45 



Coefficients in Expansion for Undisturbed Stream Potential 



1 ( JK ^^\ 



71+ l)(2n + 2)^ \ dy dz I 



"+1 (271 + l)(27i + 2) 



[78a] 



"+1 (2n + 1) (271 + 2) \ d2 dyl 



[78bl 



and in particular 



" 7i! ax" 



(9 a' 



m + < + 1 da; 



6i 



<9&1. 



m + t + 1 dx 



b°=0 



> m>t 



MJ 



(71 + 1)! dx" 



2 d" 



i4>ry-'^zz'> 



(n + 2)! dx"-'^ 



(71 + 3)! dx"-^ 



yyy ^yzz' 



2 d" 



(71 + 4)! a a;" 



(•/•xxx*: -^^yyzz^ 



6i = 



2 a"-l 



(71+1)! dx"-'^ 



62 _ 2 a"-2 



(71 + 2)! <9a!"-2 



(<^J 



(20.J 



63 =. 



2 ,9 "-3 



[82a] 



[82b] 



[87a] 



[87b] 



[87c] 



hi 



(71 + 3)! (9 a; 

 2 (9"-^* 



„_3^3^rr^-'^.z.) ^^^^^ 



(71 + 4)! a a;""'* 



(4.?Syyy, - 4,^ ) [87e] 



Source 



F/i;=-4^paX^^) 

 where ^^{^i) is the velocity at r^- due to the undisturbed stream 



[881 



