GENERATING FUNCTIONS IN THE THEORY OF NUMBERS. 
139 
Art. 42. Tlie general case. 
The matrix being that connected with the determinant 
we have the relations 
as well as 
other relations 
a 
In 
a^x — Px) 
axx^yy I - 
XX ^yy 
= V^>r- 
connected with the co-axial minors of order greater than 2. 
From the relation 
1 ^^xx^yy ! = Pxy 
is derived 
O^xy^yx = VxVy — Pxy = ^xy (sUppOSc). 
We now introduce^ 
n 
undetermined quantities such that 
(^xy — a.xyCj^xyi 
^^yx — 1 1 ^xy) 
and substitute in the remaining 
2" — [ 
relations. 
The typical relation 
I ^xx^'yy^zz 
then becomes 
i P-cyz • ■ • 
T 2 
