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Some identities of certain basic hypergeometric series and their applications to mock theta functions

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Abstract

In this paper, we first obtain the corresponding transformation formulas of the basic bilateral hypergeometric series involving universal mock theta functions. Meanwhile, some identities of bilateral series associated with classical mock theta functions are deduced. From the duals of second type for universal mock theta functions, two new Hecke-type identities are derived. Some special cases for classical mock theta functions are also obtained immediately. Finally, an identity for \(K_2(x,q)\) is discussed by a transformation formula.

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Acknowledgements

The authors are grateful to the anonymous referee for helpful comments. This research is supported by the National Natural Science Foundation of China (Grant No. 11871258, 12271234).

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Authors and Affiliations

  1. Department of Mathematics, Luoyang Normal University, Luoyang, 471934, Henan, China

    Zhizheng Zhang

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453001, Henan, China

    Zhizheng Zhang

  3. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Hanfei Song

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  1. Zhizheng Zhang
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  2. Hanfei Song
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Correspondence to Zhizheng Zhang.

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Communicated by B. Sury.

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Zhang, Z., Song, H. Some identities of certain basic hypergeometric series and their applications to mock theta functions. Indian J Pure Appl Math 54, 1214–1225 (2023). https://doi.org/10.1007/s13226-022-00335-5

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