The best approximation of the sinc function by a polynomial of degree n with the square norm

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. © 2010 Yuyang Qiu and Ling Zhu.