The third term of Equation (D.9) for x < becomes 



,_. , r A (u^,9) exp(-iu^x cos 0) 



'n TT J . 1/2 



[4(mK) ' cos 9-1] 



de 



-I 



2«'''' Kor{|(4mK-k^)'^'-i[|+2(mK)^/^] idk 



2 \ 1/2 

 l-2(mK)^/2 ([2(mK)^/2-k][k+2(mK)^^2] [k+2(mK)^^2] -1 



exp ^-|^+ [4(mK)^/2_^2^ |^ } (D.31) 



The third term of Equation (D,8) for x > can be transformed to the form similar 

 to Equation (D.31). Because of the lengthy derivation, we omit the intermediate 

 steps. 



With the change of the variable in Equation (D.31) 



^■^T7^-^^^^ (D.32, 



4(mK) '^-1 4(mK) ' -1 



(3) 

 g can be finally expressed as follows for all values of x 



ttJ 



"^ N^(k) exp 1 - ijj- [l-2(mK)-'-^^]x exp - ^ 6kx 



[k(l-k)(5k+l)(5k+2)]''-^^ 



dk 



exp {-[6(l-k)(6k+l)]^/2 -^^l (D.33) 



69 



