Wolfgang Gabcke

most citedOn a Fair Copy of Riemann's 1859 Publication Created by Alfred Clebsch

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math.CA2015

On an Inequality Related to a Certain Fourier Cosine Series

Wolfgang Gabcke

We prove that the Fourier cosine series $\sum_{k = 1}^{\infty} (- 1)^{k + 1} \frac{r ^{k} c o s k ϕ}{k + 2}$ assumes its maximum value at $ϕ = 0$ for $ϕ \in [0, π)$ regardless of $r$ if $r \in (0,…