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arXiv · 2012.01423

On some Féjer-type trigonometric sums

R. B. Paris
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Abstract

We examine the four Féjer-type trigonometric sums of the form \[S_n(x)=\sum_{k=1}^n \frac{f(g(kx))}{k}\qquad (0 0$ in $0<x<π$. The graph of the sum in this case presents a jump in the neighbourhood of $x=2π/3$. This jump is explained and is quantitatively estimated when $n\to\infty$.

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R. B. Paris. 2020-12-02. On some Féjer-type trigonometric sums. https://arxiv.org/abs/2012.01423

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