By substitution of these relations into Equation (D.17), g, becomes 



4" 



2(2u) 



^' J 



1/2 e"''!''' 

 [-mv sign x] (2m^ ) dv 



c 



- I7 sign X J 



o (m V +1) 



1/2 



dv 



sign X 



o \ m / o \ m 



(D.36) 



In Equation (D.36), H (x) is the Struve function and Y (x) is the Bessel function of 

 ^ o * o 



the second kind. 



(2) 

 When K = 0, k, = k = and k = k^ = 2. Therefore, for x < 0, g^ ' = 0. 



(2) 

 For X > 0, from Equation (D.29), g, is given by 



4" 



= 2i'2 r 

 ^ J 



-ik exp(-^^|dk 



1 [(2k)^-4-4k^] 



1/2 



_ 2i'2 r 

 ^ J 



ik 



1 [(2k)^-4-4k^] 



1/2 ""^ \ m 



exp ( I dk 



I 



kx 



1/2 



dk 



1 (k -1) 



(^) 



(D.37) 



71 



