Abstract
Hitherto consideration has been restricted to regions bounded by (finite) contours. The study of the case where the boundary is an open line, extending to infinity in both directions (“semi-infinite region”), does not meet with any essentially new difficulties. In certain cases it is convenient to map the region under consideration on to the half-plane rather than on to the circle (there being, of course, no essential difference between these two methods). The general case will not be considered in the present chapter; only the solution of the fundamental problems for the half-plane and for certain definite semi-infinite regions will be treated.
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