Some Results Useful in Multivariate Analysis

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