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On s-Stirling transform and poly-Cauchy numbers of the second kind with level 2

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Abstract

In this paper, we study the transform by Stirling numbers with higher level, and give several concrete results. When \(s=2\), we consider the transform of rational sequences. In particular, poly-Cauchy numbers of the second kind with level 2 are introduced in order to achieve some extended results. We also give several properties of poly-Cauchy numbers of the second kind with level 2, which are related to those of poly-Bernoulli numbers with level 2 and analogous to those of poly-Cauchy numbers of the first kind with level 2.

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Notes

  1. The original one is wrong. See [6, Theorem 4,Theorem 6]

  2. The original one is wrong again because it comes from the wrong Identity 38.

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  1. Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Takao Komatsu

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Komatsu, T. On s-Stirling transform and poly-Cauchy numbers of the second kind with level 2. Aequat. Math. 97, 31–61 (2023). https://doi.org/10.1007/s00010-022-00931-0

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