... from a homeoidal expansion

All Appendices are only available in electronic form at http://www.edpsciences.org

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... pairs

In the self-gravitating case $A(r)\propto C''(r) + 2C'(r)/r + 4D(r)$ and $B(r)\propto D''(r) +6D'(r)/r$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... motions

A bar over a quantity means average over phase-space velocities. In particular, $u_{\varphi}\equiv \overline{v_{\varphi}}=\int f {v_{\varphi}}~{\rm d}^3{\vec v}/\rho$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... function

The Lambert function is defined by the identity
$\ln {W}({\rm e}^z) + {W}({\rm e}^z)=z$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.