53 
of any Functions of Multinomials. 
But, that we may enter rather more into particulars, let it be 
required from the terms already given, to find ® the coeffi- 
cient of x 6 . 
To make the operation plain, I have put a star over every 
term we are to use, excepting the coefficient of x\ which is 
wholly employed. 
C’ 
/ is i ii i mil in 
«-=iW«+/W 
iiii mi 
I'+fic) 
c c c 
2 -3 
+ 
ill iiiii " linn 
c +/ ( r ) (0 
2.3 4.5.6 » 
C C * 
2.2 
and by adding these together, we get 
/ (0 c +/ (0 
1 IIIII III 
c c -f-y ( c ) 
1 
IIII IIII 
T*+/(0 
/ / 
111 inn ^ r 4 a mill , 
z . 5 c +j( c ) 2 . 3.4 c +/ ( c ) 
“| - c c 
1 II III 
c c c 
1 n 
. c 2, c x 
r z 
+ - 
1 2 
II 
r 3 
-j- — 
' 2.3 
“I” T7 
2.34.5.6- 
This process is sufficiently easy ; but, in order to find any co- 
efficient as it is by no means necessary for us to know all 
those that precede it ; it may be immediately obtained from 
by a variety of ways : but we must first learn how to express 
B • • B 
n—m by the fluxional coefficients of n _ l ; after which we shall 
only have to substitute in equations (2 ) and (3). 
Now it appears, from what has been shewn in this article, that 
