, Volume 22, Issue 2, pp 221-230
Date: 15 Apr 2010

Using Fourier–Legendre expansions to derive series for  \(\frac{1}{\pi}\) and  \(\frac{1}{\pi^{2}}\)

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Abstract

In this paper, we derive some series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\) from the Fourier–Legendre expansions of odd powers of \(\sqrt{1-x^{2}}\) .