of any Functions of Multinomials. 
75 
ZyO 
^ 2,1 — M 2 !i » an< ^- these added together give 
p = ^ (o ,,, + <? co { j'o x ^ x z % } + i {c ) y x 0 * r 
I wrote rhe terms separately, and then collected them, for the 
better explanation of the method ; but this double labour is 
by no means necessary : the coefficients may be formed and 
written down ac once, as quickly as can be wished, 
iy 4 A very little consideration will convince us, that the 
terms P B * ; P B 6 . P u & ____ K 
J m , n ^°’ 2 ’ J JL,*' 3 ^ ^ 
tirely left out of formula (^), excepting when the term we 
search is of the form 8 , in which case it is reduced to the eo<* 
o ,m 
efficient ofy M in the expansion of $ (c -j- o c ? y ° ? j % ~ |-) o ' 
If then we neglect these terms, and, in the remaining ones 
/ « ' 
I lli “ 1 ,n 
V 
put for B its value | j given by (*), equation M 
will become 
