r 



Wang 



Ai[(iK cu)'^^ e-'"*/^e] Ai[(iK co)'/^|] } (e/x /^^ [ g, (cr) + B , g3{(r)] d<r 



Tri/4 I 



- Ai[(-iKco)'^' e-'"'/'e] Ai[(-iKc.)'^' l]} U/x )'''" [ g^{^) 



+ B, g3((r)] do- \ (87) 



where ^ and x a-s functions of T are given by 



|e''' = VJe'"^*f -^;l_ , (88) 



3 J I (0-2. i)'/" 



and 



< = K:fe -')]'• 



(89) 



»v <««» 



^ and X indicate the functional values of ^ and x when the 

 variable t is replaced by the integration variable cr. 



_ i(T + Vt^- 1) - 1 r./T^ v3,, ,_x , /T^ ^2, 

 (t2_ 1)1/2 



gt^"^) = ,7 " v. [l(Kco)^M,(T) +(Kco)'m2(t)] , (90) 



g^lT) = iil-bLlll^JLl [-i(K co)^M,(T) +(Kco)2M2(r)] , (91) 



g^(T) = T^[i(T +V72T7) _ 1], (92) 



B| is an arbitrary complex constant which is derived from b|, and 

 B| is the complex conjugate of B,. The lower limits of integration 

 shown in (87) are chosen for our convenience. Therefore, when 

 necessary, homogeneous solutions of the form 



206 



