ThinkTech is an online publishing and archival service for the Texas Tech University community that scholars may use to distribute and archive their scholarly works with no limitations on content or format. ThinkTech also provides access to materials that traditional publications cannot.
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.