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Abstract <p> Spivey showed a recurrence relation for the Bell numbers which are sums of the Stirling numbers of the second kind. Recently, the degenerate Bell polynomials and the degenerate Dowling polynomials were studied, whose coefficients are, respectively, the degenerate Stirling numbers of the second kind and the degenerate Whitney numbers of the second kind. The aim of this paper is to prove Spivey-type recurrence relations for those polynomials. In addition, a recurrence relation of the same type is shown for the degenerate <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3233_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\)</EquationSource> </InlineEquation>-Bell polynomials. </p> <p> <b> DOI</b> 10.1134/S1061920825020074 </p>

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Spivey-Type Recurrence Relations for Degenerate Bell and Dowling Polynomials

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • T. Kim,
  • D. S. Kim

摘要

Abstract

Spivey showed a recurrence relation for the Bell numbers which are sums of the Stirling numbers of the second kind. Recently, the degenerate Bell polynomials and the degenerate Dowling polynomials were studied, whose coefficients are, respectively, the degenerate Stirling numbers of the second kind and the degenerate Whitney numbers of the second kind. The aim of this paper is to prove Spivey-type recurrence relations for those polynomials. In addition, a recurrence relation of the same type is shown for the degenerate \(r\) -Bell polynomials.

DOI 10.1134/S1061920825020074