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

Abstract

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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Correspondence to Yuyang Qiu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Qiu, Y., Zhu, L. The Best Approximation of the Sinc Function by a Polynomial of Degree with the Square Norm. J Inequal Appl 2010, 307892 (2010). https://doi.org/10.1155/2010/307892

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  • DOI: https://doi.org/10.1155/2010/307892

Keywords

  • Continuous Function
  • Closed Interval
  • Full Article
  • Publisher Note
  • Sinc Function