Abel's theorem in problems and solutions - School of Mathematics

Solutions 193
by the formal method, afterwards one identifies the following
coincident branches: The remaining branches are
distinct: it suffices to calculate their values at the point The
correct scheme is shown in Figure 100.
b) Let and be the single-valued continuous
branches of the function and let
be the single-valued continuous branches of
the function We build the scheme of the Riemann surface of
the function by the formal method (Figure 101) and
we identify the coincident branches:
The remaining branches are all distinct:
it suffices to calculate their values at the point The correct
scheme shown in Figure 102.
FIGURE 101
FIGURE 102
c) See Figure 103. The solution is similar to the solution of the case
(b).