A Approximate Vertex Amplitude from the Schwinger - Equations of Quantum Electrodynamics.

An approximate set of invariant functions for the dressed vertex amplitude was found. An asymptotic solution to the unrenormalized Schwinger-Dyson equations of Quantum Electrodynamics was obtained which joined smoothly with the solutions found by a perturbation technique. The photon propagator is approximated by its form near the mass shell. The vertex equation was separated from higher order members of the hierarchy at the second order in the coupling constant with the aid of H. S. Green's generalization of Ward's Identity. No infinities were substracted to obtain the solutions. The function multiplying the matrix _{~gamma} ^lambda is found to be dominant everywhere.