…
►The principal values (or principal branches) of the inverse , , and are obtained by introducing cuts in the -plane as indicated in Figure 4.37.1(i)-(iii), and requiring the integration paths in (4.37.1)–(4.37.3) not to cross these cuts.
…
►
…
Figure 4.37.1:
-plane.
Branchcuts for the inverse hyperbolic functions.
…
…
►The principal values (or principal branches) of the inverse sine, cosine, and tangent are obtained by introducing cuts in the -plane as indicated in Figures 4.23.1(i) and 4.23.1(ii), and requiring the integration paths in (4.23.1)–(4.23.3) not to cross these cuts.
…
►
…
Figure 4.23.1:
-plane.
Branchcuts for the inverse trigonometric functions.
…
…
►The branch obtained by introducing a cut from to on the real -axis, that is, the branch in the sector , is the principal
branch (or principal value) of .
…
►The difference between the principal branches on the two sides of the branchcut (§4.2(i)) is given by
…
…
►For example, by converting the Maclaurin expansion of (4.24.3), we obtain a continued fraction with the same region of convergence (, ), whereas the continued fraction (4.25.4) converges for all except on the branchcuts from to and to .
…