Some Factorable Continuants. 
227 
1913-14.] 
(5) /3 = — a = 2n— 1, y = — 8 = 2, then 
T, = (a 2 +l 2 )(a 2 + 3 2 ) # . . («2 + 2 ^Tl 2 ) j 
which is Elliott’s form.* 
(6) a = /3 = 0, y = S = 1 , and b = a, then 
T & = a 2 (a 2 — 2 2 )(a 2 - 4 2 ) . . . (a* - 2n^2 2 ) ; 
(7) a — 6 = 1, y — S = i, and b = a, then 
T & = (a 2 -l 2 )(a 2 -2 2 ) . . . (a 2 -ft 2 ); 
(8) a = — ft = 1, y = — S = ^, and b = a, then 
T & = (a 2 + l 2 )(a 2 + 2 2 ) . . . (a 2 + ft 2 ). 
7. If in T c we put : 
(1) S = a, y = /3, and b = a, then 
T ={a 2 - a 2 (/3 +2 ft - 2) 2 } {a 2 - (a . (3 + 2n - 4 + 2/1) 2 } . . . {a 2 - £ 2 (a + 2 tz - 2) 2 } ; 
(2) S = y = /3 = a and b = a, then 
T c = {a 1 - a 2 (a + 2ft - 2) 2 }’ 1 ; 
(3) S = y = /3 = a = b = a, then 
T c = a 2w (2ft + a - 1 ) w (3 - a - 2 n) n , 
or if a -f 2 tz — 2 = a;, then 
T c = (l 2 -a 2 ) B (a;-2ft-2) B . 
If a = 1, then 
T c =2*{n(l-ft)}»; 
(4) <S = y = /3 = a = l, b = a = x(2n — 1), then 
T c = (2ft - l) 2?1 (x 2 - l 2 ) w . 
If = T c = 0. 
8. It will be observed that in (2) of articles 6 and 7 we have a 
determinant of the 2r&th order expressed as the Tith power of a determinant 
of the second order. 
From (4) of article 7 it is seen that the determinant 
x 1 
1 2 n - 2 
3 — 2 n 2?i — 3 
2 2n - 3 
5 - 2ft X 2ft - 5 
- (* 2 -iy. 
i 
X ■ 
3-2 ft 
1 x 
* Proceedings of London Mathematical Society, vol. xxxiii. p. 229. 
