472 
TABLES OF THE STURMIAN FUNCTIONS FOR 
fl51 
p, 
Q 
> 
a, 
b 
x 2 P, 
xP, 
P, 
a, 
• 5 
• 5 
n x b , 
a, 
• > 
n 2 c , 
nJ>, 
a, 
n 3 d, 
n 2 c, 
n x b, 
n 2 e, 
n 3 d, 
nx, 
where the terms containing the powers of 
functions respectively, vanish identically (as 
expressions), but these terms may of course 
xP, 
P, 
xQ, 
Q 
a, 
• } 
b, 
Pi b, 
a, 
n x c, 
b 
n. 2 c, 
n x b, 
n 2 d, 
n x c 
2 Q, 
xQ, 
Q , 
<^c. 
b, ., . 
n x c, b, 
n. 2 d, n x c, b 
n 3 e, n 2 d, n x c 
nj, n 3 e, n 2 d 
x, which exceed the degrees of the several 
is in fact obvious from the form of the 
be omitted ab initio. 
The following are the results which I have obtained; it is well known that the 
last or constant function is in each case equal to the discriminant, and as the 
expressions for the discriminant of equations of the fourth and fifth degrees are given, 
Tables No. 12 and No. 26 [Q', see 143] in my ‘Second Memoir upon Quantics’^), I 
have thought it sufficient to refer to these values without repeating them at length. 
Table for the degree 2. 
The Sturmian functions for the quadric (a, b, c$x, l) 3 are 
c + 1 \T£x, l) 2 , 
!). 
Table for the degree 3. 
The Sturmian functions for the cubic (a, b, c, P§x, l) 3 are 
a + 1 
b + 3 
c + 3 
d+ 1 
1) 3 > 
1 Philosophical Transactions, t. cxlvi. p. 101 (1856), [141].