384 Mr. L. Isserlis : Application of Solid Hyper geometrical 

 which reduces to 



_ (w - r) i H ,[^], \__ 



a *-(n- r -r')\ s! [y] s [y+s] r . 

 = („-r)! 1 , [«].[?]. 



(n — r—r')\ [7],., * 5 ! \_y + r') s " 



p ', V=oc'[S,/+S 1 (2cy+...] 



or , _ ,/S 4S 1 (2y + S 2 (3)< + ...\ 



^"-"l S +S 1+ 8 S +.... 7 



n 4- J^ 2 ^- 4. «("4-DA/3+l)(3)' ■ "I 

 = C *L lfy + r') 1.2.(y+r')( 7 +r' + l) + "--J. 



i+ l.( 7 + ,.')+---- 

 Now our a, = Pearson's a, 

 our /3 = Pearson's /3, 

 and our 7 +r ; = Pearson's 7 ; 

 our //«) = Pearsons ^. 



§ 6. To find the higher moments and product moments we 

 write equations (5) (6) in the form 



( 1 -^)[%2o + %n+%io(wi-3)--%oi(^ + l)+%ooK--mi + ^ + 2)J 



+ (n — r')xio + rjeoi+-%oo(— r — ?n 2 + / — w) = 0- . . (9) 



(l-y)[Xo2 + %n+%oi(V-3)-x 10 (/ + l)+Xoo(V--^i , + / + 2)] 



+ (^- r )%oi + ^%io + %oo(-^-V + ^~w)=0, . . (10) 



or (l-tf)P + Q = 0, ..... (11) 



(l-?y)P+S = (12) 



Now 6(xu)=x(l + 6)ii, 



6\xu) = x(l + 0) k u, 



and .'. d k (l-x)u=[6 k -(l + k ]u+(l-xXl + 6) k u. 



Similarly **(l--y)w= [**-(! + ^)*>+ (l~y)(l + ^) ;fc M. 



Hence 



^[(l-ar)w] = [(^-(l + ^)*]^/ + (l-.-p)(l+^)*^ M 



^*[(l-y>] = [</>*- (1 + £)*] 0*w + (l-y)(l + 4>) k h u, 



[^(l-.i'>],^i = U^-(l + W^}i • (13) 



[^(l-^]^i={^-(l + ^)^}!. . (14) 



