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 } n i=1 and {x * i } 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.
The object of this paper is to demonstrate the existence, explicit characterization and estimation of the polynomial interpolation, related to the weighted (0;0,2) interpolation which satisfies the boundary conditions together with the interpolation conditions at the interval [−1, 1].
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