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Open AccessArticle

Degenerate Stirling Polynomials of the Second Kind and Some Applications

1
Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
2
Department of Mathematics, Sogang University, Seoul 121-742, Korea
3
Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Korea
*
Authors to whom correspondence should be addressed.
Symmetry 2019, 11(8), 1046; https://doi.org/10.3390/sym11081046
Received: 20 July 2019 / Revised: 10 August 2019 / Accepted: 13 August 2019 / Published: 14 August 2019
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Abstract

Recently, the degenerate λ -Stirling polynomials of the second kind were introduced and investigated for their properties and relations. In this paper, we continue to study the degenerate λ -Stirling polynomials as well as the r-truncated degenerate λ -Stirling polynomials of the second kind which are derived from generating functions and Newton’s formula. We derive recurrence relations and various expressions for them. Regarding applications, we show that both the degenerate λ -Stirling polynomials of the second and the r-truncated degenerate λ -Stirling polynomials of the second kind appear in the expressions of the probability distributions of appropriate random variables. View Full-Text
Keywords: degenerate λ-Stirling polynomials of the second kind; r-truncated degenerate λ-Stirling polynomials of the second kind; probability distribution degenerate λ-Stirling polynomials of the second kind; r-truncated degenerate λ-Stirling polynomials of the second kind; probability distribution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kim, T.; Kim, D.S.; Kim, H.Y.; Kwon, J. Degenerate Stirling Polynomials of the Second Kind and Some Applications. Symmetry 2019, 11, 1046.

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