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Several q-series transformation formulas and new Hecke–Rogers type series identities

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In this paper, we establish a general q-series expansion formula based on Bailey’s summation formula, whose limiting form reduces to the q-series expansion formula due to Wang and Chern (Integral Transform Special Funct 31(11):873–890, 2020). As applications, four q-series transformations are derived, which imply numerous new Hecke–Rogers type series representations for Eulerian form series and double sums, especially involving the special cases of several q-orthogonal polynomials.

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Acknowledgements

The authors thank the anonymous referee for carefully reading the manuscript and his/her helpful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Ying Zhang, Wenlong Zhang & Jingjing Zhang

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  1. Ying Zhang
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  2. Wenlong Zhang
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  3. Jingjing Zhang
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Correspondence to Wenlong Zhang.

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This work was supported in part by the National Natural Science Foundation of China (No. 12171067).

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Zhang, Y., Zhang, W. & Zhang, J. Several q-series transformation formulas and new Hecke–Rogers type series identities. Ramanujan J 60, 627–657 (2023). https://doi.org/10.1007/s11139-022-00645-6

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