HERMITE INTERPOLATION IN THE ROOTS OF UNITY

We study the polynomial H-r,H-n(f,z) which interpolates an analytic fu nction f and its derivatives up to order r - 1 at the nth roots of uni ty. In particular we relate the vanishing of the coefficients of the h ighest powers of z in the Hermite interpolant H-r,H-n(f,z) with the va nishing at certain points of the Hermite interpolants of certain funct ions related to f. (C) 1996 Academic Press, Inc.