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We provide a double-series formula for $\pi$ obtained using the Fourierseries expansion of $1/\cos(x/4)$ and applying the Parseval-Plancherelidentity. We show that such a formula involves the Grothendieck-Krivineconstant, and that the latter can therefore be expressed as a double series aswell.

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