Lg(|;il;) = -(1/4TT) J [ (/+/)-(4+'^^ ]9 (l/r-l/rO/9nda (6.4a) 



00 ^00 



L^(t;'l^) = -(1/4tt^) J dv J dyE(y,v;|)A'(y,v)/D(y.v) (6.4b) 



00 — oo 



with A^(y,v) given by 



^'(y,v) = j 



[(^^W)-('l^^+4^^]^E(y,v;x)/^nd£ 



j 



- 2i(f+ie)F I (/-ijj^)E(y,v;x)t dil 



■J {(/h 



+ F^ I {(ijJ^-t|jJ)3E/3x-[t d^^/dl-n t 3 (ij;^+i|;^)/9d]E}t d£ (6.4c) 

 X z y y 



(1) ->- 



The first iterative approximation (j) (5) can then be determined by using Equa- 

 tions (6,2), (6.3), and (6.4) in Equation (5.6). The potential L^(tA ), n ^ 1, 

 defined by Equation (5.7), for the second and subsequent iterative approximations 

 <t> (n>_l), can be expressed in a form almost identical to that given above by 



Equations (6.4) and (6.4a, b, and c) for the potential L'(5;iJj). 



The basic computational task common to Equations (6.2b and c) , (6.3), and 

 (6,4b and c) consists in evaluating a double Fourier integral, 1(C) say, of 

 the form 



.j\,! 



1(C) =1 dv I dyexp[ay^+v^)^^^-i(?y+iiv)]N(y,v)/D(y,v) (6.5) 



24 



