Some Results Useful in Multivariate Analysis
shown to be readily applicable to the moment problems of the sum of the roots and the distributions of the extreme roots. Most of the results given are in the form of certain recursion formulae for reducing special types of k-th order Vandermonde determinants in terms of those of orders (k - 1) and (k - 2). The applications of these results are given by S. N. Roy [6] and the present author [3]. 2. Vandermonde's determinant. Let us first consider a type of determinant (due to Vandermonde) which plays an important role in the development of this paper. Denote by V0 the Vandermonde's determinant of the form Xkk-l Xk-2X1 xk-1 xk-2 xk-1 k-1 ... Xk- 1