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

Author

Listed:
  • Zhizheng Zhang

    (Luoyang Normal University
    Henan Normal University)

  • Hanfei Song

    (Shanghai Normal University)

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 $$K_2(x,q)$$ K 2 ( x , q ) is discussed by a transformation formula.

Suggested Citation

  • Zhizheng Zhang & Hanfei Song, 2023. "Some identities of certain basic hypergeometric series and their applications to mock theta functions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(4), pages 1214-1225, December.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:4:d:10.1007_s13226-022-00335-5
    DOI: 10.1007/s13226-022-00335-5
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