Lee 



denoted by N^^ Is easily found to be 



00 



^, = y (b^+jcJN^(x(X,a),y(\,a))e'^\ (B-15) 



m = 

 where 



>, sin Zvciot , _, C cos (ZiTi - l)a 

 N^ = ^ +K.a • 



X2m ■ "l"\ (2m-l)\2m-J 



n=0 



and 



00 



No = - V ^ k"' k" ^^ ^ JTre"" sin K,x. (B-17) 



Substituting £q. (B-i5) into (B-14), we get 



(bm + jcJNjx(\,a),y(\,cv))e"^^ = - bo-,x^. (B-18) 



fn=0 



We choose any point on the contour of the cylinder between = and 

 9 = - ir/2 , say (x',y') in z-plane and (X^.o?') in the ^-plane, to show 

 that 



00 



e-J^ = - bo-.x;,/!^ (b„ + jcJN^(\o,c.') + QNo(x;,yi)| . (B-19) 

 m = l 

 Equation (B-19) can be substituted into (B-18) to give 



00 



) A^ NJX^,^) - N^(Xo.^')^ = No(x;,y') - No(xo.yo) (B-20) 

 where 



In principle we can choose an infinite number of points on the cylinder 

 (-Tr/2< 9 < 0) to set up an infinite number of simultaneous equations 

 from Eq. (B-20) for the unknown coefficients A^. However the 



946 



