2nis J t - 8 



Without any real loss of generality we can take the path of Integration 

 to be the real axis, and s 2 > In F. , so that 



dt 



I f tF£t) : I (*- Le|.lg.(Oli ! 



LL c - 8 l "L /u -..)» + 



Let |s| +™ In R + along a rpy with 8 X ■ Ks 2 , and divide the range of 

 integration at points t - ±M. M is chosen so that |s| » M, but so 

 that for |t| >. M, |F(t)| < c|t| for some constant c and sone X > C. 

 Then on (-M.+M) 



and the integral is fiuite and independent of s, while on (M,») say we 

 put t ■ Ks + s tan9 to get 



p tlF(t)Ldt < c_ r 2 _sec 

 J M /«t. -&,)■+< ** ^ I, (K + 



tt/2 



d9 



tan8) X 



and again the integral is convergent and independent of s. Thus under 

 these conditions 



F ± (3) - 0(s _1 ) at infinity in R ± . 

 The above is hardly a proof, but it ccn Le rigorized. In any 

 application tha behavior at infinity should be cnecked out carefully in 

 each case. 



73 



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