Copyright © 2010 Yuyang Qiu and Ling Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The polynomial of degree n which is the best approximation of the sinc function on the interval (0, π/2] with the square norm is considered. By using Lagrange's method of multipliers, we construct the polynomial explicitly. This method is also generalized to the continuous function on the closed interval [a, b]. Numerical examples are given to show the effectiveness.