On Some General Lacunary Interpolation Problems Original Research Article

The object of this paper is to give a unified and complete treatment of these related cases of lacunary interpolation whose special cases can be found scattered in the literature. We consider only the case when the nodes are the zeros ofπn(x) whose derivative is −n(n−1) Pn−1(x), the Legendre polynomial of degreen−1. We find the fundamental polynomials and give the convergence results.