ELECTRIC CIRCUIT THEORY 95 



The "inslantaneous frequency" of oscillation is ai)i)i-().\iniatcl\- 



3 m2 1 



2 x' (l-m-\'x-)-' 



By this it is meant that at any point .v(.v>;?) the interval between 

 successive zeros is approximately 7r/S2'(.v). Otherwise stated, in 

 the neighborhood of any point .v, the function behaves like a sinusoid 

 of amplitude i?„(.v) and frequency co/2t where co = 0,'(.v). 



The following approximate formulas, while not sufficiently precise 

 for the purposes of accurate computation except for quite large \alues 

 of X, clearly exhibit the character of the functions for values of the 

 argument x>n, and of the order ;/>2. 





Jn (x) = hn A COS (g„X —d„), 



1 



where 



Jn (x) = —q,Ji„ \l — sin (q„x — d„), 



\ TTX 



[ J„(x)dx = !-{-— \~ sin (q„x — d„), 



(/ \ TX 



g„ = V 1 — n^/x^, 



^ 2w+l . ,, , , 



Bn = — 1 — TT — n sm ^ («/x) . 



