Some Identities Involving Symmetric Functions.

Let a sub j be the jth elementary symmetric function of the n quantities x sub 1, x sub 2,..., x sub n that is, let a sub j be the sum of the possible products of the x sub j taken j at a time. Extending the concept, let A sub jn, k be the jth elementary symmetric function of the quantities which are the sums of the x sub j taken k at a time. The problem investigated is to obtain explicit expressions for the A sub jn, k in terms of the a sub j, i 1, 2, ..., j. Such expressions are obtained for j 1, 2, ..., 7, and general n and k. Author