Wang 



If we are travelling along S in the direction of increasing Im cr 

 and if we restrict ourself to the first, second and fourth quadrants 

 of the (T-plane only, then on the right-hand side of S Re [ i((r - t )] 

 < 0, and on the left-hand side Re [i(or^-T^)] > 0. When either Im t 

 or Re T is zero, S degenerates into the positive real and imagi- 

 nary (T-axes. 



From (88) , we note that 



e ~ a/'/3 (95) 



and 



Arg i =^ Arg T + 3 as |t | ^ oo (96) 



Therefore, for t and oo large, the arguments of the Airy functions 

 appearing in (87) are large. Their asymptotic representations are 

 (cf. Jeffreys & Jeffreys [1956]), 



Ai[(lKco)'^%] ~ 



TTi 2 Ti/4^ 3/2 

 e 



1/12 ,. 1/4 



277(Ku) ^'^ e 



1/3 -27n/3 , 

 Ai[(iKuj) e |] 



e 



Ai[(-iKco) e] ~ j=- 1/12 1 /4 



when - -7— < Arg § < -r- , 



when - -T < -Arg 5 < -j- , 



TTi 2 -■n'i/4 /r-— «-3/2 



|l.|e /K^e (97) 



when - -7-- < Arg t, < -^, 



1/3 - 27ri/3 

 Ai[(-iKco) e e] ~ 



„ .7ri/4 3/2 



5^ + ±.e /kwC 



24 3 



e 



when - 7-- < -Arg 5 < — r— 



208 



