ABSTRACT
Again, in the context of the present theorem we shall say that a path fulfilling Conditions (i) and (ii) is progressive, or more precisely, (ut)-progressive. It should be observed that a path may be progressive for some values of ph u, but not for others. In consequence, the regions =]@,aj) vary with phu. They may also vary with luJ if a, and A depend on u. As in Chapter 6, $1 1.4, the regions Ej(u,a,) are not confined to a single Riemann sheet. 3.2 The proof of Theorem 3.1 parallels proofs of similar theorems in Chapters 6 and 7. By differentiation of (3.02) and use of (2.07), we find that
Transferring the term $({)E~,~ to the right-hand side and using the method of variation of parameters, we obtain
where K(<, 0) = +(eu(C-u)-eu(u-C) 1.
