Open Access

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

Journal of Inequalities and Applications20102010:307892

Received: 9 April 2010

Accepted: 31 August 2010

Published: 7 September 2010


The polynomial of degree n which is the best approximation of the sinc function on the interval (0, ] 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.

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Authors’ Affiliations

College of Statistics and Mathematics, Zhejiang Gongshang University


© Yuyang Qiu and Ling Zhu. 2010

This article is published under license to BioMed Central Ltd. 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.