A double series for π using Fourier series and the Grothendieck-Krivine constant
Abstract
We provide a double-series formula for π obtained using the Fourier series expansion of 1/(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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