Al. a. Tchouproff 
159 
CHAPTER II 
I 
(1) Putting J ^ {Xi - ,n,Y = (1), 
we have : Efj,',. = /jl,.. 
Noting that /u,',. is the arithmetic mean of the mutually independent quantities 
(Xi-niiY, (A'a-Wi)'', ... (Xx- iihY, 
and that E (X^ — m^)'' = /x,., 
while E {Xi - vi^f'' = /Jh,-, 
we find from formulae (4) and (5) of Chapter I, when we put r = in, and replace 
1 
in 1 — 1 \ 
-L' h = l /(=(( 
1 m III — i 
= -^t t (-])'»-"-'■ /3,„,_,,, 
•(2), 
where 
h 
R\m m-h] = - Htl- a,'"-''-' S 
...(3), 
where the last summation extends to all positive integer values of y'l, j.,, ... jj, 
satisfying the condition: ••■ .'jf= *, and to all integer values of /ij, h.,, ... /if, 
satisfying the conditions : 
•2 ^ hi< h.,< ... < lif, 
Ihji + I'J^ + . . . + lifjf =h + i. 
Hence : 
-^[m, m— 1] ~ (-'in' t^r'^ ' f^ir 
,m— 2] — 
(4), 
i2 
[in, m—i] 
1056V + 1056',,/ i^r-' /X,/ /U3, + IbCj /x,"'-« y^,. 
and, on the other hand 
R[iii,l] = l^inr 
m-1 
R[m, -2]=2 2 G 11,'^ f^hr im-h) r 
h = 1 
i/( - 1 
•(0). 
