) We evaluate the virial coefficients B_k for k=5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D>=5. 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.