THE B AND T FUNCTIONS 
269 
Thus P n = G- n . But Gr n = G, hence P n , is convergent and G = 
lim P n . 
223. Euler s Constant. This is defined by the convergent series 
It is easy to see at once that 
by 218, 7). By calculation it is found that 
C=. 577215-. 
224. Another expression of G is 
Cu 
G = 
iHIf 1 + -)e " 
, n = 1, 2, 
where C is the Eulerian constant. 
For when a > 0, 
Hence 
Now 
and 
a u _ g« log a' 
u log(l+l) 
G = -tl 
U If 
n 
wlogCi+l) ~ 
e e ” 
U log tl+l ) — - 
Ue n n 
”(' + ;)•'' 
(1