2023-07-142023-07-141929Heineman, E. R. (1929). Generalized Vandermonde determinants. Transactions of the American Mathematical Society, 31(3), 464–476. https://doi.org/10.1090/s0002-9947-1929-1501494-2https://doi.org/10.1090/S0002-9947-1929-1501494-2https://hdl.handle.net/2346/95055© Copyright 1929 American Mathematical Society. Work enters the public domain on January 1, 2025.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.engArticle