Falttnsen 
+ exponentially small terms 
(Ce Soy. 
. (C-9) 
Here 6, and 6, are some very small positive numbers. '"'a'' is 
defined by (56) andis restricted to 0 <a < 1/2. C€. is given by 
by a} Vio + uK)4 [ke EOS (C-10) 
te) 
For all other values of k in Case II, I(k) will be exponentially 
small. 
Gase lll: k < k, : 
We define 
SS 
iT 
V( w, + Uk)” je -( 33) (ee 
In this case the poles of the integrand of (C-3) are also real. 
The Rayleigh viscosity mw will tell us how to indent the integration 
path around the poles. By using the residue theorem in the same way 
as for case I, we will geta similar resultas (C-8). It can be shown 
that the integral terms are exponentially small. We get 
1822 
