Computation of Cauchy-Vandermonde determinants (Q1208173)

Let a system of rational functions \(u_ k\) (\(k=1,\dots,M\)) with prescribed poles (\(\infty\) included here) and a system of interpolation nodes be given. The corresponding Hermite interpolation for \(\sum_{n=1}^ M c_ k u_ k\) leads to the determination of the coefficients \(c_ k\). Using Cramer's rule explicit formulas for the denominator determinant --- here called generalized Vandermonde determinant (if all points are situated in infinity this is the ordinary Vandermonde determinant) --- are established for several cases.