A double series for π using Fourier series and the Grothendieck-Krivine constant

2022/06/11 by Pain, Jean-Christophe
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.05610

Abstract

We provide a double-series formula for π 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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