An analysis of (0,1,0) interpolation based on the zeros of ultraspherical polynomials

Abstract

The aim of this paper is to construct an interpolatory polynomial (0,1,0) with special types of boundary conditions. Here  the  nodes {x_i}_i=1ⁿ and {x_i^∗}_i=1ⁿ⁻¹are the roots of P_n^(k)(x) and P_n−1^(k+1)(x) respectively, where P_n^(k)(x) is the Ultras spherical polynomial of degree n.  In this paper, we prove the existence, explicit representation, and order of convergence of the interpolatory polynomial.