On a generation of degenerate Daehee polynomials

Sang Jo Yun; Jin-Woo Park; Sang Jo Yun; Jin-Woo Park

doi:10.3934/math.2025556

AIMS Mathematics

2025, Volume 10, Issue 5: 12286-12298. doi: 10.3934/math.2025556

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On a generation of degenerate Daehee polynomials

Sang Jo Yun ¹,
Jin-Woo Park ^{2
,
,}

1.
Department of Information Science and Mathematics, Dong-A University, Busan 49315, Republic of Korea
2.
Department of Mathematics Education, Daegu University, 38453, Republic of Korea

Received: 11 March 2025 Revised: 10 May 2025 Accepted: 22 May 2025 Published: 27 May 2025
MSC : 05A10, 05A15, 11B73, 11B83, 60C05

Recently, probabilistic versions of certain special polynomials have been introduced, leading to the discovery of many interesting properties of these polynomials by many researchers. In this paper, we define the probabilistic degenerate Daehee polynomials, denoted by $ D_{n, \lambda} ^Y (x) $, and explore their properties along with several notable identities. We demonstrate that $ D_{n, \lambda} ^Y (x) $ and related special numbers can be expressed in terms of (degenerate) Stirling numbers of the first and second kinds, as well as falling factorial sequences.
Citation: Sang Jo Yun, Jin-Woo Park. On a generation of degenerate Daehee polynomials[J]. AIMS Mathematics, 2025, 10(5): 12286-12298. doi: 10.3934/math.2025556

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Abstract

Recently, probabilistic versions of certain special polynomials have been introduced, leading to the discovery of many interesting properties of these polynomials by many researchers. In this paper, we define the probabilistic degenerate Daehee polynomials, denoted by $ D_{n, \lambda} ^Y (x) $, and explore their properties along with several notable identities. We demonstrate that $ D_{n, \lambda} ^Y (x) $ and related special numbers can be expressed in terms of (degenerate) Stirling numbers of the first and second kinds, as well as falling factorial sequences.

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