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This is a question on Fourier series convergence. The problem is, in the applications of the Stone Weierstrass approximation theorem on wikipedia, there's stated that as a consequence of the theorem ...

Given the coefficients $a_0,\ldots,a_N$, $b_1,\ldots,b_N$ of a real trigonometric polynomial: $ f(x) = a_0 + \sum_{n=1}^N a_n \cos(nx) + \sum_{n=1}^N b_n \sin(nx) $ is there any efficient way to ...