Figure 4.15.7 illustrates the conformal mapping of the
strip onto the whole
-plane cut along the real axis from to and to ,
where and (principal value). Corresponding
points share the same letters, with bars signifying complex conjugates. Lines
parallel to the real axis in the -plane map onto ellipses in the -plane
with foci at , and lines parallel to the imaginary axis in the
-plane map onto rectangular hyperbolas confocal with the ellipses. In the labeling of corresponding points
is a
real parameter that can lie anywhere in the interval .