8 BELL SYSTEM TECHNICAL JOURNAL 



J2n( x ) =The Bessel function of the order 2w and argument x, 

 and the filter elements, in terms of the parameters w c and k, are 

 given by 



u c = 2/VLiC2, Li=2k/u e , 



k = \/L 1 /C i , C2 = 2/<t) c k. 



For values of time such that x<2n, A n (t) is very small and positive, 

 while for x>2n, the character of the solution is exhibited by the ap- 

 proximate solution 



A n {t)=\\l+Jl. ^ sin («,„*- e„,)~|. (lb) 



k L \ TX q 2n J 



The formula is deduced from the approximate formulas given in 

 Appendix II for Bessel functions, and h 2n , $%„ and €)■>„ are determined 

 by 



Aw= (l-w 2 /* 2 )' 



and 



3« = Ji-« 2 A 2 , 



2n+l . _ x , . . 



6„ = — - — TT — n sin l (n/x). 



For sufficiently large values of x, A n (t) is ultimately given by the 

 asymptotic formula 



An(t) ~| [}+<lf~ Sin (*" ^T ')]• < lc > 



Formula (la) was first given by one of the writers (Trans. A. I. E. E., 

 1919) as a special case of the solution for the dissipative low pass filter 

 (series resistance and shunt leakage). 



2. High Pass Wave-Filter, Type C X U, Fig. 2. 



am-\\+m- *fg^, w +ao ^"-'Ww- . . . 



. . . +D-"4tn(x) I (2a) 



