NUMBER OF IMPEDANCES OF AN n TERMINAL NETWORK 313 

 The inverted formula * is : 



m 

 1=1 



A short table of the Stirling numbers of the first kind follows: 



The three equations resulting from applying this transformation to 

 equations (9) are as follows: 



Tn = i[fn+4 — 6e„4.3 + 5e„+2 + 8e„+i — 3e„], (10) 



Un = lE^n+e ~ llCn+b + 30e„4-4 + 5en+3 



— 56€„+2 — 5€„+l + lle„]. 



For computing purposes, values of e„ and Ae„ up to w = 10 are 

 given in Table II. 



TABLE II 

 Exponential Numbers 



^ Noting that S a'^Sx, m = {a)m, where (a)m is the factorial symbol used through- 



out, the inverse relation may also be written: 



(e + m)"- = e"(«)m. 



In this notation, the inverses to equations (2) for the impedance numbers have the 

 following simple forms which are worth noting: 



{D)n = dn 

 iT)n = tn 

 {U)n = Un 



