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

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 $_{7} F_{6}$ -series can be utilized to construct numerous interesting Ramanujan–like infinite series expressions for $π^{\pm 1}$ and $π^{\pm 2}$ , including an elegant formula of $π^{- 2}$ due to Guillera.

$π$ -Formulae from Dual Series of the Dougall Theorem

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$π$ -Formulae from Dual Series of the Dougall Theorem

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ππ-Formulae from Dual Series of the Dougall Theorem

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ππ-Formulae from Dual Series of the Dougall Theorem

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$π$ -Formulae from Dual Series of the Dougall Theorem

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$π$ -Formulae from Dual Series of the Dougall Theorem

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