SIMULTANEOUS APPROXIMATION TO A DIFFERENTIABLE FUNCTION AND ITS DERIVATIVE ON ROOTS OF ULTRASPHERICAL POLYNOMIAL
By
Rekha Srivastava1 and Sukriti Rai2
1,2Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh, India-226007
Email: srivastava rekha@lkouniv.ac.in, rs2020math sukriti@lkouniv.ac.in
(Received: September 17, 2024; In format: October 04, 2024; Revised: June 09, 2025; Accepted: June 18, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55128
Abstract
The purpose of this paper is to find an interpolatory polynomial Sm(x) satisfying (0,1;0) interpolation under certain special type of boundary conditions at given knots. Here the knots are the zeroes of Ultraspherical polynomial for k = 1. In the following paper we prove the explicit representation of fundamental polynomials, their existence and the order of convergence has also been studied.
2020 Mathematical Sciences Classification: 41A10, 97N50
Keywords and Phrases: Lagranges interpolation, Ultraspherical polynomial, Explicit form, Order of convergence. Orcid Id:0000-0002-6508-1281 ; 0000-0003-2653-5364