On some general lacunary interpolation problems

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 thr literature. We consider only the case when the nodes are thr zeros of pi(n)(X) whose derivative is -n(n - 1) P-n-1(X), the Legendre polynomial of degree n(-1). We find the fundamental polynomials and five the convergence result. (C) 1996 Academic Press, Inc.