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Binomial sums via Bailey’s cubic transformation

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Abstract

By employing one of the cubic transformations (due to W.N. Bailey (1928)) for the 3F2(x)-series, we examine a class of 3F2(4)-series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.

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Author notes

  1. Wenchang Chu

    Present address: Department of Mathematics and Physics, University of Salento, Piazza Tancredi, 7, Lecce, 73100, Italy

Authors and Affiliations

  1. School of Mathematics and Statistics, Zhoukou Normal University, Chuanhui District, Jinshi Rd, 466001, Zhoukou (Henan), P. R. China

    Wenchang Chu

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  1. Wenchang Chu
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Correspondence to Wenchang Chu.

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Chu, W. Binomial sums via Bailey’s cubic transformation. Czech Math J 73, 1131–1150 (2023). https://doi.org/10.21136/CMJ.2023.0429-22

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  • DOI: https://doi.org/10.21136/CMJ.2023.0429-22

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