Darrozes 
solution of the homogeneous equation ( 13 ) 
(1) oO 
Ays ® ee Oe aes o (*) =6 ( 13°) 
(1) , as 
a oa ae 
Geometry of the outer The complex variable 
problem 
Figure 5 
eT ae ee ee ; 
Using the complex variable z=pe = Y+i Z , and its conjugated 
value z= Y -iZ4,it is easily shown that the n - expansion of gp '1) must 
be written with the asymptotic sequence 7 V2 CP 2 ee 
~ 11) _ (1) Wy vit) =~ (1) x, 
bi (Ry nh 22, a Os | tO [eee (14) 
Each term is obtained after resolution of a trivial Hilbert problem on 
the negative part of the real axis of the plane Z%. The final result is: 
@=c(s)+7 dj (s)p Sin 2+ "co( s )pcos +n “dl s )Psin 2. O'(7*) 
Col s), d,(s), co(s) and d,(s ) being arbitrary functions 
The full problem 
~ (1) Olt) 
We are now looking for_solutions of equation ( 16 ) 
fe) 
AMPS SY TOL EY GSO a holes SOR 
a = gies), gary o) + 7 55 (8) +0(n?) ( 16 ) 
3Z pe 
1748 
