Al. a. Tchouproff 
199 
E{p{-pif = {l - 2pd \^^,pni -Pif+w^Pd^ -Pi) [1 - 12p,: + 12M 
E (pi -Pif = ^,PHI- Pif + ^Pf (1 -Pif [5 - 26i5» (1 -pi)] 
+ ^,Pi (1 - Pd [1 - ^^P' (1 -Pd + 120iV (1 -i>.)- 
(14). 
E {p/-p^={l - 2p.) 1^ PiHl -P,r + -^PrO- -PiT [56 - 462jOi (1 -p^] 
+ ^ (1 -p,:) [1 - 60;;,: ( 1 - pd + 360pr (1 - piY]^ 
Replacing iV [-(''■ +''^)] in (5) hy'^'^^t' \- ly j3,,.+h, i N''^+'> -\we find after some 
1=0 
transformations : 
c, +)•.,-! I 
/=(! -^V- A, 
(15), 
where the summation for extends to all positive integer values from 0 to the 
smaller of the numbers/ and 7\ — 1, and the summation for to all integer values 
from 0 to the smaller of the numbers — \ and /— h^. 
Substituting the values of Epi^^~^^ Pp''~^' the development of 
E(pi'-piY>{p;-Pjy'= 2 t (-iy'-^''^Crj'C%j-'pi'p/^Epp-'-^^p/>--^-^ 
Ave find after some rather tedious transformations : 
)-, + f2-2 -1 /"(orri-l) N 
E{p;-piY^{p^-pjY'= s ^ s 
/-/J, (orr,-l) 
1 '-.tI '-2-1 
(16). 
+ 1y^r^i S 2 (-l)'' + '-^-^'-"^-l «r,,r,-7-3 
In the general case we have : 
Eip'i, -PhY' {p'i, -pO'-' ••• (p'i, - Pi^Y" 
0r,+r^.h,-h,J~h,-l,,Pl'' '''pf' '' 
'J ) 
, / (or )■,-!) /•-/(, (or/-..-l) /-7ti-/(j-...-7ij_, (or rj-l) 
2 
/=Ent.( - - 
k 
(17). 
1 '^i- 
^ A7-r,+»-,+...+r.-i . - , ^ ••• -^V ^ ' * f'^, •••P 
