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Research Article | Open Access

Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials

Taekyun Kim1( ), Dae San Kim2
Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
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Abstract

Following Spivey's pivotal discovery of a recurrence relation for Bell numbers, significant research has emerged concerning various generalizations of Bell numbers and polynomials. For example, Kim and Kim established a Spivey-type recurrence relation specifically for degenerate Bell and Dowling polynomials. In this paper, we extend this work by deriving a probabilistic generalization of Spivey-type recurrence relations for both degenerate Bell and degenerate r-Bell polynomials.

Keywords

probabilistic degenerate Bell polynomialsprobabilistic degenerate r-Bell polynomialsSpivey-type relation
CLC number: 11B73, 11B83

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AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 29488-29497
DOI: 10.3934/math.20251295

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Cite this article:
Kim T, Kim DS. Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials. AIMS Mathematics, 2025, 10(12): 29488-29497. https://doi.org/10.3934/math.20251295

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Received: 03 July 2025
Revised: 09 December 2025
Accepted: 10 December 2025
Published: 15 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)