Further, let 1> xln (w)> xZn (w)>.**> x,,(w)>-1 be the zeros of pn (w, x). For a continuous
functionf on [-1, 11, the Lagrange interpolation polynomial L,(w, f) is defined to be the unique …

For any continuous function f (x) with domain [-1, l] we define the nth Lagrange interpolation
polynomial of f (x) with respect to B to be that unique polynomial of degree at most n-1 which …

Many mathematicians have investigated the convergence of (1.6), eg, L. Fej~ r [2], Grfinwald
[4], Tur~ in [10], O. Kis [7]. Most of them proved the convergence to the function and its first …

Here interpolation is meant in the following sense: given f ε C¦ a, b¦. and given a set of
distinct points in¦ a, b¦ and a linearly independent set {ifu 0,..., un} of continuous functions on¦ …

Lagrange interpolation to any continuous function on [-1, 1] at the zeros of orthogonal
polynomials is known to converge in the mean. Here, following Bellen, we study mean …

The purpose of the paper is to investigate weighted L p convergence of Lagrange
interpolation taken at the zeros of Hermite polynomials. It is shown that if a continuous …

This letter is about my paper “Mean Comergence of Lagrange Interpolation, III,” see [4]. In
that paper I show that many theorems on weighted mean convergence of Lagrange …

2. Most of the investigations concerning these polynomials L,~(f) refer to the" finite" case, ie
when all points of A are eg in the interval [--1,+ 1]. The infinite case, ie when the points of A …

Lagrange interpolation is one of the oldest methods for approximating an arbitrary function
in C [a, 61, the space of continuous functions on the closed interval [a, b] normed with the …

In this paper we present a generalized quantitative version of a result due to DL Berman
concerning the exact convergence rate at zero of Lagrange interpolation polynomials to …