Al. a. Tchouproff 
145 
(4) Further, it is important to note certain relations connecting the coeffi- 
cients a and ^ : 
V(-iya,,,+i,<3,+i,,= 0 
j=(i 
a , Q , — S (] -ik+im-i /?. 
"■n,n—kHn—k,m — — ' ^''k,m,i 
? = 0 
.(16), 
•(17), 
where the coefficients Bic^„t,i are independent of n and are determined by the 
relations : 
-^o,«!, i ~ Bin i 
I^k,o,i = ^k,r 
+ {k + — i) \^Rk-\,m,i-\ + Rk,m-i,i-\\ ~ Rk,m-\,i-\ 
From (18) we find 
i2*,.-*,o = 1.3.5...(2s-l)C/ 
I ...(18). 
R, 
k, s—k, 1 
S-1 
3 
.1.3.5 ...(2s- 1) {0/ + CV,{ 
.(19), 
and, in general, 
Bk,s-k,h= 2) 7\h,jG''s-j 
j = 0 
.(20), 
where the coefficients t's^hj are independent of k and are determined by the 
relations : 
h 
S rs,hj = Rs,h 
7 = 0 
r<:,h,j = (2s - //. - 1 ) ?V,,;,, + (S + j - /() rs_,, + (S -j) r5_j,A_jJ_i . 
Putting 
...(21). 
.;=0 
7 = 0 
we find further : 
R 
'•Zh-l-j ' s,ih+l,j 
.(22), 
k,s-k,2h " ''s.h,/ ^ s-2!i + l 
7 = 0 
R, 
h 
'k,s-k,2h + l ~~ ,-' s,h,l s-2h + l ^A--27t+/-U 
7 = 0 
k-1 , ,ys-k-J-l 
.(23), 
Biometrika xii 
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