ELECTRIC CIRCUIT THEORY 373 



bar indicates the conjugate imaginary of the unbarred symbol and 

 (301) is therefore entirely real. 



If we now substitute (301) in the symbolic equation (293) we get, 

 by (295) and (296), 



2Z -^-^ y j 



Simplifying this equation and dropping the conjugate imaginaries 

 gives : — 



2 ^me'(«+'"")' = /oe'«'- ^ 2 ^me'<« + ('"+l)'^)' (303) 



Finally, if we write 



Z(i(^ + ;;ico) ) =Zm 

 and 



r/Zm = hn, (304) 



and equate terms of the same frequency on the two sides of the equa- 

 tion, we get 



-4 ,v = — h^A N- 1 



(30o) 



Ao = Jo-hoiA-i-\-Ai). 



It will be observed that, by (305), starting with An each coefihcient 

 is determined in terms of the coefihcient of the next lower index. 

 Thus: 



An= —JinAn-i 



An-X = -//A'-i(^A'-2+^aO 



— _ h^z^ l ^Ar-2 

 1 — h^-xkN 



Similarly 



1 



An~2 — 



l — hi^-zfiN-i 



l — hN-\hi 



