Hermite Interpolation in the Roots of Unity Original Research Article

We study the polynomialHr, n(f, z) which interpolates an analytic functionfand its derivatives up to orderr−1 at thenth roots of unity. In particular we relate the vanishing of the coefficients of the highest powers ofzin the Hermite interpolantHr, n(f, z) with the vanishing at certain points of the Hermite interpolants of certain functions related tof.