476 BF.LL SYSTEM TECHNICAL JOURNAL 



Writing c = v{h' + y' + '-v') = vrt^^ we have then 



P + 'Q = >"'-'< I v?TT + ./ - 



(5) 



J-»CO 

 

 K^(c) 





(■ ^ S i''5 "^ .^2527 



cosh- </) r-^s>"h 

 - + •••; 



jui'-i?[/(r) — (l/c^)] = M times Carson's P + i(2 with a = /j-AirXw. 



The problem is now reduced to the tedious procedure of differen- 

 tiating J'{c) and separating real and imaginary parts twice for each 

 power of e. The chief steps are given in Appendix II. The result 

 is best written in the form 



P = 



Wo 



W4 / r.y 1^ , "' 



- ( - 1 cos 80 



■mn { !'\ 



+ 



2 Ll!2!V 2/ 



6!7! V 2 



cos 120 + 



''''^'^-jwA^J "'"^'^ 



V2 



Wi 



ri cos d 

 3 



+ 5!6!ilj smlO0- + 

 r-[^ cos vS(9 ^1^ cos 50 



r/ cos 70 _ 

 + W7 3252729 + 



^1^ cos 60 



, ri2 cos 20 / , , , 2 



/fi + w/glog 



, ri'OcoslO0/. , ,2 



+ 2^^516! (^^o + w„log-)- + 



(O 



Q- - 



nt'. 



l!2!Vl^-^'^ln 1'"^"" 



+ ^ 1' -««- + 



2 See Jahnke & Emde, "Funktionentafeln," pages 171 and 93. 



