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arXiv · 2206.05610

A double series for $\pi$ using Fourier series and the Grothendieck-Krivine constant

Jean-Christophe Pain
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Abstract

We provide a double-series formula for $\pi$ obtained using the Fourier series expansion of $1/\cos(x/4)$ and applying the Parseval-Plancherel identity. We show that such a formula involves the Grothendieck-Krivine constant, and that the latter can therefore be expressed as a double series as well.

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Jean-Christophe Pain. 2022-06-11. A double series for $\pi$ using Fourier series and the Grothendieck-Krivine constant. https://arxiv.org/abs/2206.05610

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