Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 307892, 12 pages
Research Article

The Best Approximation of the Sinc Function by a Polynomial of Degree n with the Square Norm

College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Received 9 April 2010; Accepted 31 August 2010

Academic Editor: Wing-Sum Cheung

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.


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.