criDKD-WAVK IMIOI'ACATIOX Tlli;()r(ill f;YKOMAr.NETlC MEDIA 633 



1.6 



/i' 



-1.0 -0.8 -0.6 -0.4 -0.2 



Fig. 13(d) —See Fig. 13 

 remains finite, while 



'■o \f •; ^- I or ro 



0.2 0.4 0.6 0.8 1.0 



1 - Xi^ 



1 — a\i \ " '\ \ — (s\\f 



becomes infinite imaginary. Examining tlie solutions obtained under 

 these conditions it is possible to find expansions for ^ in inverse powers 

 of )\) . These are as follows: 



for p > 0, cr > 1 or /; < 0, — (To < cr < 



2V2 \ .r„" 



a — \ \ (T — 1/ To^ 



(43a) 



where the .r„ are the successive roots greater than zero of F(.r„) = 1 

 and the modes are associated with the Xn by the scheme: TEn — ^ Xi , 

 TMii -^ X2 , TE12 — > X3 , etc : 



for p > 0, < <r < o-fi or /> < 0, 0- < — 1 



p/2 \yn^ 



<r — 1 \ 0- + 1/ ro^ 



(43b) 



