2 

 3 (j), 3(f), 



- T i + 1 r- i = E(£,n) (76) 



A similar discussion is applied to the transformation of the Laplace 

 equation, and the lowest order term becomes 



3% 3% 3% 



— ^- + —^ + — =i- (77) 



3? 3n 9C 



Thus, the Laplace equation keeps its original form after the transforma- 

 tion. To find the solution which satisfies the inhomogeneous boundary 

 condition of Equation (76), we consider the basic solution which satisfies 

 the boundary condition 



9 \ H-, 



—A + — i = SCg-S'.n-n') (78) 



K 3C 



where 6(£-£' ,r)-n') is the delta function of two variables. The solution 

 which satisfies the above at £ = and the radiation condition at infi- 

 nite distance as well, is given by the function 



G(s,n,c;5\n') = ^f de I; ex P [k^+ik cos e(£-C')+ik sin ecn-n')] 



-IT 



dk 



i i 2 



1-k cos 



tt/2 

 -it/ 2 



-i- I exp[C sec 2 6+i sec 6U-?' + tan 6(n-n')}sec 2 6d6 (79) 



2tt m J 



31 



