A. Ritchie-Scott 423 
To determine G, 
= -(« + l)^„+,e--^' (121). 
Therefore J Bn+.e- i'^'dx = -^"^^'^ (122). 
Now put ?- = 0 in equation (120), 
zdxdy (r = 
0) 
1 f' 
i'^'dx.-^ r 
\/27ri -oo 
e,;e-iy'di/ 
1 V:^-*''" 
1 
V27r P 
' V27r q 
0 ff p-\ (■'■ 
^ q-\ 
HK 
p .q.l'n- 
pq 
.(123). 
Hence finally 
r r <f>p^izdxdy ^plqlHK j ^^-'^Vi ^ ^^g,-,. ^ g + (^y).^ + ... 
(124). 
When j3 = g = 0 we get the volume of the quadrant. In this case --^ becomes 
x0 _ —6 ^ 
indeterminate, since putting n = l in 6n = — " ^ ^ we get 
01 = x0(i — 6_i and = .x'^o — &i = — ■'' = 0. 
But from (61) we have 
T_,e-'^-''' = - r e-^^-^'dx (125). 
— X 
Hence we may write in this case 
C'^^f ne-i-'dx.^r T„e-'^y"dy 
* V'27r " * V27r 
- T_/r_,HK (126). 
In this case dp=^ 6q - 1 and all the other ^'s vanish; and we have 
(127), 
which is the ordinary tetrachoric expansion in terms of T. 
