110 MAJOR P. A. MAcMAHON: THEORY OF THE PARTITIONS OF NUMBERS. 

 For, in the identity 







substitute lpl for I and we find that the left-hand side is merely multiplied 

 by ar'v-'/.vO'+w W hjl 8 t O n the right hand the coefficient of PF, is multiplied by 

 *"' ~ 1} > An identity thence arises, and putting therein ^ = 0, 1, 2, ... in 



succession, we find the relations 



PF 



*- 



giving very noteworthy algebraical identities. 



