DIFFRACTION OF RADIO WAVKS HY \ I'AHAHOMC CYLINDKR 175 



Let T„(z) denote any one of Un(z), Vn(z), Wn{z), let ])riine,s denote 

 differentiation with respect to z, and let asteritsks denote complex con- 

 jugates. Then we have the following relations 



T'Uz) - 2zT'n{z) + 2n7'„(z) = 0, 



d r -22 



dz 



[e~' T'M] + 2nc-'"T,Xz) = 0, 



^, [f''"T,Xz)] + {2n + 1 - zr)(r''"Tniz) = 0, 



TUz) = 2Tn-x{z), 



nTn(z) = 2zT,Uz) - 2Tn-2(z), 



UUz) Vn{z) - Un(z) VUz) = ^■2VV7r^'' T(n + 1), 



VUz) Wn(z) - \\{z) WUz) = ire-'/T'" T(n + 1), 



WUz) Ur^iz) - Wn(z) UUz) = IT e'" h''' V{n + 1), 



Vn{z) + Yn{z) + Wniz) = 0, 

 {Yn{z)Y = WAZ*), [Wn(z)]* = VAZ*), 

 [Un(z)V = UAZ*), 



Vn{-Z) 



— V-2« ur 



Wn{z), W.(-Z) = r Vn{z), 



U„(-Z) = -i'" Vn(z) -r-" Wn(z), 

 F_„_l(t2) = -i^^'KUniz), W-n-l(iz) = -i-"-'KUn{-z), 



ti, t-PLANE 



V 



(9.5) 

 (9.6) 



(9.7) 

 (9.8) 



(9.9) 



(9.10) 



(9.11) 



(9.12) 



Fi^. n.l — Paths of integration used in tlic int(!grals of ocjuations (9.1) which 

 (lofino the functions Uniz), V„{z) and Wn{z). The sub.scripts i and / stand for the 

 "initial" and "final" points of the ])aths. 



