$\pi$-Formulae from Dual Series of the Dougall Theorem

Wenchang Chu

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arXiv · 2103.07872

$\pi$-Formulae from Dual Series of the Dougall Theorem

Wenchang Chu

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Abstract

By means of the extended Gould-Hsu inverse series relations, we find that the dual relation of Dougall's summation theorem for the well--poised $_7F_6$-series can be utilized to construct numerous interesting Ramanujan--like infinite series expressions for $\pi^{\pm1}$ and $\pi^{\pm2}$, including an elegant formula of $\pi^{-2}$ due to Guillera.

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Wenchang Chu. 2021-03-14. $\pi$-Formulae from Dual Series of the Dougall Theorem. https://arxiv.org/abs/2103.07872

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