Summary

Overall, the $Z(F,D_1,D_2)$ is found by:

$$\begin{eqnarray*} \log(\beta(\frac{D_2}{2},\frac{D_1}{2})) & = & \log(\Gamma(v... ...+ 3 Z_n^{-4})} \quad \mathrm{for~} n=1,2,3 \\ Z & \approx & Z_3 \end{eqnarray*}$$

This approximation has a relative accuracy of $10^{-3}$ or better for $\log(p) < -14.05$ and outside this range is calculated by conventional means.