An Analysis of Simultaneous Approximation on the Roots of Ultraspherical Polynomials

Abstract

In this paper, we find an interpolatory polynomial  satisfying (0;0,1) interpolation with some special kind of boundary conditions at the given knots. The knots being considered here are the zeroes of the Ultraspherical polynomial. In this paper, we find the explicit representation of the fundamental polynomials, their uniqueness, their existence, and the order of convergence.