GE^TERATING EURCTIO^S IN THE THEORY OP NUMBERS. 
141 
Art. 46. Assuming the satisfaction of these conditions we can solve the equations 
so as to express the ^ quantities y in terms of the coefficients of V„. 
Hence we can express the | [n — l) — 4) quantities 
<^x,y ^ ^ "h !•)’ 
in terms of the n — 1 quantities 
^x, ^;+ 1 ) 
thus reducing’ the number of undetermined quantities to 
n — 1. 
Art. 47. We have 
O-n 
= 2" — 
+ 11 — 2, 
while the matrix, which defines 
X, X., 
... x„ 
of the redundant form, is 
: — 
i 
Pi 
^13^Zl2 
As 
.. '7i3 
^13 
-'lu ^ ■ 
hi 
Alw 
1 
/3i3 
Ih 
^3^723 
■ ■ 
‘'24 
/3,n 
%i 
/^13 
1 
^23 
Ih 
A 34234 
Ash 
» Isn 
fill 
ifit. 
^2i 
1 
Asi 
Ih • • 
AtH 
I in 
^\)t 
(y-hl 
hi 
t^-iH 
A4« 
or the matrix similar to this with 
Cy,^ written for c^y. 
Postponing particular explanation in regard to the quantities c,cy I merely remark 
that Cj:y~^ is a value of deduced from the equations. 
The quantity has been defined to be 
'^x, x+ l^x + i, x + 2 • • • '^y -\, y 
The matrix involves n — 1 undetermined quantities 
“135 “33j • • • - 1, H5 
