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Analogues of Jacobi’s derivative formula II

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Abstract

In this work, we use Jacobi’s derivative formula to obtain analogues to theta constants with rational characteristics. Furthermore, we show that the analogues yield many product-series identities by only using the elementary fact that a holomorphic elliptic function is a constant.

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Acknowledgments

We are grateful to Professor K. Nishiyama and Professor K. S. Williams for their useful comments.

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Authors and Affiliations

  1. Faculty of Fundamental Science, National Institute of Technology Niihama College, 7-1 Yagumo-chou, Ehime, Niihama, 792-8580, Japan

    Kazuhide Matsuda

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  1. Kazuhide Matsuda
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Correspondence to Kazuhide Matsuda.

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Matsuda, K. Analogues of Jacobi’s derivative formula II. Ramanujan J 44, 37–62 (2017). https://doi.org/10.1007/s11139-016-9803-3

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  • DOI: https://doi.org/10.1007/s11139-016-9803-3

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