would have to approximate around other points. This gives rise to different values of the parameters $\lambda$ and $x_0$, which actually become functions of $R$ and $\nu(R)$. These functions then are \[cf. (\[d\])\]: $$\begin{aligned}
 \label{dR}
\lambda(R) &=& \frac{2 (1+\nu) M d'}{\nu d^2} 
\ \ \mbox{and} \nonumber \\
x(R) &:=& \frac{(1 + \nu) R}{\nu d} - \lambda \ ,\ \mbox{with} \nonumber \\
d'(R)&:=& \frac{\partial}{\partial
\gamma(R)} \frac{{\rm d} V}{ {\rm d} v} \bigg|_{\gamma(R)}   \nonumber\\
d(R) &:=&  \frac{{\rm d} V}{ {\rm d} v} \bigg|_{\gamma(R)} 
+ d'(R) [1-\gamma(R)]\ , \end{aligned}$$ from which we obtain a spectral energy flux that depends on the actual radius and the actual velocity of the mass shell: $$\begin{aligned}
 \label{dasergebnis}
\rho(\omega,R) = \frac{e^{-\pi\omega\lambda(R)}\omega^2}
{4\pi^3\lambda(R)} 
\vert \Gamma[1+{\mathrm{i}}\omega\lambda(R), x(R)]\vert^2 \; \; .\end{aligned}$$ The quality of this generalization mainly depends on the assumption that the change of velocity is small, so that $\ddot{R}$-contributions can be neglected. Should the acceleration of the mass shell get too high, the patches in which the velocity can be treated as nearly constant would get too small and effects from the boundaries would grow important.

Discussion
==========

The particle production of an expanding mass shell depends on the velocity of the mass shell $\nu$, its mass $M$, and 