280 



BELL SYSTEM TECHNICAL JOURNAL 



These tabulated values were computed from the corresponding con- 

 vergent series, the first few terms of which are: 



Qy{r',s') = \W - Is" + • • • 



-j-i{- s' log / + [f log 2 + ;A(1) + hy 



+ J^-"+ •••!. 



N^ir'y) = hs' log [(r'' + s''yi' + 5'] t (5) 



- i[nog2 + iA(i) - ly 



-hints' -tV''+ •••!. 



For values of r' greater than 2, sufificient accuracy for ordinary 

 purposes is obtained by using the first two terms in the expansions in 

 terms of s': 





^here 



(6) 



Q,(^\r') = ilU{u)K,{u) + 7i(«)^i(«)]. 



{2)(y'\ = 



Q^'^Kr') 



8i(' 



[(1 - 2«2) - (1 + 2u)e-'-':\, 



7Vi(i)(r') =-„[!- 2uh(u)Ka{u) - 2/i(m)/vi(m)], 



A^j(2)(/) 



u 



1 +•/■ 



1- (7) 



[(9 - 111') - (9 + 18;/ + \6iC~ + 8z^^)c-2„^^ 



16h 

 For actual computation we note that 



m(y'\ = 1 



Gl^^KO 



f7 - A^o(r') 



The real and imaginary parts of these four functions are shown in 

 Figs. 8, 9, 10, and 11. The dominating terms in the asymptotic 

 expansions of Q\ and A^i are thus given by those of (2i^'^ and A'l^^^ 

 For large values of r\ <2i''^ approaches zero as (1 + i)lr', and A''/') 

 as (1 + i)lr'\ 



