III-77 



A different approach to this same problem requiring a less strenuous 

 assumption on the Bessel functions is used by La Casce and Tamarkin (Ref . III- 

 18). If we factor out the term e^'^'^^, note at the same time that Yq ~ " Y> the 

 boundary condition (III- 69) becomes 



CO 



(III-74) 



m = -00 

 m;^ 



Using (III-71), this may be written as 



L^^ 



e^^P^J^(2kYh) + A^ + ^ 



Vi'^-^^A J |kh(Y +Y)| 

 / ^ m-'n-mL ' m j 



m=-=o 



e^^P^ = 



(III-75) 



For n = 0, -1, 1, we have the following: 



n = 



n = 1 



J^ (2kYh) + A^ +iA_^J^[kh(Y.^ + Y)]+i^A^J.,[kh(Y, + y)] 



00 



+ V" i'^'A J rkh(Y +y)1 - 

 ^.^ m m L m J 



m=-<n 

 Im|s2 



ij^ (2kYh) + A^J^[kh(Y, +Y)]+i*A_^J^[kh(Y., + Y)] 



(III-76a) 



^y^ .-i-m^ J rj^( +y)1= (III-76b) 



^^ m -i-mL m J 



m=-«> 

 Iin|^2 



artbur 31.1ittleJnf. 



S-7001-0307 



