441 
Also 
k 
> | SGA 
i=0 
Relations between the A’s and the B’s: 
m . 
2” = > Ai, m) m=. 
i=1 
. il . . 
29 > (-19Bj,i—1)2° 2 i = 1, 2, 8, 
j=0 
Therefore 
m al ; : 
i => AG. m) > 1 BG,i— bite 
i=1 j=0 ' 
the coefficient of x” on the right is 
m—k : 
y (-1)' Atk +i, m) BG,k+i—1) 
i=0 
and this must vanish k = 1, 2, 3, ...... m—l, and be equal to 1, for k = m. 
Whence, setting n for m — k, 
e k= 0.5 25: 
> (—1)' A(k+i, k+n) B(i,k+i—1) = 0, 
- a= 1,2, 3, 
or, setting 7 for k + 7, and n for m, 
is ; be. 2.. .n—i 
eee C21) Ae BE =k) 0. ‘ 
ee N= MND iS 5 
Similarly, starting from 
m—l1 
a™ — > (1) BG, m—1) x” * 
i=0 
we obtain 
ae i ; 5 [ssi 0 ag a 
(13) & (—1) A(k, k+n—1) Bi, k+n—1) = 0, 
i= pb PB 6 onc 
This relation may be generalized as follows: 
Set 
n . 
C(k,n,p) = > (—1)' A(k, k-+n—i) BG, k+n—p) 
i=0 
**Prestet, Elements de Mathematique, p. 178. 
