518 BELL SYSTEM TECHNICAL JOURNAL 



The coefficients C„ are easily evaluated from (8) and (13a); they are ^ 



Ci = n{l), 

 C2 = iJr — i^.fi, (17) 



V/^' 



Cn+1 = [ fX — i~r. j Cn- 



Now consider' the quasi-stationary admittance Y{iQ). Writing 

 S2 = w + n(t) and expanding as a power series, we have (assuming 

 that the series is convergent) 



F(iS2)=FM+E^J^.F(M. 

 From (16), (17) and (18) we have at once 



^here 





D, = 



. dix (P 



(18) 



(19) 



(20) 



Dm+l = Cm+1 - fi"'+K 



Consequently, the total current, after initial transients have died 

 away, is given by 



/ = I^ss + A(/) 

 = exp ( i I Udt 





1 /.. d^.d't,\d^Y 



J\V^^Tt^w)d^^ 





(21) 



We have thus succeeded in expressing the response of the network in 

 terms of the quasi-stationary current 



/g.. = Y{i^)-exp(i C 



^dt] 



^ From these recursion formulas C„ can be derived in the compact form 

 = I iU — z -r J M symbolically. 



(22) 



