118 THE ROYAL SOCIETY OF CANADA 
On the left-hand side the general term is 
i! 
C1) ——— 
D (s+) L'(2r+s+1) 
Hence we have to prove that the expression in square brackets has the 
value 
T'(v+s) T (v+s+2) 92425 2 
T (2»+2s+1) 
Replace v+s by u; we have to verify that 
42” +2s 
ip ares Mae eee En — 9-2 LH) T'(u +2). 
Pe ane ler ere ar ee Oe ee T2 0 
1.e., that ; 
u.u—1l.u—2 u.u—1l.u—2.u—38.u—4 4 
fe oN Oa ey eet fs 
FETS ee RT Wea TED aT Mea TS ge TT 
— D2u-2 Perl (w+ 1)" F 
TU) 
We have 
i i 
ye Car ai eerie Cig pec eee oman eC 
T (2Qu+1)T (u) 
nl 
’ 
- m w.p—l 
Gi) F Gp; et, A) 1 Fae eae RSS 
Ke p.u—l.u—2 Le 
EE a ee [Ui ee a 
(ges) oe ZAR i | 
eat ia 5 
TE T (2u) ei Via 
.u—l.u—2.u—3 
M D TE TION 
Red eye 
(by formula (17) of $ 7). 
Hence 
Le NT oe ea ss DOME) 
(bo SET ONE AO à T Qu) 
_ 9pu-2 REED 
T (2u+ 1) 
This establishes formula (46), viz. 
Jo, (2x) = 4 > Jy 42541 Jo -25#1 
The formula appears to be new. Its close resemblance to 
PAGE) Tu ee 
a formula characterized by Nielsen p. 299 as remarkable, should be 
noted. 
If we put »=#, we derive the elegant special result 
Fy (2a) = 4 [Fg ed gS, + Ta be] ee 
The property to which attention was called at the end of § 17 shows 
that (46) can be converted into 
Jo, (2x r= 2 eas JE Gas pe ee ee | (48) 
