An evaluation of weighted polynomial interpolation with certain conditions on the roots of Hermite polynomial

Abstract

The purpose of this paper is to construct a polynomialRnof degree atmost 3n−2 satisfying weighted (0,2; 0) interpolation under certain condi-tions at the zeroes ofHnandH′n, whereHnstands for Hermite polynomial.Furthermore, we prove a convergence theorem forRn