each of a. and o- In the following equations. Equation (27) can be approximated 

 as 





(62) 



for 1 - 1,2, ...,M 



the normal derivative of the two-dimensional Green function Is 



0G2 oG 2 ac 2 

 -r — - -r — n, + "5 — n, 

 on ox 1 oz 3 



(63) 



We use the complex variables In derivation of derivatives of the Green function 

 suitable for nuoerical evaluation. If we introduce the following complex 

 variables 



C - x + iz and C Q » x + lz , 

 G,(p,q) - Re{F(C,C )} 



(64) 

 (65) 



where 



F(C,C ) - ln(C - C ) + ln(C - C ) -1- pv 



,-ik(C - C n ) 



k - k. 



— dk (66) 



- 2k1 e 



-ik Q (C - C ) 



In Equation (66), C Is the complex conjugate of C . Then, the two derivatives 

 in Equation (63^ can be expressed as functions of F 



~r - «• I an I 



5x 



(67) 



20 



