102 THE ROYAL SOCIETY OF CANADA 
by solving which we find’ that 



A Dus AE. i B 
ay ee ee eee FLE NE OT ENTER 
1 
AO 90" 207-50 URS oer nearer aro 
1 1 
See Se nr 8 
1 RE DE 0AO Cru era LE (8) 
2 2 1 
: v+3 v+3.v+4 GO y+3...vts+2 
1 3 > M D LE 0 | ek 
y+4 7+4.7+57+4.7+5.74+6 ‘°° y+4 .v+s+3 
Cale reve (aielisre aie eo (eve: ea site ir le enonelelens erc/ate els fee ele Le\ie (en 16" he) (ee) = «he «) «ell omenn 
This provides a means for evaluating a determinant of rather 
remarkable structure. 
$ 4. By the following simple method we can get an identity which 
will serve for the algebraic basis of (i) a theorem in Gamma Functions 
and (ii) a theorem in Bessel Series, and which at the same time exhibits 
the factors v, v+2, v+4, v+6, ... 


Fe pts 
~ AT 
Tae? y+tstl 
> ae i ea EEE 
Aa ae y+2 & 1 
pa Steen so eta en 
DURE +2 Be yts+2 
Sr pay UG ay ey ae A et eee EO 
2 y+2 yv+4 
ott Gee EE 0e Dee SE 
ees (v+6)-+(s—3) 
ASS iG 2a ny a ae ee eR (9) 
By continuing this process until zero factors make their appearance, 
we infer that 
ee yp y+2 y+4 
Eg te ed Pe ae eh eS 
' yv+2s 
Cae eee ET TN EEE 
When both sides are multiplied by TS , the identity takes the 

form 
1 ve yp y+2 i v + 4 
DB eo IGE Done) Cine 
y+2s : 
set) GET D ee (10) 
