1194 

 and 



THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 







0. 



(86) 



A(x)o 



-3 



■3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 



X 



Fig. 1 — The transcendental function A {x). 



•14 -12 



Fig. 2 — The transcendental function A (x). 



For the integration of (85) we need the transcendental algebraic function 

 of a single real variable defined by 



A{x) + In I A{x) - 1 I = :r. 



(87) 



This function is plotted in Figs. 1 and 2. It will be observed that x is always 

 a single-valued function of A; while A is a single- valued function of x for 

 X > 0, a, double-valued function for x — 0, and a triple-valued function for 



