as illustrated above. Second, the identification of a true bound-state pole requires careful examination of the $P^2-q^2$ plane. Finally, with regard to electron scattering, in general the singularity structure of the QPV in the time-like region of photon momentum squared dominates the behavior in the low momentum region of space-like $q^2$. This feature is exhibited here despite the absence of a bound-state pole. The intercept at $q^2=0$, is provided by the constraints, (\[2.10\]), derived from the WI, which the coefficient functions given in (\[3.4\]) satisfy explicitly. Further out in the space-like region a transition to asymptotic behavior is expected. As is illustrated in Fig.3b, an unphysically sharp transition occurs here due to the nonanalytic structure of the self-energy amplitude, $B$, in (\[3.2\]). Based on these observations, the approximation (\[3.1\]) does not provide a useful description of bound states or the approach to asymptopia, but is of pedagogical value for investigating the behavior of the QPV for the situation where the confinement length scale, defined here as the quark separation at which the vacuum becomes apparent, is taken to infinity.

Numerical evaluation
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Methods and approximations
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The set of equations for the five transverse coefficient functions represented in (\[2.16\]), and 