ABSTRACT
Figure 13.3 indicates how a , and a, can be linked by a (-progressive path in S', consisting of Y, , Y2, and either one or two arcs of the type (13.06), depending whether or not Jpha,-pha,I < n/a. The corresponding path in the t plane is indicated approximately by Fig. 13.4. On letting the b parameters of the arcs tend to infinity, it is seen from (13.02) that the variations of F(z) along 9, and 9, tend to zero. For the contribution to the variation from the arcs (13.06). we observe that the corresponding values of )z-' -* dzl are bounded by
14 The Gans-Jeffreys Formulas: Complex-Variable Method
14.1 In this section the problem treated in $7 is solved by application of the fundamental formula of $1 1. In the equation
d 2 w/dz2 = { f (z) +g(z)) w (14.01)
it is assumed that f(z) and g(z) are holomorphic in a simply connected domain D which includes the whole of the real axis. The only zero off (z) in D is assumed to be z = 0, and f(z) and g(z) are required to be real when z is real. Then, without loss of generality, f(z)/z is taken to be positive on the real axis.
