Analytic continuation of the principal value of yields a multi-valued function with branch points at and . The general value of is given by
compare (6.2.4) and (4.2.6). Thus
The general values of the other functions are defined in a similar manner, and
Unless indicated otherwise, in the rest of this chapter and elsewhere in the DLMF the functions , , , , and assume their principal values, that is, the branches that are real on the positive real axis and two-valued on the negative real axis.