668 



BELL SYSTEM TECHNICAL JOURNAL 

 TABLE I (Continued) 



Pair 

 No. 



410/ 



Coefficient F{f) for the 

 Cisoidal Oscillation 



Coefficient G{g) for the 

 Unit Impulse 



p-" = lim p-''e-'"'^^\ 



a— »-0 



< w 



.„(g) = lim -Dg-"e-^''~"" 



= (^'^2(drr)!)^"- 



2(« 

 + X„, < ± g 



411. 



p-" = lim ^— - -f 



(^+/3)" 

 Xfc(w-)fe)! Xt(w-^)! 



-n{g) 



< w 



)] 



415. 



416. 



421.' 



- = lim 



P 



o\p- 



-X i+_X\ 



p-\- ^J 



1 r r ^- 



— = lim -^ — 



^2 ^_^o L (^ — 



+ 



X_ 



/3)2 



^ + X 2^/x 



(^4-^)2 ^2_^2 



431. 

 432. 

 433. 



F(/) = lim Fi(f), where Fis any proper 



a— »-o 

 rational fraction in p with w distinct 

 poles, the degree of pole Zj being w,-. 

 All pure imaginary poles in F are the 

 limits of corresponding poles in Fi which 

 have assigned real parts ± a. 



<n 

 < « 



< w 



-lis) = X it I, < ± g, unit step at 



:= 



-2(g) = iki + xg + M 



< ± g, ± i?(3;) < 0, 



and the upper or lower signs for each 

 term are employed according as the real' 

 part of z, (either actual or vestigial) is 

 less than or greater than zero. 



1 



(w-1)!^ ^ ' 



<g 



{n - 1)1 ^ 



(P2 _ ^2)„ ' 



g <0 



(-1)" ^-m X- (n + fe-2)!|g»-M 



E 



(«-l)! /fri()fe-l)!(«-^)!(2/3)»+*-i 



_ (- i)"U""MA^n-iOkl) 



(« - l)!7rH2|8)»-i 



« A star marks a pair as being the limit approached by regular pairs. 



