Generalized Vandermonde determinants

The object of this paper is to develop a new method of treating this problem, consisting in first expressing every generalized Vandermonde determinant as an integral rational function of certain special Vandermonde determinants. This leads to a solution of the problem mentioned above; and it gives, in conjunction with a theorem of Muir's, a direct method for expressing an integral symmetric function of n variables in terms of the elementary symmetric functions.