ON WEIGHTED PÀL TYPE (0,2) - INTERPOLATION ON THE UNIT CIRCLE
By
Swarnima Bahadur and Sariya Bano
Department of Mathematics and Astronomy, University of Lucknow,
Lucknow, Uttar Pradesh, India - 226007
swarnimabahadur@ymail.com, sariya2406@gmail.com
(Received: December 31, 2022; In format: January 15, 2023; Revised: March 23, 2023;
Accepted: September 02, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53203
Abstract
In this paper, we study the explicit representation of weighted Pàl - type (0,2) - interpolation on two pairwise disjoint sets of nodes on the unit circle, which are obtained by projecting vertically the zeros of (1 - x2)Pn(x) and P''n(x) respectively, where Pn(x) stands for nth Legendre polynomial.
2020 Mathematical Sciences Classification: 65D05, 41A10, 41A05, 40A30, 30E10
Keywords and Phrases: Legendre polynomial: weight function; interpolatory polynomials; Existence; Explicit forms; Convergence.