An Analysis of Interpolatory polynomials on finite interval

Abstract

The main object of this paper is to construct a interpolatory polynomial with hermite conditions at end points of interval [-1,1] based on the zeros of the polynomials $P_n^{(k)}(x)$ and $P_{n-1}^{(k+1)}(x)$ where $P_{n}^{(k)}(x)$ is the ultraspherical polynomial of degree n .In this paper, we prove existence ,explicit representation and order of convergence of the interpolatory polynomials.