86 BELL SYSTEM TECHNICAL JOURNAL 



as to make the circuit (luasi-distortionless. We therefore take, 



operationalJN', 



z, = pL + R = L{p + \) 



(230) 

 l/z2=pC-\-G = C{p+\) 



where X^R/L = G/C. 

 We then have 



Sl22 = L/C, 



Zi/z2 = LCip+\y, ^23]) 



Now by reference to formula (229) we see that ^„ is a function of 

 {p-\-\); thus 



^""Z.(/> + X)~(^ + p) 



(p + X)Z„(p + X)- 

 Now write 



" z,.(py 



It follows at once from reference to theorem VII that 



An=(^l+\j^'dt'jA:,e ^' (232) 



so that the problem is reduced to the solution of the operational 

 equation for A',',. Writing w, = 2/\^LC, we have 



_ (233) 



Now refer to formula (;;) of the table of integrals; writing \/ L/C=k, 

 we see by Theorem \ that 



where J2,i{t) is the Bessel function of order 2w and argument r. We 

 note also that this is the indicial admittance of the non-dissipative 

 low-pass wave filter; that is, the current in the w*^'' section in response 



