446 Proceedings of Royal Society of Edinburgh. 
a b n 
(1) 
T-/9-1 
y - a- P — \ 
~P 
(2) 
y-/S-l 
7-1 
a 
(3) 
y - a — 1 
1 
P 
1 
1 
— a 
(+) 
y — a — 1 
7-1 
P 
* h “ 
and the equation takes the forms 
F(W[)8][y] I 2 ( >' 2 [y] [y + l][y + 2] . . Ly + r - 1] [»■]! D< ’ y J 
„ nr-i[S][S+l][/3 + 2]... f/J + r — 1] xrt'i , „ 
-2(- 1 )>^ — ®- 2 [y - a] [y - a +1 ] . . . [y - a + r - 1 ] • W V 
-M 
1 + 
1 
I A 1 + 
F([ a+ l][/5][ 7+ l]) [1]! ^ f 
1 XPl i] 
r T F([a + l]M[ y+ l]) [ 1 ]! 
+ 
(12) 
F(HMH 
( r_r- 1 fal la - 11 [a - 21 fa-r+11 „ ) 
| Z P ' iy + 2 [y-a-/3][y-a-/3+. 1] . . [y- a - ft + r - 1] ‘ [r]! 0 ^ } 
2> ry+ ’ 2 
= A < 1 + 
1 [aira-l][a-2] . . . a-r+1] _ &*rl 
b-flb-0 + ih .[y-P+r- 1] [r]l 
1 
Df+B 
F([a]D»-l][y] P]i 
+ . . . 
1 + 
1 
F([a][/?-l][y]) [1] 
xpW ) 
n- « 131 
and two others obtained by interchanging a and (3 in the above. 
