Normalization of the hypervirial distribution function
= Normalization of the hypervirial distribution function
{title2=$C=\frac{(p+1)\Gamma(2p+2)}{2^{(p+5)/2}\pi^{5/2}\Gamma(p/2)\Gamma((3p+3)/2)}$}
In units $G=M=a=1$, velocity integration of $F=CL^{p-2}E^{(3p+1)/2}$ gives $C=(p+1)\Gamma(2p+2)/[2^{(p+5)/2}\pi^{5/2}\Gamma(p/2)\Gamma((3p+3)/2)]$. The <beta function> separates the radial-speed and angular integrals. This constant is positive for every $p>0$.