ABSTRACT
Consider first the expansion of Iv(vz). Here the reference point is a, = - oo, and the monotonicity condition precludes extension across the boundaries E F and E'F', but not across DE and D'E'. The z maps of the shaded regions can be constructed by use of the relation
t (ze"') = t(z) + xi obtained from (7.07) by making a small half-circuit about z = 0. The first stage in the continuation of the mapping across DE is indicated in Figs. 8.1 and 8.2. The former is the reflection of Fig. 7.1 in the imaginary z axis; the latter is Fig. 7.2 translated through ni. There is a new singularity of $(6) at the point El of affix 3xi/2. The next continuation-across DIE,-is achieved by another reflection in the imaginary z axis, and a further translation xi in the t: plane. And so on.
