

1/2 



-l[mu cos 9+2 (mK) ]exp(-ixu cos 9) 



'^ 2'ff^\-' -^ -t -l / .^,l/2_^l/2 o^^ 



^~ ~ " ^ ' u-(K +m u cos 9) 



(116) 



Tr/2 



1/2 



.,, , , _[mu cos 9-2(mK) ]exp(lxu cos 6) 



+ \ d9 du r 



2tt J J ,^1/2 1/2 Q. 



•^ - L u-(K -m u cos 9) 



?j -{-'' 



With the change of the integral paths and the change of the variables, we can 

 derive the equations suitable for the numerical computation from Equations (115) and 

 (116) . Following the derivation of Joosen, we can express g„ and g, as follows 

 (see Appendix D) : 



g = g*-"^^ + g*-^^ + g^'^-' for n = 3 and 4 (117) 



where 





1/2 ^/2 1/2 ^/2 



(1) 1 I I 2 2 2 2 



- 1/2" Rn(v)<' [(m^+m^) +m^] +i(sign m^) [(m^+m2) -m^] 



-V |x I 



dv (118) 



2 2 ^/2 

 Cm^+m^) 



,(2) 2ik 



^n IT 



2ik^ /-^ K or -i|_^ +2(mK)^/^J / k^k \ 



~J 1/2/ „ 2, 2,^/^ ^"'r^ 7 



dk for X < (119) 

 L/ z " \ zm / 



*o {[k^k+2(mK)'-'^] -4k^k^} 



32 



