546 BELL SYSTEM TECHNICAL JOURNAL 



which heis been worked out and communicated to me by R. M. Foster. 

 It is 



^|A',(a/3)+G(a3) \ 



where K\{x) is the Bessel function of the second kind and ilrst order 

 as defined by Jahnke und Emde, Funktionentafeln, pg. 93, and 

 G(x) is the absolutely convergent series 



3 32.5 ' 32.52.7 ■ ■ ■ ■ 



On the basis of this solution, it is a straightforward though intricate 

 and tedious process to derive the following solution for J(p,q) of 

 equation (29). 



Writing r= V^H^" and Q = tan-^{q/p), it is J^P-\-iQ 



in which 



1 , 1 4_ 1 



7^ 0"! + -?r '''2 i 7=^ 0-3, 



(32) 



(? = ^ + |(iog-|^)(i-..)-|e../ 



(33) 



In these eciuations log 7 is Euler's constant: 



7 = 1.7811, log — =0.11593, log 7 = 0.57722 and en, (t,. a-,, (h, 5,, s.', 

 7 



54, S4 , are infinite series defined as follows: 



