447 
T [l] 
1902-3.] 0^ the Series y = 1 + F([a] [/3] [y]) . |-yj + , etc. 
( 5 .) 
If p = 1, equations (9) and (10) reduce to 
, p.fi+ip+2 . . . fi + r-l 
F(a^7)-2(- 1 ' 
a. y — a + 1 . . . y — a + r — 1 
r d r+1 2/ 
- V / _ IV /?♦/? + 1-^ + 2 . . . / 3 + r- 1 af 
^ y. y+l.y + 2 . . ,y + r— 1 r! 
flte r+1 
r! 
= 0... (14) 
PY ,-^a. a— l.a-2 ... a — r + 1 x r d r y 
\ a fiy)2-iy — a, y — <x -f- 1 .. .y-a + 7*-l ' r! cfaf 
^ a. a— la— 2 ... a — r+1 £C ? ’ d r ^y 
^ y— a — /?. y— a — /?+l . . . y — a — /3 + r -• 1 r\ dx r + 1 ^ 
and other two equations which can be obtained by interchanging 
a and /3 in these equations (14) and (15) : 
y= i + F(«/3 y)fj + F(aft) • F( °-.p.y + 1) • |j + ... 
is a solution of equations (14) and (15) and two others obtained 
from them by interchanging a and p. 
( Issued separately August 3, 1903.) 
