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arXiv · 1404.5413

A remark concerning sinc integrals

Uwe Bäsel
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Abstract

We give a simple proof of Hanspeter Schmid's result that $K_n:=2\int_0^\infty\cos t\,\prod_{k=0}^n\mathrm{sinc}\left(\frac{t}{2k+1}\right)\mathrm{d}t=π/2$ if $n\in\{0,1,\ldots,55\}$, and $K_n<π/2$ if $n\geq 56$. Furthermore, we present two sinc integrals where the value $π/2$ is undercut as soon as $n\geq 418$ and $n\geq 3091$, respectively.

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Uwe Bäsel. 2014-04-22. A remark concerning sinc integrals. https://arxiv.org/abs/1404.5413

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