or from Eq. (\[bcsde\]) to Eq. (\[bcie\]), creates a pinch singularity at $k'_4 = k_4$ in the error function term in Eq. (\[bareie\]) or Eq. (\[bcie\]).

We have carried out a search for poles in the propagator function $\sigma_Q(k_4)$ for a range of values of $\alpha$ for both the bare and Ball-Chiu vertex. Our results are listed in Table \[tab\]. In all cases we find that the only observed poles occur for ${\rm Im}\, k_4 > 0$, and that $\sigma_Q$ dies away to small values and is free from singularities over that part of the shaded region in Fig. \[fig1\] accessible to our computer program. Of course we are unable to pass the contour of numerical integration through the pole itself, and these results are attained by extrapolation from results of contours which we gradually moved deeper into the complex plane. We were unable to obtain a reasonable extrapolation for the Ball-Chiu vertex at $\alpha = 1$, again because of the iterative instability problem associated with the derivative-like term in Eq. (\[bcie\]).

We also list in Table \[tab\] the results of using the model gluon propagator $$g^2 D_{\mu \nu}(k^2) = 
  \delta_{\mu \nu} \Delta_{\rm G}(k^2) ,    \label{flg}$$ where $\Delta_{\rm G}$ is 