The residue is 



w-PLANE 



K exp(-iu X cos 9) -K exp(-iu x cos G) 



-m cos^ eCu^-u^ [l-4(inK)^/2 ^^^ qj^ ^ 



The integral along c becomes zero as shown in (a) and the integral along c becomes 



j ( ) dw = f - 



K exp(-iivx cos 9) idv 



, . r/T.Nl/2../ xl/2 „T^ o iv+[(K)-^^^-i(m)-^^^v cos 9] 



_oo iv-[(K) +i(m) V cos 6] 



-J 



IK exp(-ivx cos 9) 



dv 



Therefore, the second integral of Equation (115) is given by 



J 



( ) du =- 2TTKi 



K exp(-iu X cos 9) 



+ r iK exp(-vx cos 9) ^^ ^^.^^ 



' J . .r.„si/2 ., a/2 ./ 



[l-4(mK)-'-^^ cos 9] o iv+[ (K)-'"^^-i(m)"'-^'-v cos 9] 



59 



