Hard hyperspheres

Hard hyperspheres are hard spheres in more than three dimensions. The volume of an n-sphere of unit diameter is given by

$v_{n}={\frac {(\pi /4)^{n/2}}{\Gamma (1+n/2)}}$

where $\Gamma (m)$ 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)
3. M. Adda-Bedia, E. Katzav, and D. Vella "Solution of the Percus–Yevick equation for hard hyperspheres in even dimensions", Journal of Chemical Physics 129 144506 (2008)