Convergence of derivative of (0, 2) interpolatory polynomial

Swarnima Bahadur ,Sariya Bano

doi:10.28919/jmcs/3762

Abstract

In this paper, we consider the non-uniformly distributed zeros on the unit circle of nth Legendre polynomial. Here, we are interested to establish the convergence theorem for the derivative of (0,2) interpolatory polynomial on the above said nodes.

Highlights

We are interested to establish the convergence theorem for the derivative of (0,2) interpolatory polynomial on the above said nodes
Mathur) [1] considered the weighted (0,2)*-interpolation on the set of nodes obtained by projecting vertically the zeros of on the unit circle and established a convergence theorem for that interpolatory polynomial
Convergence: we prove the main theorem

Summary

Introduction

Later on several Mathematicians have considered the Lacunary interpolation on the unit circle. K. Mathur) [1] considered the weighted (0,2)*-interpolation on the set of nodes obtained by projecting vertically the zeros of on the unit circle and established a convergence theorem for that interpolatory polynomial. Shukla) [3] considered (0,2)-interpolation on the nodes, which are obtained by projecting vertically the zeros of on the unit circle, where stands for Jacobi polynomial, obtained the explicit forms and establish a convergence theorem for the same. Authors [2] considered weighted (0,2)-interpolation on the nodes, which are obtained by projecting vertically the zeros of the onto the unit circle, established a convergence theorem for the same. (2.12) (2.13) For more details, one can see [9]

The Problem

Estimation of Fundamental Polynomials: Lemma 1

Convergence