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arXiv · 2205.14805

Some identities on $\lambda$-analogues of $r$-stirling numbers of the second kind

Dae San Kim·Hye Kyung Kim·Taekyun Kim
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Abstract

Recently, the $\lambda$-analogues of $r$-Stirling numbers of the first kind were studied by Kim-Kim. The aim of this paper is to introduce the $\lambda$-analogues of $r$-Stirling numbers of the second kind and to investigate some properties, recurrence relations and certain identities on those numbers. We also introduce the $\lambda$-analogues of Whitney-type $r$-Stirling numbers of the second and derive similar results to the case of the $\lambda$-analogues of r-Stirling numbers of the second kind. In addition, we consider the $\lambda$-analogues of Dowling polynomials and deduce a Dobinski-like formula.

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Dae San Kim, Hye Kyung Kim, Taekyun Kim. 2022-05-30. Some identities on $\lambda$-analogues of $r$-stirling numbers of the second kind. https://arxiv.org/abs/2205.14805

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