16 THE REV. F. H. JACKSON ON 
and since 
eee UN eed pois eee SE re 
Prue) = TCC Teen vm 
[2] [22-1] ° 
putting 
Sy 
a = | 
we have 
a(t) ree I([m+v] + ys . : : 15 
Sot PE) = arash oe 
If v= 0 this gives 
Era ee ; . Gy 
which was obtained in art. 9, Part L, by another method. 
When v=4 
; py ee meals a - an 
mm TES) - 4) 
which when p= 1 gives ; 
py ly, Mee) ; Pay lS 
So oge Wes a 
3. 
Consider 
l qin+») ae F gpl2n—2]) 2n—2 \ 
- eee FE Saas : le) 
mE wer, ~  layrey, 
the general term of the series within the bracket being 
[ n|! gphn—21] 2n—2r 
( a iia es [n = 7! . (OOS. 
(20) 
dh +yv) 
ae we obtain a series of which the 
x 
Then if we perform the operations indicated by 
general term is 
(Qe =r! ono ee yer 
Neelys [7]! 
=wi\t prer+2 : a 21 
ea Masry)... a 
This reduces to 
Ty tut [2n — 27]! oe +*D/ 8 = Dray ™ 1 = y= 27] 
(“Ve a= =o 
viz., the general term of 
AMP (ate d) 
» Alig 1 lend, 2n gl2n—2]Q 2n—2 : 
NP ie? 1 a De | = Pn} se ; - 22) 
[»]! (2)n (2),(2)n—1 
reducing when p=1 to 
2"-"P, (xd) = + pet , x? 1 ie OR 
n! 
The expression 
NE Singers ER ere oe . (24) 
Q,  » Y Oiays 
