114 THE ROYAL SOCIETY OF CANADA 
and evaluating the residues Ao, Ai, Bi, ... by the ordinary method of 
partial fractions, we find that 
Ao SERRE A1=B;= ——— — Ag 
6) Lu ne) 
2 
TC Ce 
Thus 
SG) Tie wa EX — it 
(EG) Eye 
Dy? 
NRA Gay ne (35) 
2 2 
If we replace u by n+2s+2, we seeithat the factor containing 
Gamma functions in the general term 
ge eee rn Re PP ees Gye of 
a 0 Ss 2 
pee = can be replaced by 


1 
T (vy) T(1—») T (1—») tem r(g +i) 
a 
mCuEDUGIED 
ARE nr (= 7) ; 
nvr 
p furnish a series =the product of by 
The terms in = 

(Ie 
2 ("24 OM 2s 
2 Sear 
2 2; TE ns iS Ho s+1) 
Dy? 
(= ete Te 
2 
od sin vr 
VT 
Hence adding all the terms obtained by putting f successively =0, 
1, 2, 3, ..., and replacing ¢ by s, 
