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π-Formulas from Dual Series of the Dougall Theorem

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Ukrainian Mathematical Journal Aims and scope

By means of the extended Gould–Hsu inverse series relations, we show that the dual relation of Dougall’s summation theorem for a well-poised 7F6-series can be used to construct numerous interesting Ramanujanlike infinite-series expressions for π±1 and π±2, including an elegant formula for π −2 due to Guillera.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan, China

    W. Chu

  2. University of Salento, Lecce, Italy

    W. Chu

Authors
  1. W. Chu
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Correspondence to W. Chu.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 12, pp. 1686–1708, December, 2022. Ukrainian https://doi.org/10.37863/umzh.v74i12.6587.

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Chu, W. π-Formulas from Dual Series of the Dougall Theorem. Ukr Math J 74, 1924–1949 (2023). https://doi.org/10.1007/s11253-023-02179-6

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  • DOI: https://doi.org/10.1007/s11253-023-02179-6

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