广义范德蒙行列式

On the General Vandermonde's Determinant

把n阶范德蒙行列式D中任一行(设为第i行)上元素的幂指数一般化,换成任意的整数k(正,零或负),这样得到的行列式与三个参数有关:阶数n,行数i,指数k.它既包含了原来的行列式D,又涵盖了其他许多不同的行列式.本文对指数k的不同情形分别进行讨论,并以D与D第二行元素的初等对称多项式分别表示出k≥n与k<0时行列式之值.

Turn the exponent of all elements in a row of a Nth-order Vandermonde^s Determinant D into same integral k, the resulted determinant is related with three parameters： order n, row number i and exponent k. For different k, such as k ≥ n or k〈0, the new determinant is valued with D and a elementary symmetric polynomial of the elements in the second row of D.