Expansions for the Fundamental Hermite Interpolation Polynomials in Terms of Chebyshev Polynomials

Abstract

We obtain explicit expansions of the fundamental Hermite interpolation polynomials in terms of Chebyshev polynomials in the case where the nodes considered are either zeros of the (n + 1)th-degree Chebyshev polynomial or extremum points of the nth-degree Chebyshev polynomial.