c. Third Integral of Equation (115) 



Evaluate the following integral in the complex plane of w 



K exp(i^^^ cos 6) ^^ ^ f ^ f 



,,^,1/2 , ,1/2 ,,^ J J , 



w-[(K) -(m) w cos OJ c^ c„ c„ 



= 27Ti (residue) 



«=1 = '-2 



The residue is 



w-PLANE 



K exp(iu,x cos 9) K exp(iu„x cos 9) 



tL_ __ + d 



2 2 



-m cos 9(u,-u_) -m cos 9(u_-u,) 



-K exp(iu,x cos 9) K exp(iu„x cos 9) 



1/2 ^/2 / 1/2 



[l+4(inK) ' cos 0] [H-4(mK) ' cos 9] 



The integral along c becomes zero as shown in previous cases and the integral along 

 c_ becomes 



j ( ) dw = 



K exp(iivx cos 9) ., 

 — ^ 2 ^^^ 



iv-[(K)-'-/^-(m)-'-^^iv cos 0] 



c 



'I 



iK exp(-vx cos 9) dv 

 'o iv-[(K)''-^^-i(m)-'-^^v cos 9] 



60 



