DIFFRACTION OF RADIO WAVES UY \ 1' A I{ A H< )I.I(' CYLINDER 483 



respectively, for Im\f(to) - /(/i)] = ami Re [/(/o) - fih)] = 0. These 

 equations are plotted in Fig. 10.3. It will l)e noted that a curve is shown 

 for V > IT even though this puts w outside the allowed rectangle. This 

 is done because one of the paths of integration, W, passes through both 

 ^0 and /i exp ( — t27r) when m is in a certain region, and the correspond- 

 ing zeros of Wn(z) lie on the curve defined by 



Re If (to) - f(h exp I -i2r})] = 0. 



It may be shown that a curve corresponding to 



KU) - fihexp {-^•27^}) 



with — TT < y < TT may be obtained from the curve corresponding to 

 /(^) ~ /(^i) ^vith TT < y < Stt by simply subtracting 27r from v. This is 

 done on Fig. 10.3. 



ARG m =-90° 



BOUNDARIES 



■lm[fao)-f(ti)] = o 



LINES OF ZEROS (EXCEPT CURVE (a)) 



■Re[f{to)-f(t,)] = o 



ARG m = 90° 



/ Re[f(to)-f(t,e-L27r)] = o 



(a) 



ARG m = 270 



m — »»0 270 



Fi|2;. 10.3 — Boundaries of the regions shown in Kiff. 11.2 and lines of zeros 

 shown in Fig. 12.1 as they appear on the u' = n + ir plane when z = ?'/V- 



