Hard hyperspheres

Volume

The volume of a Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d} sphere of unit diameter is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_d=\frac{(\pi / 4)^{d/2}}{\Gamma(1+ d/2)}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Gamma(m)} is the Gamma function.

See also

• Hard sphere: virial coefficients

References

1. Paula A. Whitlock, Marvin Bishop and John L. Tiglias "Structure factor for hard hyperspheres in higher dimensions", Journal of Chemical Physics 126 224505 (2007)
2. René D. Rohrmann, Miguel Robles, Mariano López de Haro, and Andrés Santos "Virial series for fluids of hard hyperspheres in odd dimensions", Journal of Chemical Physics 129 014510 (2008)