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

The aim of this paper is to construct an interpolatory polynomial (0,1;0) with special types of boundary conditions. Here the nodes {xi}i=1 and {xi } n−1 i=1 are the roots of P (k) n (x) and P (k+1) n−1 (x) respectively, where P (k) n (x) is the Ultraspherical polynomial of degree n. In this paper, we prove, existence, explicit representation and order of convergence of the interpolatory polynomial. 2000 Mathematics Subject Classification: 41A10, 97N50.