Approximation Error

The absolute error term in equation 29 is

$$E = \frac{5D}{D+4} I_{m,6}$$ (32)

which is bounded since $\vert I_{m,6} \vert < L^{-6} \vert I_{m,0} \vert$ for $T > L$. Therefore the relative error in $I_{m,0}$ is bounded by

$$\vert \epsilon \vert < \frac{15 D^2}{(D+2)(D+4)} L^{-6}.$$ (33)

This is also the relative error in $\log(p)$ since it is proportional to $I_{m,0}$.

So, to obtain a relative accuracy of less than $10^{-3}$ requires $T^6 > 10^3 \frac{15 D^2}{(D+2)(D+4)}$. For large $D$ this asymptotes at $T>4.97$, with smaller values for lower $D$. In practice, a relative accuracy of $10^{-3}$ is achieved (as measured in MATLAB) when:

$T>4.97$	and	$28 \le D$
$T>4.5$	and	$9 \le D < 28$
$T>4.0$	and	$6 \le D < 9$
$T>3.5$	and	$D \le 4$