Boss — Verh-Fimctions. 



53 



coefficients of the original multinomial, each combination being 

 affected by its proper linomial coefficient ; and (2) that the form of the 

 multinomial coefficients {rii\ (m)2, . . . does not change whatever the 

 value of that is, the exponent of the original multinomial, may be 

 (unless it is unity). Hence the form of each coefficient of [<^„]"^ 

 must be the same as that of the corresponding coefficient of (<^„)"S the 

 only difference being that the binomial coefficients are different. In 

 order, then, to write out the value of [^«]~^ we have only to write out 

 that of (^„)~^ and then make the necessary changes in the binomial 

 coefficients of the various combinations of P\, P2, Pz • - • A few terms 

 of the series are now written out for comparison and use. 



- {p,-S {2prp,+p^^) + 2lp,% - Up,'} (B' 



- [V-^ {Pilh + W3) + 28 {p^p, + p,p^^) - 84p^p, + 42p,^ j /? 



+ etc. 



