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 P_n^(k)(x) and P_n−1^(k+1)(x) respectively, where P_n^(k)(x) is the ultraspherical polynomial of degree n.