deriving Mutual- and Self-Inductance Series. 

 or putting 



283 



k 2 =x, a=, 



d 



dx' 



u=x*y } 



»(*+ !)«=*(*+ ?)(«-!)«, 



(9) 



an equation of the type (4). 



The solutions of (9) with the various possible independent 

 variables yield the following series : — 



L= 



(F) 

 (G) 

 (H) 



= ^( (1 _, a)F( o,l, 2 ,, 2) _^}, . 

 in which F(«, /3, 7, #) denotes the hypergeometrie series 



,..«£_. q(«+l)ff(/3 + l) . , 



L+ l.y X+ 1.2. 7 ( 7 + 1)"' 1 + -'-- 



The above series are suitable for long coils. (F) and (G) 

 are convergent for all lengths. (H) and (I) converge only 

 if b >2a. 



in which 



1.3.5.7 

 2.4.4.6 



2.4 

 1.3, 

 2.4.6.4.6.8' 



i*V , , fi ,. fi ./ f.+ ... k • (J) 



.,45 1 



r 1111 

 ^-+i*= 2 +-f- 1-5 



t 1 11111- 



, , 1111 

 +*-*»= 6 + 8-5-9 



