6. NUMERICAL EVALUATION OF ITERATIVE APPROXIMATIONS 

 Equation (3.5) for the Green function may be written in the form 



00 _ 00 



'tt) I dv 



4uG(?,x) = -d/r-l/rO - (1/tt) dv dyE(y,v;OE(y,v;x)/D(y,v) (6.1) 



00 — oo 



where r, r , E(y,V;x), E(y,V;0, and D(y,v) are defined as 



r = [(x-02+(y-n)^+(z-C)2]^/2 (6.1a) 



r' = [(x-C)^+(y-n)^+(z+C)^]^''^ (6.1b) 



E(y,v;x) = exp[z(y^+v^)"'-'^+i(xy+yv)] (6.1c) 



E(y,v;t) = exp[(;(y^+v^)-'-/^-i(Cy+nv)] (6. Id) 



D(y,v) = (y^+v^)-'-/^-(f-Fy+ie)^ (6.1e) 



The potential i['(^) defined by Equation (5.3) can then be expressed in the 

 form 



^(t) = /(t) + /(t) (6.2) 



S R 

 where the potentials ip and ip correspond to the singular terms 1/r - 1/r^ and the 



regular term defined by the double integral, respectively, in Equation (6.1) for 



the Green function. Specifically, the potential 4^ is given by the hull-surface 



integral 



22 



