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On two double series for \(\pi \) and their q-analogues

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Abstract

By applying the partial derivative operator to a summation of hypergeometric series, we prove two double series for \(\pi \), which were conjectured by Guo and Lian recently. Employing the operator just mentioned and a summation formula for basic hypergeometric series, we also give q-analogues of these two double series.

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Acknowledgements

The author is grateful to the reviewer for a careful reading and valuable comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, China

    Chuanan Wei

  2. School of Biomedical Information and Engineering, Hainan Medical University, Haikou, 571199, China

    Chuanan Wei

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  1. Chuanan Wei
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Correspondence to Chuanan Wei.

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This work is supported by the National Natural Science Foundation of China (No. 12071103).

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Wei, C. On two double series for \(\pi \) and their q-analogues. Ramanujan J 60, 615–625 (2023). https://doi.org/10.1007/s11139-022-00615-y

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  • DOI: https://doi.org/10.1007/s11139-022-00615-y

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