چکیده (انگلیسی):

By aHermite interpolation sequencewemeana sequence ofHermite interpolation polynomials of degree 0, 1, . . . such that consecutive terms satisfy the differentiation conditions of the previous ones. We extend this concept to arbitrary fields from the reals by purely algebraicmeans based on the possibility of formal Taylor expansions of rational fractions around any point of the underlying field. As an applicationwe obtain recursion-free explicit formulas for the entries of triangular decompositions of generalizedHermite–Vandermonde matrices.