With Equations (D.12) and (D.14), g„ can be written for all values of x as 

 follows 



^(1) K 



'3 



2(2) 





where 



'22^/2 

 (ra^+m ) +ni^ 



1/2 



+i(sign m^) 



: 2 2//2 w^\ 



i (4 



+m2) 



1/2 



dv 



(D.15) 



4(mK)-'''^ V (K-mv^) (sign x) 



(D.16) 



When n = 4, by following the same procedure, the double-integral terms in 

 Equations (D.8) and (D.9) can be expressed for all values of x 



4" 



00 



2(2)1/2 J 4 



"22^/2 - 

 (m^+m ) +m^ 



1/2 



+i(sign m ) 



(m +m ) 



1/2 



1/2 



2 2 

 (m^+m„) 



1/2 



dv 



(D.17) 



where 



1/2 

 R, (v) = -i 2(mK) - mv sign x 



(D.18) 



The rest of the terms in Equations (D.8) and (D.9) can be further reduced to 

 the forms that are more useful for numerical computations. 

 For x < 0, let the last term of Equation (D.9) be 



^/2 ^ , 



A (u 9) exp(-iu X cos 0) 



[l-4(mK)-'-/2 ^Qg Q] 



1/2 



(D.19) 



66 



