where 



1/2- 



A„(u ,9) = K and A,(u 0) = -i[mu cos e+2(mK) ' ] 



With the change of the variable 



2 mu^ cos 6 = k, k 



(D.20) 



where u.. is given in Equation (108) and 



1/2 1/2 "*" 1/2 



k^ = 1 - 2(mK) ''^ -[l-4(mK) '^] for (mK) '^ < 0.25 



= 2(niK) 



1/2 



for (mK)-'-''^ > 0.25 (D.21) 



(2) 



g is transformed as 



(2) 



^'j-,Jl^bi 



'^l^ 1/2 

 -^ +2(niK)^^^ 



1/2 2 2 

 [k^k+2(mK) '^] -4k^k^ 



k^k 



1/2 ^""P V^ 2^ ""' ^^ ^°-^^^ 



In the numerator of Equation (D.22), the first term is for n = 3 and the second for 

 n = 4. 



For X > 0, to the fourth, fifth, and sixth terms of Equation (D.8), we sub- 

 stitute the following variables 



2 mu cos = k„k 



2 mu, cos = k.k 

 4 4 



(D.23) 

 (D.24) 



2 muo cos = k~k 



(D.25) 



67 



