?3&S«i&KftiS9mmMWM«iMm 



We carry the analyses through in a general form as far as possible, to 

 indicate the procedure which has to be followed in more complicated 

 problems . 



First of all we extract a factor exp isi. from Y (s) , writing 



Y + (s) - exp(isil) Z + (s) (7.20) 



so that Z.(s) - 0(s -1 ) at infinity in R . The necessity for doing 

 this will be apparent in a moment. Then write K(s) - K (s) K (s) as 

 usual, and divide through by K_(s) to get 



e is *Z + (s> Y (s) 



K (s) + FTiT + K + (8) Y i (3) ° ( 8 + k ) K (s) 



— — o — 



The second term on the left is analytic in R and 0(a _1 ) at infinity 

 there, the third is analytic in R and 0(s _1 ) at infinity there. The 

 term on the right can be split in the familiar way as 



G. (s) + G (s) (7.21) 



(s + k Q ) K_(s) + 



and we also make an additive split of the first term in this way, 



e Z v a; 



- U(s) + U (s) (7.22) 



K_(s) 



using a general theorem to be given in a moment. G . (s) are each 

 0(s -1 ) at infinity in R + , and we assume that is also true of U + (s). 

 Then we have 



U + (s) + K + (s) Yj (s) - G + (s) 

 Y.(s) 



- G - (8) " KliT " u - (8) 



40 



