An analysis of (0,1,2;0) polynomial interpolation including interpolation on boundary points of interval [-1,1

Abstract

In this paper, we survey an interpolation on polynomials with Hermite conditions on the zeros of ultraspherical polynomials at intervals [-1,1]. Our aim is to demonstrate the existence, uniqueness, explicit representation, and convergence theorem of the interpolatory polynomials, which are the zeros of the polynomials Pn(k)(x) and Pn−1(k+1)(x) respectively, where Pn(k)(x) is the ultraspherical polynomial of degree n.