P´AL TYPE (0;1) INTERPOLATION ON THE ULTRASPHERICAL ABSCISSAS

Abstract

We study about the P´al-type interpolation on the roots of Ultraspherical polynomials along with the boundary (Hermite) conditions placed at the endpoints of the finite interval [-1,1], which gives a simultaneous approximation of a differentiable function and the function’s derivative. The order of convergence depends only on the smoothness of the function. In this paper, we study about interpolation on polynomials (along-with the Hermite boundary conditions) where the nodes are the zeroes of Ultraspherical polynomials) and) respectively. Here ) represents the Ultraspherical polynomial of degree n. Our focus is to find the existence, uniqueness, explicit representation, and order of convergence of the interpolatory polynomials.