6a 
Mr. Knight on the Expansion 
i a e e e ~i / ' " 
(cx + qcxx-{-)-$-J j B-J-Bx-j- m e x-\- 2 e x x +)+ &c. 
whence, after taking the fluents, and comparing the coeffi- 
cients of the powers of x, with those of the same powers in 
(7), we find 
C € 
B = c B e B -f- See. 
1 
/, C ,c 
2 c B -J- c B 
»»« » « 
2 e B -f e B 
B = 
2 
B 
3 
- + 
- -{- &c. 
m c a c 1 c 111 c I, c 1 e 
3 c B + 2 c B 4 c B 3gB-J-2<?B-feB 
_L_i + __i 2 + &c. 
"...nc 1 ) c 
n c B + (ti— 1) c B -f 
1 
n 
"...tie "...{n — 1 ) 
n e B 4- («— 1) e 
e 
B + 
+ 
1 
n 
11 c , c 
4 2 c B 4c B 
n — 2 n — 1 
n 
4 2C 
e 1 e 
B 4- e B 
n — 2 ti — l 
+ &C. 
(*)' 
But B = <p[f ( c),f(e ), &c.j whence all the coefficients are 
known. 
10. This solution, however, gives no very expeditious way 
of actually expanding the function in question ; particularly 
when we get to the higher powers : but by proceeding as in 
the second method, made use of for a function of one single 
multinomial, we find 
~f & c (0 
C , c 
where we must neglect in B all terms which contain c; in B 
n—z n — 3 
