If we add all such functions which have the same weight we obtain,
algebraically speaking, all the products together of the quantities
, repetitions permissible.
Such a sum is called the Homogeneous Product-Sum of weight of
It is usually denoted by .
and so forth.
We have before us the three sets of functions
The first and third sets contain an infinite number of members, but
the second set only involves members where is the number of the
6. The identity of Art. 4 which connects the functions
with may be written, by putting for ,
or in the form
If we expand the last fraction in ascending powers of , we obtain, in
the first place,
It is clear that the coefficient of is the homogeneous product-sum
of weight , so that we may write