SERIES FOR WAVE FUNCTION OF RADIATING DIPOLE 



107 



over to B and G is to move over to A. This deformation of the 

 contour does not alter the value of the integral as long as we pay 

 attention to the arguments of w — 1 and w + 1. In Fig. 2{b) the 

 deformation is almost completed; all that remains is for G to coincide 

 with A and // to coincide with B. 



A A' 'G 



Fig. 2 — Deformation of contour in w plane. 



Using this deformation of the contour we may write equation (2) 

 as follows: 



"^ (1 - T-)r\ I ~ I ~ J (w~- \yi- 



^ > I- 'Jkils Jkii's Jk^ls ^ ' 



r{w- — \y'- 



(1+) gixrw^d^ 



with the understanding that arg w — 1 and arg w -\- \ have their 

 principal values at the beginning of each integration. Upon referring 

 to (2) we see that the middle integral is — ni(r, 0) and hence 



TIi(r, 0) = 



- iLih) - Lihn 



where 



L{kO 



2r{\ - r') 

 •(1+) e'^'''''wdw ^ (isr)" r^^+'> w"+^dw 





{w- - ly'-' 



(15) 



(16) 



and L{k2) is obtained from L(ki) by interchanging ki and ki. 

 Let w- — 1 = T-(l — t), or sw — kl^J]. — ts~jk-f, then 



.(1+) ^n^idw h / kiY f^'+'[(l - (5-///^2-)]"'- 



tJkils 



(7t'2 - 1)3/2 



2^1 \ 5 



Jo 



(1 - ty^'^ 



dt 



= 2^(-^\ F{\, -n/2;\/2;syk,'), 



(17) 



where it is understood that at the initial point of the contour 



