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Two generalizations of Jacobi’s triple product identity and their applications

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Abstract

In terms of Andrews’ series rearrangement method, we establish two generalizations of Jacobi’s triple product identity. Their applications to mock theta functions and Rogers–Ramanujan identities are also discussed.

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Acknowledgements

The author are 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 & Yuanbo Yu

  3. Department of Mathematics, Luoyang Normal University, Luoyang, 471934, China

    Qiuxia Hu

Authors
  1. Chuanan Wei
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  2. Yuanbo Yu
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  3. Qiuxia Hu
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Correspondence to Qiuxia Hu.

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The work is supported by the National Natural Science Foundations of China (Nos. 12101287, 12071103), the Natural Science Foundation of Henan Province (No. 212300410211), and the National Project Cultivation Foundation of Luoyang Normal University (No. 2020-PYJJ-011).

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Wei, C., Yu, Y. & Hu, Q. Two generalizations of Jacobi’s triple product identity and their applications. Ramanujan J 60, 925–937 (2023). https://doi.org/10.1007/s11139-022-00640-x

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