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Three cubic q-series of Gasper and Rahman

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Abstract

New and elementary proofs for three cubic q-series transformations due to Gasper and Rahman (Am Math Soc 312:1, 1989; Can J Math 42, 1990) are presented by means of the Abel lemma on summation by parts. As consequences, q-analogues for Gosper’s two summation formulae of \(_3F_2(3/4)\)-series are established.

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Acknowledgements

The authors are sincerely grateful to the anonymous referee for their careful reading and useful suggestions, which have improved the manuscript to the present version.

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  1. School of Mathematics & Statistics, Nan**g University of Information Science & Technology, Nan**g, 210044, People’s Republic of China

    Chenying Wang & Jianan Xu

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  1. Chenying Wang
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  2. Jianan Xu
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Correspondence to Chenying Wang.

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The author Chenying Wang was partially supported for this work by the National Natural Science Foundation of China under Grant No. 12071103.

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Wang, C., Xu, J. Three cubic q-series of Gasper and Rahman. Ramanujan J 59, 199–210 (2022). https://doi.org/10.1007/s11139-021-00502-y

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  • DOI: https://doi.org/10.1007/s11139-021-00502-y

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