Motion in the complex plane of the poles of the quantum-mechanical partial amplitude for a bond

Details are given of the analytic features of this amplitudefg(l, k) in the g plane for a very large class of potentials that satisfy conditions (1). It is shown that there is a region ɛ(l, k2) around the point g = 0 that is free from singularities infg(l, k), so the Mittag-Leffler method can be applied to findfg(l, k) and hence also the total amplitude Tg(k, t) for any g to any specified degree of accuracy with reference to the information contained in the coefficients of a finite number of terms of the series given by perturbation methods forfg(l, k).