AND ON DEFINITE INTEGRATION. 495 
Other series may be obtained from equation 
(23), even more convergent than the above, by 
taking y a larger number. 
The foregoing general formula may be applied 
with advantage to determine the continued pro- 
duct of 2 factors, whose general factor is ® (2). 
Let us denote the product of « factors, as 
above described, between the limits of w=y and 
a=x by [ oe) ] , which is a function of #, say 
F(z). Then, agreeably to this notation, we shall 
have [ (x) ] = 0(1) x 0(2) x@(3) x0(4) X..cs.ste 
ee =a) 12 4 Uae Se eee (24) 
and [2 ] = (1) x (2) x 0(8)x0(4) x... 
eG) xa(@+1) SF(@4L) es (25) 
Divide equation (25) by equation (24), and 
we shall have 
F(a+1 
BED Saw bay lle RULE. (26) 
Hence, it appears, that in order to find the 
continued product of a factors, we shall have to 
determine a function of #, such, that its reciprocal 
