DIFFRACTION OF RADIO WAVES BY A PARABOLIC CYLINDER 485 



have been if we had elected to study a case in which neither nir nor m,- 

 were zero. 



Most of the vahies of m/p' studied in this section are listed in Table 

 11.1. The point numbers are those listed below and shown in Fif>;. 11.2. 

 Paths of steepest descent are shown for all but the last two entries of 

 the table. We now take up these values of m one by one. 



1. m = pV2. Fig. 11.1 (a). Since Re f(h) > Rej{h), h is higher than 

 ^0. In all of the figures dealing with the /-plane in this section, solid 

 lines mean | arg t | < tt while dashes indicate | arg t\ > ir. 



2. ni = p\ Fig. 11.1 (c). As m goes from p^/2 to p^ the path through 

 ti changes its type, h is higher than ^o- 



■INDICATES ARG t >77 



UL.Wf 



Vf, W(. 



WP 



Fig. 11.1 — Paths of steepest descent in / = i, + ?7, phme when z = I'/^p and 

 m^n + 1 is real and positive. Ui and U/ denote initial and final branches of the 

 path of integration for f/„(i"2p), and so on. to and ti are saddle points. 



