A Proof, Based on the Euler Sum Acceleration, of the Recovery of an Exponential (Geometric) Rate of Convergence for the Fourier Series of a Function with Gibbs Phenomenon

John P. Boyd

When a function $f(x)$ is singular at a point $x_s$ on the real axis, its Fourier series, when truncated at the $N$-th term, gives a pointwise error of only $O(1/N)$ over the ent…