Heterogeneous Elliptic Cylinders at an External Point. Ml 

 density. Then 



J -0 Jo 



J-/3 Jo B =i 



being supposed to be greater than SC and the point A 

 ing outside the limiting circle described with centre S and 



r 



lying 

 radius SC ; 



n+2 ' C? cosn(^-f)) d<f>. 



2j_,(H-.cos^) 2 ° g? * i n(n + 2)i"J_ fl (l + e 



cos </>) 



n + 2 



go 



where 



i to \ _ P cos ncj)d(l> 

 i nK ^e) -j^ (1 + 6!C0S ^- 



and 



I (A <0 = 1 (T^TcoT^ 



2 , .J, P 1 /l-«l e sin 

 tan tan -r \ / - — — „ . t— 







(1 — 03)*" I"" 2 v l + gj l-^'l + ^cos/3* 

 We shall put l n {j3, e) in the form of a series. Putting 



(1 + e cos (/>) "("+ 2 ) = 2 A;^ 2 cos m0, 



A »+ 2 _ / i \ Wl ( , » + wJ -l) ■ _£^ F / n + m 4- 2 ?i4-ffl-f 3 

 A m - ^-l; ^ +1 ^ j ^ , 2w _ 1 . 1 ^ 2 , 2 , 



m + 1, e 2 ) (« <1) §2 



where 



since 



C t rsin(wH-n)/3 sin(wi— n)£" 



1 cos »«<f> cos wob acb = t " H — 



} T L w* -r n m — n 



fro ,1- f cos "'^^ _i< 4 »+^ 



