Hermite Lagrange Interpolation on the Unit Circle

Abstract

In this paper, we consider explicit representations and convergence of Hermite- Lagrange Interpolation on two disjoint sets of nodes, which are obtained by projecting vertically the zeros of (1- x²) P_n ^{(? ,? )} (x) and P_n ^{( ? ,?)}(x)  respectively on the unit circle, where P_n^{( ?, ?)}  (x) stands for Jacobi polynomials.