Wang 



We note that along Li the hyperbolic sine function in (101) may be- 

 come exponentially large, however, since L| lies on the right of 

 S, the factor exp [iKu)(cr^ - t^)] will be overwhelmingly small there. 

 Let us now integrate (101) by parts once to get 



.(e) eB,i 1 ( i««»(t-KT +KO- ) 



^1 T^rT7IT^TWrs\^ °" sinh^(e,e) 



7ri/4 

 ooe 



- \ ^i/4^ U'^ smh$(e,e) 



*^ooe 



+ o-5^'^^cosh*(e,l')] d(r| . (103) 



The integrated part in (103) i§^ identically zero; when we evaluate it 

 at the upper limit, sinh $(^,^) = 0, and at the lower limit, the 

 factor exp ^Kcotr ) is overwhelmingly small. If we integrate the 

 integrad (103) successively by parts and note the relation that 



d* '■i/4 > r^/2 jT I 1/2 



^= - e VKtol ^~V2Kcoo- . (104) 



rl/2 rf , r- 3Tri/4 .|/2 



where § dg/do- ~ V2e a is obtained from (88), we can show 



that 



ffe)^ €B,i io^y.^ (105) 



4Tr(Kco) 



Since t = 0(z ) as |z| -* cx>. from (104), we see that the contri- 

 bution to the potential due to f\^' is of order | z j' for |z | 

 large. This type of potential is acceptable. Now, let us denote the 

 part of the potential represented by the second integral in (87) by 

 &^ . 



f.-, _ _j^ (e/x)'^' r 



(w) _ 2€ (^/x) r J!-ia,{t-Kr+K(r ) 



'/^AT ..r, .,, .1/3 -2^ri/3J^', 



(Koo)'/^ (T - Vt^-1 - i) -"ooe" 



X } Ai[(-iW^ e] Ai[(-IK c.)''%-'^-'^T] 



- Ai[(-iK<o)'/V''^'/%]Ai[(-lKco)'/^nj(r/x)'^'*[g2(cr) + B| 83(^)1 dcr. 



(106) 



210 



