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Some extensions for Ramanujan’s circular summation formulas and applications

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Abstract

In this paper, we give some extensions for Ramanujan’s circular summation formulas with the mixed products of two Jacobi’s theta functions. As applications, we also obtain many interesting identities of Jacobi’s theta functions.

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Acknowledgements

The authors greatly appreciate to the referee for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Intelligent Technology and Engineering, Chongqing University of Science and Technology, Chongqing Higher Education Mega Center, Huxi Campus, 401331, Chongqing, People’s Republic of China

    Ji-Ke Ge

  2. Department of Mathematics, Chongqing Normal University, Chongqing Higher Education Mega Center, Huxi Campus, 401331, Chongqing, People’s Republic of China

    Qiu-Ming Luo

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  1. Ji-Ke Ge
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  2. Qiu-Ming Luo
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Correspondence to Qiu-Ming Luo.

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The present investigation was supported by Natural Science Foundation General Project of Chongqing, China under Grant cstc2019jcyj-msxmX0143 and National Social Science Foundation, China under Grant 19XTQ010.

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Ge, JK., Luo, QM. Some extensions for Ramanujan’s circular summation formulas and applications. Ramanujan J 56, 491–518 (2021). https://doi.org/10.1007/s11139-020-00293-8

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